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EKF: replacement of covariance prediction autocode with sympy generated output (#870)
* added python script with ekf derivation (WIP) Signed-off-by: RomanBapst <bapstroman@gmail.com> * worked on c code auto-generation Signed-off-by: RomanBapst <bapstroman@gmail.com> * save before variable name change Signed-off-by: RomanBapst <bapstroman@gmail.com> * changed symbol names Signed-off-by: RomanBapst <bapstroman@gmail.com> * added codegeneration class Signed-off-by: RomanBapst <bapstroman@gmail.com> * improve 3D mag fusion derivation Signed-off-by: RomanBapst <bapstroman@gmail.com> * EKF: Extend ekf sympy derivation to include all observation types * EKF: Add custom ecl::powf function for integer powers * EKF: Convert ekf covariance prediction to use sympy output * EKF: Add test program to compare sympy and matlab covariance prediction Also tests ecl::powf(x,exp) function * EKF: simplify ecl::powf function * Generate code to subfolder generated/ * Add printouts for showing code generation progress * Move generated covariance code to generated folder * Upgrade code generation to python3 * main.py: Remove unused create_symbols function & making code more compact * main.py: move main part into function * Code generation: fix passing wrong rotation matrix to yaw_observation () * EKF: Amend generated code filename for consistency * Move ecl::powf function test to unit tests * EKF: Use updated ecl:powf functionality in test program * Move ecl::powf to utils.hpp * Update ecl::powf test * Update output change indication * test: update expected output for change indicator * test: update expected output for change indicator again Co-authored-by: RomanBapst <bapstroman@gmail.com> Co-authored-by: kamilritz <kritz@ethz.ch>
This commit is contained in:
Paul Riseborough
+453
-271
@@ -35,12 +35,14 @@
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* @file covariance.cpp
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* Contains functions for initialising, predicting and updating the state
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* covariance matrix
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* equations generated using EKF/python/ekf_derivation/main.py
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*
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* @author Roman Bast <bastroman@gmail.com>
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*
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*/
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#include "ekf.h"
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#include "utils.hpp"
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#include <ecl.h>
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#include <math.h>
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@@ -114,26 +116,26 @@ Vector3f Ekf::getVelocityVariance() const
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void Ekf::predictCovariance()
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{
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// assign intermediate state variables
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const float q0 = _state.quat_nominal(0);
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const float q1 = _state.quat_nominal(1);
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const float q2 = _state.quat_nominal(2);
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const float q3 = _state.quat_nominal(3);
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const float &q0 = _state.quat_nominal(0);
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const float &q1 = _state.quat_nominal(1);
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const float &q2 = _state.quat_nominal(2);
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const float &q3 = _state.quat_nominal(3);
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const float dax = _imu_sample_delayed.delta_ang(0);
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const float day = _imu_sample_delayed.delta_ang(1);
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const float daz = _imu_sample_delayed.delta_ang(2);
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const float &dax = _imu_sample_delayed.delta_ang(0);
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const float &day = _imu_sample_delayed.delta_ang(1);
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const float &daz = _imu_sample_delayed.delta_ang(2);
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const float dvx = _imu_sample_delayed.delta_vel(0);
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const float dvy = _imu_sample_delayed.delta_vel(1);
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const float dvz = _imu_sample_delayed.delta_vel(2);
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const float &dvx = _imu_sample_delayed.delta_vel(0);
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const float &dvy = _imu_sample_delayed.delta_vel(1);
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const float &dvz = _imu_sample_delayed.delta_vel(2);
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const float dax_b = _state.delta_ang_bias(0);
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const float day_b = _state.delta_ang_bias(1);
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const float daz_b = _state.delta_ang_bias(2);
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const float &dax_b = _state.delta_ang_bias(0);
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const float &day_b = _state.delta_ang_bias(1);
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const float &daz_b = _state.delta_ang_bias(2);
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const float dvx_b = _state.delta_vel_bias(0);
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const float dvy_b = _state.delta_vel_bias(1);
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const float dvz_b = _state.delta_vel_bias(2);
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const float &dvx_b = _state.delta_vel_bias(0);
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const float &dvy_b = _state.delta_vel_bias(1);
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const float &dvz_b = _state.delta_vel_bias(2);
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// Use average update interval to reduce accumulated covariance prediction errors due to small single frame dt values
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const float dt = FILTER_UPDATE_PERIOD_S;
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@@ -266,158 +268,290 @@ void Ekf::predictCovariance()
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dvzVar = sq(dt * BADACC_BIAS_PNOISE);
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}
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// predict the covariance
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// equations generated using EKF/python/ekf_derivation/main.py
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// intermediate calculations
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float SF[21];
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SF[0] = dvz - dvz_b;
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SF[1] = dvy - dvy_b;
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SF[2] = dvx - dvx_b;
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SF[3] = 2*q1*SF[2] + 2*q2*SF[1] + 2*q3*SF[0];
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SF[4] = 2*q0*SF[1] - 2*q1*SF[0] + 2*q3*SF[2];
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SF[5] = 2*q0*SF[2] + 2*q2*SF[0] - 2*q3*SF[1];
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SF[6] = day*0.5f - day_b*0.5f;
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SF[7] = daz*0.5f - daz_b*0.5f;
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SF[8] = dax*0.5f - dax_b*0.5f;
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SF[9] = dax_b*0.5f - dax*0.5f;
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SF[10] = daz_b*0.5f - daz*0.5f;
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SF[11] = day_b*0.5f - day*0.5f;
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SF[12] = 2*q1*SF[1];
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SF[13] = 2*q0*SF[0];
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SF[14] = q1*0.5f;
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SF[15] = q2*0.5f;
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SF[16] = q3*0.5f;
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SF[17] = sq(q3);
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SF[18] = sq(q2);
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SF[19] = sq(q1);
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SF[20] = sq(q0);
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float SG[8];
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SG[0] = q0*0.5f;
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SG[1] = sq(q3);
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SG[2] = sq(q2);
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SG[3] = sq(q1);
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SG[4] = sq(q0);
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SG[5] = 2*q2*q3;
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SG[6] = 2*q1*q3;
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SG[7] = 2*q1*q2;
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float SQ[11];
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SQ[0] = dvzVar*(SG[5] - 2*q0*q1)*(SG[1] - SG[2] - SG[3] + SG[4]) - dvyVar*(SG[5] + 2*q0*q1)*(SG[1] - SG[2] + SG[3] - SG[4]) + dvxVar*(SG[6] - 2*q0*q2)*(SG[7] + 2*q0*q3);
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SQ[1] = dvzVar*(SG[6] + 2*q0*q2)*(SG[1] - SG[2] - SG[3] + SG[4]) - dvxVar*(SG[6] - 2*q0*q2)*(SG[1] + SG[2] - SG[3] - SG[4]) + dvyVar*(SG[5] + 2*q0*q1)*(SG[7] - 2*q0*q3);
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SQ[2] = dvzVar*(SG[5] - 2*q0*q1)*(SG[6] + 2*q0*q2) - dvyVar*(SG[7] - 2*q0*q3)*(SG[1] - SG[2] + SG[3] - SG[4]) - dvxVar*(SG[7] + 2*q0*q3)*(SG[1] + SG[2] - SG[3] - SG[4]);
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SQ[3] = (dayVar*q1*SG[0])*0.5f - (dazVar*q1*SG[0])*0.5f - (daxVar*q2*q3)*0.25f;
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SQ[4] = (dazVar*q2*SG[0])*0.5f - (daxVar*q2*SG[0])*0.5f - (dayVar*q1*q3)*0.25f;
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SQ[5] = (daxVar*q3*SG[0])*0.5f - (dayVar*q3*SG[0])*0.5f - (dazVar*q1*q2)*0.25f;
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SQ[6] = (daxVar*q1*q2)*0.25f - (dazVar*q3*SG[0])*0.5f - (dayVar*q1*q2)*0.25f;
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SQ[7] = (dazVar*q1*q3)*0.25f - (daxVar*q1*q3)*0.25f - (dayVar*q2*SG[0])*0.5f;
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SQ[8] = (dayVar*q2*q3)*0.25f - (daxVar*q1*SG[0])*0.5f - (dazVar*q2*q3)*0.25f;
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SQ[9] = sq(SG[0]);
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SQ[10] = sq(q1);
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float SPP[11];
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SPP[0] = SF[12] + SF[13] - 2*q2*SF[2];
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SPP[1] = SF[17] - SF[18] - SF[19] + SF[20];
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SPP[2] = SF[17] - SF[18] + SF[19] - SF[20];
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SPP[3] = SF[17] + SF[18] - SF[19] - SF[20];
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SPP[4] = 2*q0*q2 - 2*q1*q3;
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SPP[5] = 2*q0*q1 - 2*q2*q3;
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SPP[6] = 2*q0*q3 - 2*q1*q2;
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SPP[7] = 2*q0*q1 + 2*q2*q3;
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SPP[8] = 2*q0*q3 + 2*q1*q2;
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SPP[9] = 2*q0*q2 + 2*q1*q3;
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SPP[10] = SF[16];
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const float PS0 = ecl::powf(q1, 2);
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const float PS1 = 0.25F*daxVar;
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const float PS2 = ecl::powf(q2, 2);
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const float PS3 = 0.25F*dayVar;
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const float PS4 = ecl::powf(q3, 2);
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const float PS5 = 0.25F*dazVar;
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const float PS6 = 0.5F*q1;
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const float PS7 = 0.5F*q2;
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const float PS8 = P(10,11)*PS7;
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const float PS9 = 0.5F*q3;
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const float PS10 = P(10,12)*PS9;
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const float PS11 = 0.5F*dax - 0.5F*dax_b;
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const float PS12 = 0.5F*day - 0.5F*day_b;
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const float PS13 = 0.5F*daz - 0.5F*daz_b;
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const float PS14 = P(0,10) - P(1,10)*PS11 + P(10,10)*PS6 - P(2,10)*PS12 - P(3,10)*PS13 + PS10 + PS8;
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const float PS15 = P(10,11)*PS6;
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const float PS16 = P(11,12)*PS9;
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const float PS17 = P(0,11) - P(1,11)*PS11 + P(11,11)*PS7 - P(2,11)*PS12 - P(3,11)*PS13 + PS15 + PS16;
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const float PS18 = P(10,12)*PS6;
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const float PS19 = P(11,12)*PS7;
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const float PS20 = P(0,12) - P(1,12)*PS11 + P(12,12)*PS9 - P(2,12)*PS12 - P(3,12)*PS13 + PS18 + PS19;
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const float PS21 = P(1,2)*PS12;
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const float PS22 = -P(1,3)*PS13;
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const float PS23 = P(0,1) - P(1,1)*PS11 + P(1,10)*PS6 + P(1,11)*PS7 + P(1,12)*PS9 - PS21 + PS22;
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const float PS24 = -P(1,2)*PS11;
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const float PS25 = P(2,3)*PS13;
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const float PS26 = P(0,2) + P(2,10)*PS6 + P(2,11)*PS7 + P(2,12)*PS9 - P(2,2)*PS12 + PS24 - PS25;
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const float PS27 = P(1,3)*PS11;
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const float PS28 = -P(2,3)*PS12;
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const float PS29 = P(0,3) + P(3,10)*PS6 + P(3,11)*PS7 + P(3,12)*PS9 - P(3,3)*PS13 - PS27 + PS28;
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const float PS30 = P(0,1)*PS11;
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const float PS31 = P(0,2)*PS12;
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const float PS32 = P(0,3)*PS13;
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const float PS33 = P(0,0) + P(0,10)*PS6 + P(0,11)*PS7 + P(0,12)*PS9 - PS30 - PS31 - PS32;
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const float PS34 = 0.5F*q0;
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const float PS35 = q2*q3;
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const float PS36 = q0*q1;
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const float PS37 = q1*q3;
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const float PS38 = q0*q2;
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const float PS39 = q1*q2;
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const float PS40 = q0*q3;
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const float PS41 = -PS2;
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const float PS42 = ecl::powf(q0, 2);
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const float PS43 = -PS4 + PS42;
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const float PS44 = PS0 + PS41 + PS43;
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const float PS45 = P(0,13) - P(1,13)*PS11 + P(10,13)*PS6 + P(11,13)*PS7 + P(12,13)*PS9 - P(2,13)*PS12 - P(3,13)*PS13;
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const float PS46 = PS37 + PS38;
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const float PS47 = P(0,15) - P(1,15)*PS11 + P(10,15)*PS6 + P(11,15)*PS7 + P(12,15)*PS9 - P(2,15)*PS12 - P(3,15)*PS13;
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const float PS48 = 2*PS47;
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const float PS49 = dvy - dvy_b;
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const float PS50 = dvx - dvx_b;
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const float PS51 = dvz - dvz_b;
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const float PS52 = PS49*q0 + PS50*q3 - PS51*q1;
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const float PS53 = 2*PS29;
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const float PS54 = -PS39 + PS40;
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const float PS55 = P(0,14) - P(1,14)*PS11 + P(10,14)*PS6 + P(11,14)*PS7 + P(12,14)*PS9 - P(2,14)*PS12 - P(3,14)*PS13;
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const float PS56 = 2*PS55;
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const float PS57 = -PS49*q3 + PS50*q0 + PS51*q2;
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const float PS58 = 2*PS33;
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const float PS59 = PS49*q1 - PS50*q2 + PS51*q0;
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const float PS60 = 2*PS59;
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const float PS61 = PS49*q2 + PS50*q1 + PS51*q3;
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const float PS62 = 2*PS61;
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const float PS63 = P(0,4) - P(1,4)*PS11 - P(2,4)*PS12 - P(3,4)*PS13 + P(4,10)*PS6 + P(4,11)*PS7 + P(4,12)*PS9;
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const float PS64 = -PS0;
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const float PS65 = PS2 + PS43 + PS64;
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const float PS66 = PS39 + PS40;
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const float PS67 = 2*PS45;
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const float PS68 = -PS35 + PS36;
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const float PS69 = P(0,5) - P(1,5)*PS11 - P(2,5)*PS12 - P(3,5)*PS13 + P(5,10)*PS6 + P(5,11)*PS7 + P(5,12)*PS9;
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const float PS70 = PS4 + PS41 + PS42 + PS64;
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const float PS71 = PS35 + PS36;
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const float PS72 = 2*PS57;
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const float PS73 = -PS37 + PS38;
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const float PS74 = 2*PS52;
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const float PS75 = P(0,6) - P(1,6)*PS11 - P(2,6)*PS12 - P(3,6)*PS13 + P(6,10)*PS6 + P(6,11)*PS7 + P(6,12)*PS9;
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const float PS76 = -P(10,11)*PS34;
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const float PS77 = P(0,11)*PS11 + P(1,11) + P(11,11)*PS9 + P(2,11)*PS13 - P(3,11)*PS12 - PS19 + PS76;
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const float PS78 = P(0,2)*PS13;
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const float PS79 = P(0,3)*PS12;
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const float PS80 = P(0,0)*PS11 + P(0,1) - P(0,10)*PS34 + P(0,11)*PS9 - P(0,12)*PS7 + PS78 - PS79;
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const float PS81 = P(0,2)*PS11;
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const float PS82 = P(1,2) - P(2,10)*PS34 + P(2,11)*PS9 - P(2,12)*PS7 + P(2,2)*PS13 + PS28 + PS81;
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const float PS83 = P(10,11)*PS9;
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const float PS84 = P(10,12)*PS7;
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const float PS85 = P(0,10)*PS11 + P(1,10) - P(10,10)*PS34 + P(2,10)*PS13 - P(3,10)*PS12 + PS83 - PS84;
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const float PS86 = -P(10,12)*PS34;
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const float PS87 = P(0,12)*PS11 + P(1,12) - P(12,12)*PS7 + P(2,12)*PS13 - P(3,12)*PS12 + PS16 + PS86;
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const float PS88 = P(0,3)*PS11;
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const float PS89 = P(1,3) - P(3,10)*PS34 + P(3,11)*PS9 - P(3,12)*PS7 - P(3,3)*PS12 + PS25 + PS88;
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const float PS90 = P(1,2)*PS13;
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const float PS91 = P(1,3)*PS12;
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const float PS92 = P(1,1) - P(1,10)*PS34 + P(1,11)*PS9 - P(1,12)*PS7 + PS30 + PS90 - PS91;
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const float PS93 = P(0,13)*PS11 + P(1,13) - P(10,13)*PS34 + P(11,13)*PS9 - P(12,13)*PS7 + P(2,13)*PS13 - P(3,13)*PS12;
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const float PS94 = P(0,15)*PS11 + P(1,15) - P(10,15)*PS34 + P(11,15)*PS9 - P(12,15)*PS7 + P(2,15)*PS13 - P(3,15)*PS12;
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const float PS95 = 2*PS94;
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const float PS96 = P(0,14)*PS11 + P(1,14) - P(10,14)*PS34 + P(11,14)*PS9 - P(12,14)*PS7 + P(2,14)*PS13 - P(3,14)*PS12;
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const float PS97 = 2*PS96;
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const float PS98 = P(0,4)*PS11 + P(1,4) + P(2,4)*PS13 - P(3,4)*PS12 - P(4,10)*PS34 + P(4,11)*PS9 - P(4,12)*PS7;
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const float PS99 = 2*PS93;
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const float PS100 = P(0,5)*PS11 + P(1,5) + P(2,5)*PS13 - P(3,5)*PS12 - P(5,10)*PS34 + P(5,11)*PS9 - P(5,12)*PS7;
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const float PS101 = P(0,6)*PS11 + P(1,6) + P(2,6)*PS13 - P(3,6)*PS12 - P(6,10)*PS34 + P(6,11)*PS9 - P(6,12)*PS7;
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const float PS102 = -P(11,12)*PS34;
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const float PS103 = P(0,12)*PS12 - P(1,12)*PS13 + P(12,12)*PS6 + P(2,12) + P(3,12)*PS11 - PS10 + PS102;
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const float PS104 = P(2,3) - P(3,10)*PS9 - P(3,11)*PS34 + P(3,12)*PS6 + P(3,3)*PS11 + PS22 + PS79;
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const float PS105 = P(0,1)*PS13;
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const float PS106 = P(0,0)*PS12 - P(0,10)*PS9 - P(0,11)*PS34 + P(0,12)*PS6 + P(0,2) - PS105 + PS88;
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const float PS107 = P(11,12)*PS6;
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const float PS108 = P(0,11)*PS12 - P(1,11)*PS13 - P(11,11)*PS34 + P(2,11) + P(3,11)*PS11 + PS107 - PS83;
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const float PS109 = P(0,10)*PS12 - P(1,10)*PS13 - P(10,10)*PS9 + P(2,10) + P(3,10)*PS11 + PS18 + PS76;
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const float PS110 = P(0,1)*PS12;
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const float PS111 = -P(1,1)*PS13 - P(1,10)*PS9 - P(1,11)*PS34 + P(1,12)*PS6 + P(1,2) + PS110 + PS27;
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const float PS112 = P(2,3)*PS11;
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const float PS113 = -P(2,10)*PS9 - P(2,11)*PS34 + P(2,12)*PS6 + P(2,2) + PS112 + PS31 - PS90;
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const float PS114 = P(0,13)*PS12 - P(1,13)*PS13 - P(10,13)*PS9 - P(11,13)*PS34 + P(12,13)*PS6 + P(2,13) + P(3,13)*PS11;
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const float PS115 = P(0,15)*PS12 - P(1,15)*PS13 - P(10,15)*PS9 - P(11,15)*PS34 + P(12,15)*PS6 + P(2,15) + P(3,15)*PS11;
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const float PS116 = 2*PS115;
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const float PS117 = P(0,14)*PS12 - P(1,14)*PS13 - P(10,14)*PS9 - P(11,14)*PS34 + P(12,14)*PS6 + P(2,14) + P(3,14)*PS11;
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const float PS118 = 2*PS117;
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const float PS119 = P(0,4)*PS12 - P(1,4)*PS13 + P(2,4) + P(3,4)*PS11 - P(4,10)*PS9 - P(4,11)*PS34 + P(4,12)*PS6;
|
||||
const float PS120 = 2*PS114;
|
||||
const float PS121 = P(0,5)*PS12 - P(1,5)*PS13 + P(2,5) + P(3,5)*PS11 - P(5,10)*PS9 - P(5,11)*PS34 + P(5,12)*PS6;
|
||||
const float PS122 = P(0,6)*PS12 - P(1,6)*PS13 + P(2,6) + P(3,6)*PS11 - P(6,10)*PS9 - P(6,11)*PS34 + P(6,12)*PS6;
|
||||
const float PS123 = P(0,10)*PS13 + P(1,10)*PS12 + P(10,10)*PS7 - P(2,10)*PS11 + P(3,10) - PS15 + PS86;
|
||||
const float PS124 = P(1,1)*PS12 + P(1,10)*PS7 - P(1,11)*PS6 - P(1,12)*PS34 + P(1,3) + PS105 + PS24;
|
||||
const float PS125 = P(0,0)*PS13 + P(0,10)*PS7 - P(0,11)*PS6 - P(0,12)*PS34 + P(0,3) + PS110 - PS81;
|
||||
const float PS126 = P(0,12)*PS13 + P(1,12)*PS12 - P(12,12)*PS34 - P(2,12)*PS11 + P(3,12) - PS107 + PS84;
|
||||
const float PS127 = P(0,11)*PS13 + P(1,11)*PS12 - P(11,11)*PS6 - P(2,11)*PS11 + P(3,11) + PS102 + PS8;
|
||||
const float PS128 = P(2,10)*PS7 - P(2,11)*PS6 - P(2,12)*PS34 - P(2,2)*PS11 + P(2,3) + PS21 + PS78;
|
||||
const float PS129 = P(3,10)*PS7 - P(3,11)*PS6 - P(3,12)*PS34 + P(3,3) - PS112 + PS32 + PS91;
|
||||
const float PS130 = P(0,13)*PS13 + P(1,13)*PS12 + P(10,13)*PS7 - P(11,13)*PS6 - P(12,13)*PS34 - P(2,13)*PS11 + P(3,13);
|
||||
const float PS131 = P(0,15)*PS13 + P(1,15)*PS12 + P(10,15)*PS7 - P(11,15)*PS6 - P(12,15)*PS34 - P(2,15)*PS11 + P(3,15);
|
||||
const float PS132 = 2*PS131;
|
||||
const float PS133 = P(0,14)*PS13 + P(1,14)*PS12 + P(10,14)*PS7 - P(11,14)*PS6 - P(12,14)*PS34 - P(2,14)*PS11 + P(3,14);
|
||||
const float PS134 = 2*PS133;
|
||||
const float PS135 = P(0,4)*PS13 + P(1,4)*PS12 - P(2,4)*PS11 + P(3,4) + P(4,10)*PS7 - P(4,11)*PS6 - P(4,12)*PS34;
|
||||
const float PS136 = 2*PS130;
|
||||
const float PS137 = P(0,5)*PS13 + P(1,5)*PS12 - P(2,5)*PS11 + P(3,5) + P(5,10)*PS7 - P(5,11)*PS6 - P(5,12)*PS34;
|
||||
const float PS138 = P(0,6)*PS13 + P(1,6)*PS12 - P(2,6)*PS11 + P(3,6) + P(6,10)*PS7 - P(6,11)*PS6 - P(6,12)*PS34;
|
||||
const float PS139 = 2*PS46;
|
||||
const float PS140 = 2*PS54;
|
||||
const float PS141 = P(0,13)*PS72 + P(1,13)*PS62 - P(13,13)*PS44 + P(13,14)*PS140 - P(13,15)*PS139 + P(2,13)*PS60 - P(3,13)*PS74 + P(4,13);
|
||||
const float PS142 = P(0,15)*PS72 + P(1,15)*PS62 - P(13,15)*PS44 + P(14,15)*PS140 - P(15,15)*PS139 + P(2,15)*PS60 - P(3,15)*PS74 + P(4,15);
|
||||
const float PS143 = P(1,3)*PS62;
|
||||
const float PS144 = P(0,3)*PS72;
|
||||
const float PS145 = P(2,3)*PS60 - P(3,13)*PS44 + P(3,14)*PS140 - P(3,15)*PS139 - P(3,3)*PS74 + P(3,4) + PS143 + PS144;
|
||||
const float PS146 = P(0,14)*PS72 + P(1,14)*PS62 - P(13,14)*PS44 + P(14,14)*PS140 - P(14,15)*PS139 + P(2,14)*PS60 - P(3,14)*PS74 + P(4,14);
|
||||
const float PS147 = P(0,2)*PS60;
|
||||
const float PS148 = P(0,3)*PS74;
|
||||
const float PS149 = P(0,0)*PS72 + P(0,1)*PS62 - P(0,13)*PS44 + P(0,14)*PS140 - P(0,15)*PS139 + P(0,4) + PS147 - PS148;
|
||||
const float PS150 = P(1,2)*PS62;
|
||||
const float PS151 = P(0,2)*PS72;
|
||||
const float PS152 = -P(2,13)*PS44 + P(2,14)*PS140 - P(2,15)*PS139 + P(2,2)*PS60 - P(2,3)*PS74 + P(2,4) + PS150 + PS151;
|
||||
const float PS153 = P(1,2)*PS60;
|
||||
const float PS154 = P(1,3)*PS74;
|
||||
const float PS155 = P(0,1)*PS72 + P(1,1)*PS62 - P(1,13)*PS44 + P(1,14)*PS140 - P(1,15)*PS139 + P(1,4) + PS153 - PS154;
|
||||
const float PS156 = 4*dvyVar;
|
||||
const float PS157 = 4*dvzVar;
|
||||
const float PS158 = P(0,4)*PS72 + P(1,4)*PS62 + P(2,4)*PS60 - P(3,4)*PS74 - P(4,13)*PS44 + P(4,14)*PS140 - P(4,15)*PS139 + P(4,4);
|
||||
const float PS159 = 2*PS141;
|
||||
const float PS160 = 2*PS68;
|
||||
const float PS161 = PS65*dvyVar;
|
||||
const float PS162 = 2*PS66;
|
||||
const float PS163 = PS44*dvxVar;
|
||||
const float PS164 = P(0,5)*PS72 + P(1,5)*PS62 + P(2,5)*PS60 - P(3,5)*PS74 + P(4,5) - P(5,13)*PS44 + P(5,14)*PS140 - P(5,15)*PS139;
|
||||
const float PS165 = 2*PS71;
|
||||
const float PS166 = 2*PS73;
|
||||
const float PS167 = PS70*dvzVar;
|
||||
const float PS168 = P(0,6)*PS72 + P(1,6)*PS62 + P(2,6)*PS60 - P(3,6)*PS74 + P(4,6) - P(6,13)*PS44 + P(6,14)*PS140 - P(6,15)*PS139;
|
||||
const float PS169 = P(0,14)*PS74 - P(1,14)*PS60 - P(13,14)*PS162 - P(14,14)*PS65 + P(14,15)*PS160 + P(2,14)*PS62 + P(3,14)*PS72 + P(5,14);
|
||||
const float PS170 = P(0,13)*PS74 - P(1,13)*PS60 - P(13,13)*PS162 - P(13,14)*PS65 + P(13,15)*PS160 + P(2,13)*PS62 + P(3,13)*PS72 + P(5,13);
|
||||
const float PS171 = P(0,1)*PS74;
|
||||
const float PS172 = -P(1,1)*PS60 - P(1,13)*PS162 - P(1,14)*PS65 + P(1,15)*PS160 + P(1,3)*PS72 + P(1,5) + PS150 + PS171;
|
||||
const float PS173 = P(0,15)*PS74 - P(1,15)*PS60 - P(13,15)*PS162 - P(14,15)*PS65 + P(15,15)*PS160 + P(2,15)*PS62 + P(3,15)*PS72 + P(5,15);
|
||||
const float PS174 = P(2,3)*PS62;
|
||||
const float PS175 = -P(1,3)*PS60 - P(3,13)*PS162 - P(3,14)*PS65 + P(3,15)*PS160 + P(3,3)*PS72 + P(3,5) + PS148 + PS174;
|
||||
const float PS176 = P(0,1)*PS60;
|
||||
const float PS177 = P(0,0)*PS74 - P(0,13)*PS162 - P(0,14)*PS65 + P(0,15)*PS160 + P(0,2)*PS62 + P(0,5) + PS144 - PS176;
|
||||
const float PS178 = P(2,3)*PS72;
|
||||
const float PS179 = P(0,2)*PS74 - P(2,13)*PS162 - P(2,14)*PS65 + P(2,15)*PS160 + P(2,2)*PS62 + P(2,5) - PS153 + PS178;
|
||||
const float PS180 = 4*dvxVar;
|
||||
const float PS181 = P(0,5)*PS74 - P(1,5)*PS60 + P(2,5)*PS62 + P(3,5)*PS72 - P(5,13)*PS162 - P(5,14)*PS65 + P(5,15)*PS160 + P(5,5);
|
||||
const float PS182 = P(0,6)*PS74 - P(1,6)*PS60 + P(2,6)*PS62 + P(3,6)*PS72 + P(5,6) - P(6,13)*PS162 - P(6,14)*PS65 + P(6,15)*PS160;
|
||||
const float PS183 = P(0,15)*PS60 + P(1,15)*PS74 + P(13,15)*PS166 - P(14,15)*PS165 - P(15,15)*PS70 - P(2,15)*PS72 + P(3,15)*PS62 + P(6,15);
|
||||
const float PS184 = P(0,14)*PS60 + P(1,14)*PS74 + P(13,14)*PS166 - P(14,14)*PS165 - P(14,15)*PS70 - P(2,14)*PS72 + P(3,14)*PS62 + P(6,14);
|
||||
const float PS185 = P(0,13)*PS60 + P(1,13)*PS74 + P(13,13)*PS166 - P(13,14)*PS165 - P(13,15)*PS70 - P(2,13)*PS72 + P(3,13)*PS62 + P(6,13);
|
||||
const float PS186 = P(0,6)*PS60 + P(1,6)*PS74 - P(2,6)*PS72 + P(3,6)*PS62 + P(6,13)*PS166 - P(6,14)*PS165 - P(6,15)*PS70 + P(6,6);
|
||||
|
||||
// covariance update
|
||||
SquareMatrix24f nextP;
|
||||
|
||||
// calculate variances and upper diagonal covariances for quaternion, velocity, position and gyro bias states
|
||||
nextP(0,0) = P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10] + (daxVar*SQ[10])*0.25f + SF[9]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) + SF[11]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[10]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) + SF[14]*(P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10]) + SF[15]*(P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10]) + SPP[10]*(P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10]) + (dayVar*sq(q2))*0.25f + (dazVar*sq(q3))*0.25f;
|
||||
nextP(0,1) = P(0,1) + SQ[8] + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10] + SF[8]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[7]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[11]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) - SF[15]*(P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10]) + SPP[10]*(P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10]) - (q0*(P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10]))*0.5f;
|
||||
nextP(1,1) = P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] + daxVar*SQ[9] - (P(10,1)*q0)*0.5f + SF[8]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[7]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SF[11]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) - SF[15]*(P(1,12) + P(0,12)*SF[8] + P(2,12)*SF[7] + P(3,12)*SF[11] - P(12,12)*SF[15] + P(11,12)*SPP[10] - (P(10,12)*q0)*0.5f) + SPP[10]*(P(1,11) + P(0,11)*SF[8] + P(2,11)*SF[7] + P(3,11)*SF[11] - P(12,11)*SF[15] + P(11,11)*SPP[10] - (P(10,11)*q0)*0.5f) + (dayVar*sq(q3))*0.25f + (dazVar*sq(q2))*0.25f - (q0*(P(1,10) + P(0,10)*SF[8] + P(2,10)*SF[7] + P(3,10)*SF[11] - P(12,10)*SF[15] + P(11,10)*SPP[10] - (P(10,10)*q0)*0.5f))*0.5f;
|
||||
nextP(0,2) = P(0,2) + SQ[7] + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10] + SF[6]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[10]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) + SF[8]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) + SF[14]*(P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10]) - SPP[10]*(P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10]) - (q0*(P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10]))*0.5f;
|
||||
nextP(1,2) = P(1,2) + SQ[5] + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f + SF[6]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[10]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) + SF[8]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) + SF[14]*(P(1,12) + P(0,12)*SF[8] + P(2,12)*SF[7] + P(3,12)*SF[11] - P(12,12)*SF[15] + P(11,12)*SPP[10] - (P(10,12)*q0)*0.5f) - SPP[10]*(P(1,10) + P(0,10)*SF[8] + P(2,10)*SF[7] + P(3,10)*SF[11] - P(12,10)*SF[15] + P(11,10)*SPP[10] - (P(10,10)*q0)*0.5f) - (q0*(P(1,11) + P(0,11)*SF[8] + P(2,11)*SF[7] + P(3,11)*SF[11] - P(12,11)*SF[15] + P(11,11)*SPP[10] - (P(10,11)*q0)*0.5f))*0.5f;
|
||||
nextP(2,2) = P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] + dayVar*SQ[9] + (dazVar*SQ[10])*0.25f - (P(11,2)*q0)*0.5f + SF[6]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SF[10]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) + SF[8]*(P(2,3) + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f) + SF[14]*(P(2,12) + P(0,12)*SF[6] + P(1,12)*SF[10] + P(3,12)*SF[8] + P(12,12)*SF[14] - P(10,12)*SPP[10] - (P(11,12)*q0)*0.5f) - SPP[10]*(P(2,10) + P(0,10)*SF[6] + P(1,10)*SF[10] + P(3,10)*SF[8] + P(12,10)*SF[14] - P(10,10)*SPP[10] - (P(11,10)*q0)*0.5f) + (daxVar*sq(q3))*0.25f - (q0*(P(2,11) + P(0,11)*SF[6] + P(1,11)*SF[10] + P(3,11)*SF[8] + P(12,11)*SF[14] - P(10,11)*SPP[10] - (P(11,11)*q0)*0.5f))*0.5f;
|
||||
nextP(0,3) = P(0,3) + SQ[6] + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10] + SF[7]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[6]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) + SF[9]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[15]*(P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10]) - SF[14]*(P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10]) - (q0*(P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10]))*0.5f;
|
||||
nextP(1,3) = P(1,3) + SQ[4] + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f + SF[7]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[6]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) + SF[9]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SF[15]*(P(1,10) + P(0,10)*SF[8] + P(2,10)*SF[7] + P(3,10)*SF[11] - P(12,10)*SF[15] + P(11,10)*SPP[10] - (P(10,10)*q0)*0.5f) - SF[14]*(P(1,11) + P(0,11)*SF[8] + P(2,11)*SF[7] + P(3,11)*SF[11] - P(12,11)*SF[15] + P(11,11)*SPP[10] - (P(10,11)*q0)*0.5f) - (q0*(P(1,12) + P(0,12)*SF[8] + P(2,12)*SF[7] + P(3,12)*SF[11] - P(12,12)*SF[15] + P(11,12)*SPP[10] - (P(10,12)*q0)*0.5f))*0.5f;
|
||||
nextP(2,3) = P(2,3) + SQ[3] + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f + SF[7]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SF[6]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) + SF[9]*(P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] - (P(11,2)*q0)*0.5f) + SF[15]*(P(2,10) + P(0,10)*SF[6] + P(1,10)*SF[10] + P(3,10)*SF[8] + P(12,10)*SF[14] - P(10,10)*SPP[10] - (P(11,10)*q0)*0.5f) - SF[14]*(P(2,11) + P(0,11)*SF[6] + P(1,11)*SF[10] + P(3,11)*SF[8] + P(12,11)*SF[14] - P(10,11)*SPP[10] - (P(11,11)*q0)*0.5f) - (q0*(P(2,12) + P(0,12)*SF[6] + P(1,12)*SF[10] + P(3,12)*SF[8] + P(12,12)*SF[14] - P(10,12)*SPP[10] - (P(11,12)*q0)*0.5f))*0.5f;
|
||||
nextP(3,3) = P(3,3) + P(0,3)*SF[7] + P(1,3)*SF[6] + P(2,3)*SF[9] + P(10,3)*SF[15] - P(11,3)*SF[14] + (dayVar*SQ[10])*0.25f + dazVar*SQ[9] - (P(12,3)*q0)*0.5f + SF[7]*(P(3,0) + P(0,0)*SF[7] + P(1,0)*SF[6] + P(2,0)*SF[9] + P(10,0)*SF[15] - P(11,0)*SF[14] - (P(12,0)*q0)*0.5f) + SF[6]*(P(3,1) + P(0,1)*SF[7] + P(1,1)*SF[6] + P(2,1)*SF[9] + P(10,1)*SF[15] - P(11,1)*SF[14] - (P(12,1)*q0)*0.5f) + SF[9]*(P(3,2) + P(0,2)*SF[7] + P(1,2)*SF[6] + P(2,2)*SF[9] + P(10,2)*SF[15] - P(11,2)*SF[14] - (P(12,2)*q0)*0.5f) + SF[15]*(P(3,10) + P(0,10)*SF[7] + P(1,10)*SF[6] + P(2,10)*SF[9] + P(10,10)*SF[15] - P(11,10)*SF[14] - (P(12,10)*q0)*0.5f) - SF[14]*(P(3,11) + P(0,11)*SF[7] + P(1,11)*SF[6] + P(2,11)*SF[9] + P(10,11)*SF[15] - P(11,11)*SF[14] - (P(12,11)*q0)*0.5f) + (daxVar*sq(q2))*0.25f - (q0*(P(3,12) + P(0,12)*SF[7] + P(1,12)*SF[6] + P(2,12)*SF[9] + P(10,12)*SF[15] - P(11,12)*SF[14] - (P(12,12)*q0)*0.5f))*0.5f;
|
||||
nextP(0,4) = P(0,4) + P(1,4)*SF[9] + P(2,4)*SF[11] + P(3,4)*SF[10] + P(10,4)*SF[14] + P(11,4)*SF[15] + P(12,4)*SPP[10] + SF[5]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[3]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) - SF[4]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) + SPP[0]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SPP[3]*(P(0,13) + P(1,13)*SF[9] + P(2,13)*SF[11] + P(3,13)*SF[10] + P(10,13)*SF[14] + P(11,13)*SF[15] + P(12,13)*SPP[10]) + SPP[6]*(P(0,14) + P(1,14)*SF[9] + P(2,14)*SF[11] + P(3,14)*SF[10] + P(10,14)*SF[14] + P(11,14)*SF[15] + P(12,14)*SPP[10]) - SPP[9]*(P(0,15) + P(1,15)*SF[9] + P(2,15)*SF[11] + P(3,15)*SF[10] + P(10,15)*SF[14] + P(11,15)*SF[15] + P(12,15)*SPP[10]);
|
||||
nextP(1,4) = P(1,4) + P(0,4)*SF[8] + P(2,4)*SF[7] + P(3,4)*SF[11] - P(12,4)*SF[15] + P(11,4)*SPP[10] - (P(10,4)*q0)*0.5f + SF[5]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[3]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) - SF[4]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) + SPP[0]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SPP[3]*(P(1,13) + P(0,13)*SF[8] + P(2,13)*SF[7] + P(3,13)*SF[11] - P(12,13)*SF[15] + P(11,13)*SPP[10] - (P(10,13)*q0)*0.5f) + SPP[6]*(P(1,14) + P(0,14)*SF[8] + P(2,14)*SF[7] + P(3,14)*SF[11] - P(12,14)*SF[15] + P(11,14)*SPP[10] - (P(10,14)*q0)*0.5f) - SPP[9]*(P(1,15) + P(0,15)*SF[8] + P(2,15)*SF[7] + P(3,15)*SF[11] - P(12,15)*SF[15] + P(11,15)*SPP[10] - (P(10,15)*q0)*0.5f);
|
||||
nextP(2,4) = P(2,4) + P(0,4)*SF[6] + P(1,4)*SF[10] + P(3,4)*SF[8] + P(12,4)*SF[14] - P(10,4)*SPP[10] - (P(11,4)*q0)*0.5f + SF[5]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SF[3]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) - SF[4]*(P(2,3) + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f) + SPP[0]*(P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] - (P(11,2)*q0)*0.5f) + SPP[3]*(P(2,13) + P(0,13)*SF[6] + P(1,13)*SF[10] + P(3,13)*SF[8] + P(12,13)*SF[14] - P(10,13)*SPP[10] - (P(11,13)*q0)*0.5f) + SPP[6]*(P(2,14) + P(0,14)*SF[6] + P(1,14)*SF[10] + P(3,14)*SF[8] + P(12,14)*SF[14] - P(10,14)*SPP[10] - (P(11,14)*q0)*0.5f) - SPP[9]*(P(2,15) + P(0,15)*SF[6] + P(1,15)*SF[10] + P(3,15)*SF[8] + P(12,15)*SF[14] - P(10,15)*SPP[10] - (P(11,15)*q0)*0.5f);
|
||||
nextP(3,4) = P(3,4) + P(0,4)*SF[7] + P(1,4)*SF[6] + P(2,4)*SF[9] + P(10,4)*SF[15] - P(11,4)*SF[14] - (P(12,4)*q0)*0.5f + SF[5]*(P(3,0) + P(0,0)*SF[7] + P(1,0)*SF[6] + P(2,0)*SF[9] + P(10,0)*SF[15] - P(11,0)*SF[14] - (P(12,0)*q0)*0.5f) + SF[3]*(P(3,1) + P(0,1)*SF[7] + P(1,1)*SF[6] + P(2,1)*SF[9] + P(10,1)*SF[15] - P(11,1)*SF[14] - (P(12,1)*q0)*0.5f) - SF[4]*(P(3,3) + P(0,3)*SF[7] + P(1,3)*SF[6] + P(2,3)*SF[9] + P(10,3)*SF[15] - P(11,3)*SF[14] - (P(12,3)*q0)*0.5f) + SPP[0]*(P(3,2) + P(0,2)*SF[7] + P(1,2)*SF[6] + P(2,2)*SF[9] + P(10,2)*SF[15] - P(11,2)*SF[14] - (P(12,2)*q0)*0.5f) + SPP[3]*(P(3,13) + P(0,13)*SF[7] + P(1,13)*SF[6] + P(2,13)*SF[9] + P(10,13)*SF[15] - P(11,13)*SF[14] - (P(12,13)*q0)*0.5f) + SPP[6]*(P(3,14) + P(0,14)*SF[7] + P(1,14)*SF[6] + P(2,14)*SF[9] + P(10,14)*SF[15] - P(11,14)*SF[14] - (P(12,14)*q0)*0.5f) - SPP[9]*(P(3,15) + P(0,15)*SF[7] + P(1,15)*SF[6] + P(2,15)*SF[9] + P(10,15)*SF[15] - P(11,15)*SF[14] - (P(12,15)*q0)*0.5f);
|
||||
nextP(4,4) = P(4,4) + P(0,4)*SF[5] + P(1,4)*SF[3] - P(3,4)*SF[4] + P(2,4)*SPP[0] + P(13,4)*SPP[3] + P(14,4)*SPP[6] - P(15,4)*SPP[9] + dvyVar*sq(SG[7] - 2*q0*q3) + dvzVar*sq(SG[6] + 2*q0*q2) + SF[5]*(P(4,0) + P(0,0)*SF[5] + P(1,0)*SF[3] - P(3,0)*SF[4] + P(2,0)*SPP[0] + P(13,0)*SPP[3] + P(14,0)*SPP[6] - P(15,0)*SPP[9]) + SF[3]*(P(4,1) + P(0,1)*SF[5] + P(1,1)*SF[3] - P(3,1)*SF[4] + P(2,1)*SPP[0] + P(13,1)*SPP[3] + P(14,1)*SPP[6] - P(15,1)*SPP[9]) - SF[4]*(P(4,3) + P(0,3)*SF[5] + P(1,3)*SF[3] - P(3,3)*SF[4] + P(2,3)*SPP[0] + P(13,3)*SPP[3] + P(14,3)*SPP[6] - P(15,3)*SPP[9]) + SPP[0]*(P(4,2) + P(0,2)*SF[5] + P(1,2)*SF[3] - P(3,2)*SF[4] + P(2,2)*SPP[0] + P(13,2)*SPP[3] + P(14,2)*SPP[6] - P(15,2)*SPP[9]) + SPP[3]*(P(4,13) + P(0,13)*SF[5] + P(1,13)*SF[3] - P(3,13)*SF[4] + P(2,13)*SPP[0] + P(13,13)*SPP[3] + P(14,13)*SPP[6] - P(15,13)*SPP[9]) + SPP[6]*(P(4,14) + P(0,14)*SF[5] + P(1,14)*SF[3] - P(3,14)*SF[4] + P(2,14)*SPP[0] + P(13,14)*SPP[3] + P(14,14)*SPP[6] - P(15,14)*SPP[9]) - SPP[9]*(P(4,15) + P(0,15)*SF[5] + P(1,15)*SF[3] - P(3,15)*SF[4] + P(2,15)*SPP[0] + P(13,15)*SPP[3] + P(14,15)*SPP[6] - P(15,15)*SPP[9]) + dvxVar*sq(SG[1] + SG[2] - SG[3] - SG[4]);
|
||||
nextP(0,5) = P(0,5) + P(1,5)*SF[9] + P(2,5)*SF[11] + P(3,5)*SF[10] + P(10,5)*SF[14] + P(11,5)*SF[15] + P(12,5)*SPP[10] + SF[4]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[3]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[5]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) - SPP[0]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) - SPP[8]*(P(0,13) + P(1,13)*SF[9] + P(2,13)*SF[11] + P(3,13)*SF[10] + P(10,13)*SF[14] + P(11,13)*SF[15] + P(12,13)*SPP[10]) + SPP[2]*(P(0,14) + P(1,14)*SF[9] + P(2,14)*SF[11] + P(3,14)*SF[10] + P(10,14)*SF[14] + P(11,14)*SF[15] + P(12,14)*SPP[10]) + SPP[5]*(P(0,15) + P(1,15)*SF[9] + P(2,15)*SF[11] + P(3,15)*SF[10] + P(10,15)*SF[14] + P(11,15)*SF[15] + P(12,15)*SPP[10]);
|
||||
nextP(1,5) = P(1,5) + P(0,5)*SF[8] + P(2,5)*SF[7] + P(3,5)*SF[11] - P(12,5)*SF[15] + P(11,5)*SPP[10] - (P(10,5)*q0)*0.5f + SF[4]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[3]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SF[5]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) - SPP[0]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) - SPP[8]*(P(1,13) + P(0,13)*SF[8] + P(2,13)*SF[7] + P(3,13)*SF[11] - P(12,13)*SF[15] + P(11,13)*SPP[10] - (P(10,13)*q0)*0.5f) + SPP[2]*(P(1,14) + P(0,14)*SF[8] + P(2,14)*SF[7] + P(3,14)*SF[11] - P(12,14)*SF[15] + P(11,14)*SPP[10] - (P(10,14)*q0)*0.5f) + SPP[5]*(P(1,15) + P(0,15)*SF[8] + P(2,15)*SF[7] + P(3,15)*SF[11] - P(12,15)*SF[15] + P(11,15)*SPP[10] - (P(10,15)*q0)*0.5f);
|
||||
nextP(2,5) = P(2,5) + P(0,5)*SF[6] + P(1,5)*SF[10] + P(3,5)*SF[8] + P(12,5)*SF[14] - P(10,5)*SPP[10] - (P(11,5)*q0)*0.5f + SF[4]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SF[3]*(P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] - (P(11,2)*q0)*0.5f) + SF[5]*(P(2,3) + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f) - SPP[0]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) - SPP[8]*(P(2,13) + P(0,13)*SF[6] + P(1,13)*SF[10] + P(3,13)*SF[8] + P(12,13)*SF[14] - P(10,13)*SPP[10] - (P(11,13)*q0)*0.5f) + SPP[2]*(P(2,14) + P(0,14)*SF[6] + P(1,14)*SF[10] + P(3,14)*SF[8] + P(12,14)*SF[14] - P(10,14)*SPP[10] - (P(11,14)*q0)*0.5f) + SPP[5]*(P(2,15) + P(0,15)*SF[6] + P(1,15)*SF[10] + P(3,15)*SF[8] + P(12,15)*SF[14] - P(10,15)*SPP[10] - (P(11,15)*q0)*0.5f);
|
||||
nextP(3,5) = P(3,5) + P(0,5)*SF[7] + P(1,5)*SF[6] + P(2,5)*SF[9] + P(10,5)*SF[15] - P(11,5)*SF[14] - (P(12,5)*q0)*0.5f + SF[4]*(P(3,0) + P(0,0)*SF[7] + P(1,0)*SF[6] + P(2,0)*SF[9] + P(10,0)*SF[15] - P(11,0)*SF[14] - (P(12,0)*q0)*0.5f) + SF[3]*(P(3,2) + P(0,2)*SF[7] + P(1,2)*SF[6] + P(2,2)*SF[9] + P(10,2)*SF[15] - P(11,2)*SF[14] - (P(12,2)*q0)*0.5f) + SF[5]*(P(3,3) + P(0,3)*SF[7] + P(1,3)*SF[6] + P(2,3)*SF[9] + P(10,3)*SF[15] - P(11,3)*SF[14] - (P(12,3)*q0)*0.5f) - SPP[0]*(P(3,1) + P(0,1)*SF[7] + P(1,1)*SF[6] + P(2,1)*SF[9] + P(10,1)*SF[15] - P(11,1)*SF[14] - (P(12,1)*q0)*0.5f) - SPP[8]*(P(3,13) + P(0,13)*SF[7] + P(1,13)*SF[6] + P(2,13)*SF[9] + P(10,13)*SF[15] - P(11,13)*SF[14] - (P(12,13)*q0)*0.5f) + SPP[2]*(P(3,14) + P(0,14)*SF[7] + P(1,14)*SF[6] + P(2,14)*SF[9] + P(10,14)*SF[15] - P(11,14)*SF[14] - (P(12,14)*q0)*0.5f) + SPP[5]*(P(3,15) + P(0,15)*SF[7] + P(1,15)*SF[6] + P(2,15)*SF[9] + P(10,15)*SF[15] - P(11,15)*SF[14] - (P(12,15)*q0)*0.5f);
|
||||
nextP(4,5) = P(4,5) + SQ[2] + P(0,5)*SF[5] + P(1,5)*SF[3] - P(3,5)*SF[4] + P(2,5)*SPP[0] + P(13,5)*SPP[3] + P(14,5)*SPP[6] - P(15,5)*SPP[9] + SF[4]*(P(4,0) + P(0,0)*SF[5] + P(1,0)*SF[3] - P(3,0)*SF[4] + P(2,0)*SPP[0] + P(13,0)*SPP[3] + P(14,0)*SPP[6] - P(15,0)*SPP[9]) + SF[3]*(P(4,2) + P(0,2)*SF[5] + P(1,2)*SF[3] - P(3,2)*SF[4] + P(2,2)*SPP[0] + P(13,2)*SPP[3] + P(14,2)*SPP[6] - P(15,2)*SPP[9]) + SF[5]*(P(4,3) + P(0,3)*SF[5] + P(1,3)*SF[3] - P(3,3)*SF[4] + P(2,3)*SPP[0] + P(13,3)*SPP[3] + P(14,3)*SPP[6] - P(15,3)*SPP[9]) - SPP[0]*(P(4,1) + P(0,1)*SF[5] + P(1,1)*SF[3] - P(3,1)*SF[4] + P(2,1)*SPP[0] + P(13,1)*SPP[3] + P(14,1)*SPP[6] - P(15,1)*SPP[9]) - SPP[8]*(P(4,13) + P(0,13)*SF[5] + P(1,13)*SF[3] - P(3,13)*SF[4] + P(2,13)*SPP[0] + P(13,13)*SPP[3] + P(14,13)*SPP[6] - P(15,13)*SPP[9]) + SPP[2]*(P(4,14) + P(0,14)*SF[5] + P(1,14)*SF[3] - P(3,14)*SF[4] + P(2,14)*SPP[0] + P(13,14)*SPP[3] + P(14,14)*SPP[6] - P(15,14)*SPP[9]) + SPP[5]*(P(4,15) + P(0,15)*SF[5] + P(1,15)*SF[3] - P(3,15)*SF[4] + P(2,15)*SPP[0] + P(13,15)*SPP[3] + P(14,15)*SPP[6] - P(15,15)*SPP[9]);
|
||||
nextP(5,5) = P(5,5) + P(0,5)*SF[4] + P(2,5)*SF[3] + P(3,5)*SF[5] - P(1,5)*SPP[0] - P(13,5)*SPP[8] + P(14,5)*SPP[2] + P(15,5)*SPP[5] + dvxVar*sq(SG[7] + 2*q0*q3) + dvzVar*sq(SG[5] - 2*q0*q1) + SF[4]*(P(5,0) + P(0,0)*SF[4] + P(2,0)*SF[3] + P(3,0)*SF[5] - P(1,0)*SPP[0] - P(13,0)*SPP[8] + P(14,0)*SPP[2] + P(15,0)*SPP[5]) + SF[3]*(P(5,2) + P(0,2)*SF[4] + P(2,2)*SF[3] + P(3,2)*SF[5] - P(1,2)*SPP[0] - P(13,2)*SPP[8] + P(14,2)*SPP[2] + P(15,2)*SPP[5]) + SF[5]*(P(5,3) + P(0,3)*SF[4] + P(2,3)*SF[3] + P(3,3)*SF[5] - P(1,3)*SPP[0] - P(13,3)*SPP[8] + P(14,3)*SPP[2] + P(15,3)*SPP[5]) - SPP[0]*(P(5,1) + P(0,1)*SF[4] + P(2,1)*SF[3] + P(3,1)*SF[5] - P(1,1)*SPP[0] - P(13,1)*SPP[8] + P(14,1)*SPP[2] + P(15,1)*SPP[5]) - SPP[8]*(P(5,13) + P(0,13)*SF[4] + P(2,13)*SF[3] + P(3,13)*SF[5] - P(1,13)*SPP[0] - P(13,13)*SPP[8] + P(14,13)*SPP[2] + P(15,13)*SPP[5]) + SPP[2]*(P(5,14) + P(0,14)*SF[4] + P(2,14)*SF[3] + P(3,14)*SF[5] - P(1,14)*SPP[0] - P(13,14)*SPP[8] + P(14,14)*SPP[2] + P(15,14)*SPP[5]) + SPP[5]*(P(5,15) + P(0,15)*SF[4] + P(2,15)*SF[3] + P(3,15)*SF[5] - P(1,15)*SPP[0] - P(13,15)*SPP[8] + P(14,15)*SPP[2] + P(15,15)*SPP[5]) + dvyVar*sq(SG[1] - SG[2] + SG[3] - SG[4]);
|
||||
nextP(0,6) = P(0,6) + P(1,6)*SF[9] + P(2,6)*SF[11] + P(3,6)*SF[10] + P(10,6)*SF[14] + P(11,6)*SF[15] + P(12,6)*SPP[10] + SF[4]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) - SF[5]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[3]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) + SPP[0]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SPP[4]*(P(0,13) + P(1,13)*SF[9] + P(2,13)*SF[11] + P(3,13)*SF[10] + P(10,13)*SF[14] + P(11,13)*SF[15] + P(12,13)*SPP[10]) - SPP[7]*(P(0,14) + P(1,14)*SF[9] + P(2,14)*SF[11] + P(3,14)*SF[10] + P(10,14)*SF[14] + P(11,14)*SF[15] + P(12,14)*SPP[10]) - SPP[1]*(P(0,15) + P(1,15)*SF[9] + P(2,15)*SF[11] + P(3,15)*SF[10] + P(10,15)*SF[14] + P(11,15)*SF[15] + P(12,15)*SPP[10]);
|
||||
nextP(1,6) = P(1,6) + P(0,6)*SF[8] + P(2,6)*SF[7] + P(3,6)*SF[11] - P(12,6)*SF[15] + P(11,6)*SPP[10] - (P(10,6)*q0)*0.5f + SF[4]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) - SF[5]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SF[3]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) + SPP[0]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SPP[4]*(P(1,13) + P(0,13)*SF[8] + P(2,13)*SF[7] + P(3,13)*SF[11] - P(12,13)*SF[15] + P(11,13)*SPP[10] - (P(10,13)*q0)*0.5f) - SPP[7]*(P(1,14) + P(0,14)*SF[8] + P(2,14)*SF[7] + P(3,14)*SF[11] - P(12,14)*SF[15] + P(11,14)*SPP[10] - (P(10,14)*q0)*0.5f) - SPP[1]*(P(1,15) + P(0,15)*SF[8] + P(2,15)*SF[7] + P(3,15)*SF[11] - P(12,15)*SF[15] + P(11,15)*SPP[10] - (P(10,15)*q0)*0.5f);
|
||||
nextP(2,6) = P(2,6) + P(0,6)*SF[6] + P(1,6)*SF[10] + P(3,6)*SF[8] + P(12,6)*SF[14] - P(10,6)*SPP[10] - (P(11,6)*q0)*0.5f + SF[4]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) - SF[5]*(P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] - (P(11,2)*q0)*0.5f) + SF[3]*(P(2,3) + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f) + SPP[0]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SPP[4]*(P(2,13) + P(0,13)*SF[6] + P(1,13)*SF[10] + P(3,13)*SF[8] + P(12,13)*SF[14] - P(10,13)*SPP[10] - (P(11,13)*q0)*0.5f) - SPP[7]*(P(2,14) + P(0,14)*SF[6] + P(1,14)*SF[10] + P(3,14)*SF[8] + P(12,14)*SF[14] - P(10,14)*SPP[10] - (P(11,14)*q0)*0.5f) - SPP[1]*(P(2,15) + P(0,15)*SF[6] + P(1,15)*SF[10] + P(3,15)*SF[8] + P(12,15)*SF[14] - P(10,15)*SPP[10] - (P(11,15)*q0)*0.5f);
|
||||
nextP(3,6) = P(3,6) + P(0,6)*SF[7] + P(1,6)*SF[6] + P(2,6)*SF[9] + P(10,6)*SF[15] - P(11,6)*SF[14] - (P(12,6)*q0)*0.5f + SF[4]*(P(3,1) + P(0,1)*SF[7] + P(1,1)*SF[6] + P(2,1)*SF[9] + P(10,1)*SF[15] - P(11,1)*SF[14] - (P(12,1)*q0)*0.5f) - SF[5]*(P(3,2) + P(0,2)*SF[7] + P(1,2)*SF[6] + P(2,2)*SF[9] + P(10,2)*SF[15] - P(11,2)*SF[14] - (P(12,2)*q0)*0.5f) + SF[3]*(P(3,3) + P(0,3)*SF[7] + P(1,3)*SF[6] + P(2,3)*SF[9] + P(10,3)*SF[15] - P(11,3)*SF[14] - (P(12,3)*q0)*0.5f) + SPP[0]*(P(3,0) + P(0,0)*SF[7] + P(1,0)*SF[6] + P(2,0)*SF[9] + P(10,0)*SF[15] - P(11,0)*SF[14] - (P(12,0)*q0)*0.5f) + SPP[4]*(P(3,13) + P(0,13)*SF[7] + P(1,13)*SF[6] + P(2,13)*SF[9] + P(10,13)*SF[15] - P(11,13)*SF[14] - (P(12,13)*q0)*0.5f) - SPP[7]*(P(3,14) + P(0,14)*SF[7] + P(1,14)*SF[6] + P(2,14)*SF[9] + P(10,14)*SF[15] - P(11,14)*SF[14] - (P(12,14)*q0)*0.5f) - SPP[1]*(P(3,15) + P(0,15)*SF[7] + P(1,15)*SF[6] + P(2,15)*SF[9] + P(10,15)*SF[15] - P(11,15)*SF[14] - (P(12,15)*q0)*0.5f);
|
||||
nextP(4,6) = P(4,6) + SQ[1] + P(0,6)*SF[5] + P(1,6)*SF[3] - P(3,6)*SF[4] + P(2,6)*SPP[0] + P(13,6)*SPP[3] + P(14,6)*SPP[6] - P(15,6)*SPP[9] + SF[4]*(P(4,1) + P(0,1)*SF[5] + P(1,1)*SF[3] - P(3,1)*SF[4] + P(2,1)*SPP[0] + P(13,1)*SPP[3] + P(14,1)*SPP[6] - P(15,1)*SPP[9]) - SF[5]*(P(4,2) + P(0,2)*SF[5] + P(1,2)*SF[3] - P(3,2)*SF[4] + P(2,2)*SPP[0] + P(13,2)*SPP[3] + P(14,2)*SPP[6] - P(15,2)*SPP[9]) + SF[3]*(P(4,3) + P(0,3)*SF[5] + P(1,3)*SF[3] - P(3,3)*SF[4] + P(2,3)*SPP[0] + P(13,3)*SPP[3] + P(14,3)*SPP[6] - P(15,3)*SPP[9]) + SPP[0]*(P(4,0) + P(0,0)*SF[5] + P(1,0)*SF[3] - P(3,0)*SF[4] + P(2,0)*SPP[0] + P(13,0)*SPP[3] + P(14,0)*SPP[6] - P(15,0)*SPP[9]) + SPP[4]*(P(4,13) + P(0,13)*SF[5] + P(1,13)*SF[3] - P(3,13)*SF[4] + P(2,13)*SPP[0] + P(13,13)*SPP[3] + P(14,13)*SPP[6] - P(15,13)*SPP[9]) - SPP[7]*(P(4,14) + P(0,14)*SF[5] + P(1,14)*SF[3] - P(3,14)*SF[4] + P(2,14)*SPP[0] + P(13,14)*SPP[3] + P(14,14)*SPP[6] - P(15,14)*SPP[9]) - SPP[1]*(P(4,15) + P(0,15)*SF[5] + P(1,15)*SF[3] - P(3,15)*SF[4] + P(2,15)*SPP[0] + P(13,15)*SPP[3] + P(14,15)*SPP[6] - P(15,15)*SPP[9]);
|
||||
nextP(5,6) = P(5,6) + SQ[0] + P(0,6)*SF[4] + P(2,6)*SF[3] + P(3,6)*SF[5] - P(1,6)*SPP[0] - P(13,6)*SPP[8] + P(14,6)*SPP[2] + P(15,6)*SPP[5] + SF[4]*(P(5,1) + P(0,1)*SF[4] + P(2,1)*SF[3] + P(3,1)*SF[5] - P(1,1)*SPP[0] - P(13,1)*SPP[8] + P(14,1)*SPP[2] + P(15,1)*SPP[5]) - SF[5]*(P(5,2) + P(0,2)*SF[4] + P(2,2)*SF[3] + P(3,2)*SF[5] - P(1,2)*SPP[0] - P(13,2)*SPP[8] + P(14,2)*SPP[2] + P(15,2)*SPP[5]) + SF[3]*(P(5,3) + P(0,3)*SF[4] + P(2,3)*SF[3] + P(3,3)*SF[5] - P(1,3)*SPP[0] - P(13,3)*SPP[8] + P(14,3)*SPP[2] + P(15,3)*SPP[5]) + SPP[0]*(P(5,0) + P(0,0)*SF[4] + P(2,0)*SF[3] + P(3,0)*SF[5] - P(1,0)*SPP[0] - P(13,0)*SPP[8] + P(14,0)*SPP[2] + P(15,0)*SPP[5]) + SPP[4]*(P(5,13) + P(0,13)*SF[4] + P(2,13)*SF[3] + P(3,13)*SF[5] - P(1,13)*SPP[0] - P(13,13)*SPP[8] + P(14,13)*SPP[2] + P(15,13)*SPP[5]) - SPP[7]*(P(5,14) + P(0,14)*SF[4] + P(2,14)*SF[3] + P(3,14)*SF[5] - P(1,14)*SPP[0] - P(13,14)*SPP[8] + P(14,14)*SPP[2] + P(15,14)*SPP[5]) - SPP[1]*(P(5,15) + P(0,15)*SF[4] + P(2,15)*SF[3] + P(3,15)*SF[5] - P(1,15)*SPP[0] - P(13,15)*SPP[8] + P(14,15)*SPP[2] + P(15,15)*SPP[5]);
|
||||
nextP(6,6) = P(6,6) + P(1,6)*SF[4] - P(2,6)*SF[5] + P(3,6)*SF[3] + P(0,6)*SPP[0] + P(13,6)*SPP[4] - P(14,6)*SPP[7] - P(15,6)*SPP[1] + dvxVar*sq(SG[6] - 2*q0*q2) + dvyVar*sq(SG[5] + 2*q0*q1) + SF[4]*(P(6,1) + P(1,1)*SF[4] - P(2,1)*SF[5] + P(3,1)*SF[3] + P(0,1)*SPP[0] + P(13,1)*SPP[4] - P(14,1)*SPP[7] - P(15,1)*SPP[1]) - SF[5]*(P(6,2) + P(1,2)*SF[4] - P(2,2)*SF[5] + P(3,2)*SF[3] + P(0,2)*SPP[0] + P(13,2)*SPP[4] - P(14,2)*SPP[7] - P(15,2)*SPP[1]) + SF[3]*(P(6,3) + P(1,3)*SF[4] - P(2,3)*SF[5] + P(3,3)*SF[3] + P(0,3)*SPP[0] + P(13,3)*SPP[4] - P(14,3)*SPP[7] - P(15,3)*SPP[1]) + SPP[0]*(P(6,0) + P(1,0)*SF[4] - P(2,0)*SF[5] + P(3,0)*SF[3] + P(0,0)*SPP[0] + P(13,0)*SPP[4] - P(14,0)*SPP[7] - P(15,0)*SPP[1]) + SPP[4]*(P(6,13) + P(1,13)*SF[4] - P(2,13)*SF[5] + P(3,13)*SF[3] + P(0,13)*SPP[0] + P(13,13)*SPP[4] - P(14,13)*SPP[7] - P(15,13)*SPP[1]) - SPP[7]*(P(6,14) + P(1,14)*SF[4] - P(2,14)*SF[5] + P(3,14)*SF[3] + P(0,14)*SPP[0] + P(13,14)*SPP[4] - P(14,14)*SPP[7] - P(15,14)*SPP[1]) - SPP[1]*(P(6,15) + P(1,15)*SF[4] - P(2,15)*SF[5] + P(3,15)*SF[3] + P(0,15)*SPP[0] + P(13,15)*SPP[4] - P(14,15)*SPP[7] - P(15,15)*SPP[1]) + dvzVar*sq(SG[1] - SG[2] - SG[3] + SG[4]);
|
||||
nextP(0,7) = P(0,7) + P(1,7)*SF[9] + P(2,7)*SF[11] + P(3,7)*SF[10] + P(10,7)*SF[14] + P(11,7)*SF[15] + P(12,7)*SPP[10] + dt*(P(0,4) + P(1,4)*SF[9] + P(2,4)*SF[11] + P(3,4)*SF[10] + P(10,4)*SF[14] + P(11,4)*SF[15] + P(12,4)*SPP[10]);
|
||||
nextP(1,7) = P(1,7) + P(0,7)*SF[8] + P(2,7)*SF[7] + P(3,7)*SF[11] - P(12,7)*SF[15] + P(11,7)*SPP[10] - (P(10,7)*q0)*0.5f + dt*(P(1,4) + P(0,4)*SF[8] + P(2,4)*SF[7] + P(3,4)*SF[11] - P(12,4)*SF[15] + P(11,4)*SPP[10] - (P(10,4)*q0)*0.5f);
|
||||
nextP(2,7) = P(2,7) + P(0,7)*SF[6] + P(1,7)*SF[10] + P(3,7)*SF[8] + P(12,7)*SF[14] - P(10,7)*SPP[10] - (P(11,7)*q0)*0.5f + dt*(P(2,4) + P(0,4)*SF[6] + P(1,4)*SF[10] + P(3,4)*SF[8] + P(12,4)*SF[14] - P(10,4)*SPP[10] - (P(11,4)*q0)*0.5f);
|
||||
nextP(3,7) = P(3,7) + P(0,7)*SF[7] + P(1,7)*SF[6] + P(2,7)*SF[9] + P(10,7)*SF[15] - P(11,7)*SF[14] - (P(12,7)*q0)*0.5f + dt*(P(3,4) + P(0,4)*SF[7] + P(1,4)*SF[6] + P(2,4)*SF[9] + P(10,4)*SF[15] - P(11,4)*SF[14] - (P(12,4)*q0)*0.5f);
|
||||
nextP(4,7) = P(4,7) + P(0,7)*SF[5] + P(1,7)*SF[3] - P(3,7)*SF[4] + P(2,7)*SPP[0] + P(13,7)*SPP[3] + P(14,7)*SPP[6] - P(15,7)*SPP[9] + dt*(P(4,4) + P(0,4)*SF[5] + P(1,4)*SF[3] - P(3,4)*SF[4] + P(2,4)*SPP[0] + P(13,4)*SPP[3] + P(14,4)*SPP[6] - P(15,4)*SPP[9]);
|
||||
nextP(5,7) = P(5,7) + P(0,7)*SF[4] + P(2,7)*SF[3] + P(3,7)*SF[5] - P(1,7)*SPP[0] - P(13,7)*SPP[8] + P(14,7)*SPP[2] + P(15,7)*SPP[5] + dt*(P(5,4) + P(0,4)*SF[4] + P(2,4)*SF[3] + P(3,4)*SF[5] - P(1,4)*SPP[0] - P(13,4)*SPP[8] + P(14,4)*SPP[2] + P(15,4)*SPP[5]);
|
||||
nextP(6,7) = P(6,7) + P(1,7)*SF[4] - P(2,7)*SF[5] + P(3,7)*SF[3] + P(0,7)*SPP[0] + P(13,7)*SPP[4] - P(14,7)*SPP[7] - P(15,7)*SPP[1] + dt*(P(6,4) + P(1,4)*SF[4] - P(2,4)*SF[5] + P(3,4)*SF[3] + P(0,4)*SPP[0] + P(13,4)*SPP[4] - P(14,4)*SPP[7] - P(15,4)*SPP[1]);
|
||||
nextP(7,7) = P(7,7) + P(4,7)*dt + dt*(P(7,4) + P(4,4)*dt);
|
||||
nextP(0,8) = P(0,8) + P(1,8)*SF[9] + P(2,8)*SF[11] + P(3,8)*SF[10] + P(10,8)*SF[14] + P(11,8)*SF[15] + P(12,8)*SPP[10] + dt*(P(0,5) + P(1,5)*SF[9] + P(2,5)*SF[11] + P(3,5)*SF[10] + P(10,5)*SF[14] + P(11,5)*SF[15] + P(12,5)*SPP[10]);
|
||||
nextP(1,8) = P(1,8) + P(0,8)*SF[8] + P(2,8)*SF[7] + P(3,8)*SF[11] - P(12,8)*SF[15] + P(11,8)*SPP[10] - (P(10,8)*q0)*0.5f + dt*(P(1,5) + P(0,5)*SF[8] + P(2,5)*SF[7] + P(3,5)*SF[11] - P(12,5)*SF[15] + P(11,5)*SPP[10] - (P(10,5)*q0)*0.5f);
|
||||
nextP(2,8) = P(2,8) + P(0,8)*SF[6] + P(1,8)*SF[10] + P(3,8)*SF[8] + P(12,8)*SF[14] - P(10,8)*SPP[10] - (P(11,8)*q0)*0.5f + dt*(P(2,5) + P(0,5)*SF[6] + P(1,5)*SF[10] + P(3,5)*SF[8] + P(12,5)*SF[14] - P(10,5)*SPP[10] - (P(11,5)*q0)*0.5f);
|
||||
nextP(3,8) = P(3,8) + P(0,8)*SF[7] + P(1,8)*SF[6] + P(2,8)*SF[9] + P(10,8)*SF[15] - P(11,8)*SF[14] - (P(12,8)*q0)*0.5f + dt*(P(3,5) + P(0,5)*SF[7] + P(1,5)*SF[6] + P(2,5)*SF[9] + P(10,5)*SF[15] - P(11,5)*SF[14] - (P(12,5)*q0)*0.5f);
|
||||
nextP(4,8) = P(4,8) + P(0,8)*SF[5] + P(1,8)*SF[3] - P(3,8)*SF[4] + P(2,8)*SPP[0] + P(13,8)*SPP[3] + P(14,8)*SPP[6] - P(15,8)*SPP[9] + dt*(P(4,5) + P(0,5)*SF[5] + P(1,5)*SF[3] - P(3,5)*SF[4] + P(2,5)*SPP[0] + P(13,5)*SPP[3] + P(14,5)*SPP[6] - P(15,5)*SPP[9]);
|
||||
nextP(5,8) = P(5,8) + P(0,8)*SF[4] + P(2,8)*SF[3] + P(3,8)*SF[5] - P(1,8)*SPP[0] - P(13,8)*SPP[8] + P(14,8)*SPP[2] + P(15,8)*SPP[5] + dt*(P(5,5) + P(0,5)*SF[4] + P(2,5)*SF[3] + P(3,5)*SF[5] - P(1,5)*SPP[0] - P(13,5)*SPP[8] + P(14,5)*SPP[2] + P(15,5)*SPP[5]);
|
||||
nextP(6,8) = P(6,8) + P(1,8)*SF[4] - P(2,8)*SF[5] + P(3,8)*SF[3] + P(0,8)*SPP[0] + P(13,8)*SPP[4] - P(14,8)*SPP[7] - P(15,8)*SPP[1] + dt*(P(6,5) + P(1,5)*SF[4] - P(2,5)*SF[5] + P(3,5)*SF[3] + P(0,5)*SPP[0] + P(13,5)*SPP[4] - P(14,5)*SPP[7] - P(15,5)*SPP[1]);
|
||||
nextP(7,8) = P(7,8) + P(4,8)*dt + dt*(P(7,5) + P(4,5)*dt);
|
||||
nextP(8,8) = P(8,8) + P(5,8)*dt + dt*(P(8,5) + P(5,5)*dt);
|
||||
nextP(0,9) = P(0,9) + P(1,9)*SF[9] + P(2,9)*SF[11] + P(3,9)*SF[10] + P(10,9)*SF[14] + P(11,9)*SF[15] + P(12,9)*SPP[10] + dt*(P(0,6) + P(1,6)*SF[9] + P(2,6)*SF[11] + P(3,6)*SF[10] + P(10,6)*SF[14] + P(11,6)*SF[15] + P(12,6)*SPP[10]);
|
||||
nextP(1,9) = P(1,9) + P(0,9)*SF[8] + P(2,9)*SF[7] + P(3,9)*SF[11] - P(12,9)*SF[15] + P(11,9)*SPP[10] - (P(10,9)*q0)*0.5f + dt*(P(1,6) + P(0,6)*SF[8] + P(2,6)*SF[7] + P(3,6)*SF[11] - P(12,6)*SF[15] + P(11,6)*SPP[10] - (P(10,6)*q0)*0.5f);
|
||||
nextP(2,9) = P(2,9) + P(0,9)*SF[6] + P(1,9)*SF[10] + P(3,9)*SF[8] + P(12,9)*SF[14] - P(10,9)*SPP[10] - (P(11,9)*q0)*0.5f + dt*(P(2,6) + P(0,6)*SF[6] + P(1,6)*SF[10] + P(3,6)*SF[8] + P(12,6)*SF[14] - P(10,6)*SPP[10] - (P(11,6)*q0)*0.5f);
|
||||
nextP(3,9) = P(3,9) + P(0,9)*SF[7] + P(1,9)*SF[6] + P(2,9)*SF[9] + P(10,9)*SF[15] - P(11,9)*SF[14] - (P(12,9)*q0)*0.5f + dt*(P(3,6) + P(0,6)*SF[7] + P(1,6)*SF[6] + P(2,6)*SF[9] + P(10,6)*SF[15] - P(11,6)*SF[14] - (P(12,6)*q0)*0.5f);
|
||||
nextP(4,9) = P(4,9) + P(0,9)*SF[5] + P(1,9)*SF[3] - P(3,9)*SF[4] + P(2,9)*SPP[0] + P(13,9)*SPP[3] + P(14,9)*SPP[6] - P(15,9)*SPP[9] + dt*(P(4,6) + P(0,6)*SF[5] + P(1,6)*SF[3] - P(3,6)*SF[4] + P(2,6)*SPP[0] + P(13,6)*SPP[3] + P(14,6)*SPP[6] - P(15,6)*SPP[9]);
|
||||
nextP(5,9) = P(5,9) + P(0,9)*SF[4] + P(2,9)*SF[3] + P(3,9)*SF[5] - P(1,9)*SPP[0] - P(13,9)*SPP[8] + P(14,9)*SPP[2] + P(15,9)*SPP[5] + dt*(P(5,6) + P(0,6)*SF[4] + P(2,6)*SF[3] + P(3,6)*SF[5] - P(1,6)*SPP[0] - P(13,6)*SPP[8] + P(14,6)*SPP[2] + P(15,6)*SPP[5]);
|
||||
nextP(6,9) = P(6,9) + P(1,9)*SF[4] - P(2,9)*SF[5] + P(3,9)*SF[3] + P(0,9)*SPP[0] + P(13,9)*SPP[4] - P(14,9)*SPP[7] - P(15,9)*SPP[1] + dt*(P(6,6) + P(1,6)*SF[4] - P(2,6)*SF[5] + P(3,6)*SF[3] + P(0,6)*SPP[0] + P(13,6)*SPP[4] - P(14,6)*SPP[7] - P(15,6)*SPP[1]);
|
||||
nextP(7,9) = P(7,9) + P(4,9)*dt + dt*(P(7,6) + P(4,6)*dt);
|
||||
nextP(8,9) = P(8,9) + P(5,9)*dt + dt*(P(8,6) + P(5,6)*dt);
|
||||
nextP(9,9) = P(9,9) + P(6,9)*dt + dt*(P(9,6) + P(6,6)*dt);
|
||||
nextP(0,10) = P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10];
|
||||
nextP(1,10) = P(1,10) + P(0,10)*SF[8] + P(2,10)*SF[7] + P(3,10)*SF[11] - P(12,10)*SF[15] + P(11,10)*SPP[10] - (P(10,10)*q0)*0.5f;
|
||||
nextP(2,10) = P(2,10) + P(0,10)*SF[6] + P(1,10)*SF[10] + P(3,10)*SF[8] + P(12,10)*SF[14] - P(10,10)*SPP[10] - (P(11,10)*q0)*0.5f;
|
||||
nextP(3,10) = P(3,10) + P(0,10)*SF[7] + P(1,10)*SF[6] + P(2,10)*SF[9] + P(10,10)*SF[15] - P(11,10)*SF[14] - (P(12,10)*q0)*0.5f;
|
||||
nextP(4,10) = P(4,10) + P(0,10)*SF[5] + P(1,10)*SF[3] - P(3,10)*SF[4] + P(2,10)*SPP[0] + P(13,10)*SPP[3] + P(14,10)*SPP[6] - P(15,10)*SPP[9];
|
||||
nextP(5,10) = P(5,10) + P(0,10)*SF[4] + P(2,10)*SF[3] + P(3,10)*SF[5] - P(1,10)*SPP[0] - P(13,10)*SPP[8] + P(14,10)*SPP[2] + P(15,10)*SPP[5];
|
||||
nextP(6,10) = P(6,10) + P(1,10)*SF[4] - P(2,10)*SF[5] + P(3,10)*SF[3] + P(0,10)*SPP[0] + P(13,10)*SPP[4] - P(14,10)*SPP[7] - P(15,10)*SPP[1];
|
||||
nextP(7,10) = P(7,10) + P(4,10)*dt;
|
||||
nextP(8,10) = P(8,10) + P(5,10)*dt;
|
||||
nextP(9,10) = P(9,10) + P(6,10)*dt;
|
||||
nextP(0,0) = PS0*PS1 - PS11*PS23 - PS12*PS26 - PS13*PS29 + PS14*PS6 + PS17*PS7 + PS2*PS3 + PS20*PS9 + PS33 + PS4*PS5;
|
||||
nextP(0,1) = -PS1*PS36 + PS11*PS33 - PS12*PS29 + PS13*PS26 - PS14*PS34 + PS17*PS9 - PS20*PS7 + PS23 + PS3*PS35 - PS35*PS5;
|
||||
nextP(1,1) = PS1*PS42 + PS11*PS80 - PS12*PS89 + PS13*PS82 + PS2*PS5 + PS3*PS4 - PS34*PS85 - PS7*PS87 + PS77*PS9 + PS92;
|
||||
nextP(0,2) = -PS1*PS37 + PS11*PS29 + PS12*PS33 - PS13*PS23 - PS14*PS9 - PS17*PS34 + PS20*PS6 + PS26 - PS3*PS38 + PS37*PS5;
|
||||
nextP(1,2) = PS1*PS40 + PS11*PS89 + PS12*PS80 - PS13*PS92 - PS3*PS40 - PS34*PS77 - PS39*PS5 + PS6*PS87 + PS82 - PS85*PS9;
|
||||
nextP(2,2) = PS0*PS5 + PS1*PS4 + PS103*PS6 + PS104*PS11 + PS106*PS12 - PS108*PS34 - PS109*PS9 - PS111*PS13 + PS113 + PS3*PS42;
|
||||
nextP(0,3) = PS1*PS39 - PS11*PS26 + PS12*PS23 + PS13*PS33 + PS14*PS7 - PS17*PS6 - PS20*PS34 + PS29 - PS3*PS39 - PS40*PS5;
|
||||
nextP(1,3) = -PS1*PS38 - PS11*PS82 + PS12*PS92 + PS13*PS80 - PS3*PS37 - PS34*PS87 + PS38*PS5 - PS6*PS77 + PS7*PS85 + PS89;
|
||||
nextP(2,3) = -PS1*PS35 - PS103*PS34 + PS104 + PS106*PS13 - PS108*PS6 + PS109*PS7 - PS11*PS113 + PS111*PS12 + PS3*PS36 - PS36*PS5;
|
||||
nextP(3,3) = PS0*PS3 + PS1*PS2 - PS11*PS128 + PS12*PS124 + PS123*PS7 + PS125*PS13 - PS126*PS34 - PS127*PS6 + PS129 + PS42*PS5;
|
||||
nextP(0,4) = PS23*PS62 + PS26*PS60 - PS44*PS45 - PS46*PS48 - PS52*PS53 + PS54*PS56 + PS57*PS58 + PS63;
|
||||
nextP(1,4) = -PS44*PS93 - PS46*PS95 + PS54*PS97 + PS60*PS82 + PS62*PS92 + PS72*PS80 - PS74*PS89 + PS98;
|
||||
nextP(2,4) = -PS104*PS74 + PS106*PS72 + PS111*PS62 + PS113*PS60 - PS114*PS44 - PS116*PS46 + PS118*PS54 + PS119;
|
||||
nextP(3,4) = PS124*PS62 + PS125*PS72 + PS128*PS60 - PS129*PS74 - PS130*PS44 - PS132*PS46 + PS134*PS54 + PS135;
|
||||
nextP(4,4) = -PS139*PS142 + PS140*PS146 - PS141*PS44 - PS145*PS74 + PS149*PS72 + PS152*PS60 + PS155*PS62 + PS156*ecl::powf(PS54, 2) + PS157*ecl::powf(PS46, 2) + PS158 + ecl::powf(PS44, 2)*dvxVar;
|
||||
nextP(0,5) = -PS23*PS60 + PS26*PS62 + PS48*PS68 + PS52*PS58 + PS53*PS57 - PS55*PS65 - PS66*PS67 + PS69;
|
||||
nextP(1,5) = PS100 - PS60*PS92 + PS62*PS82 - PS65*PS96 - PS66*PS99 + PS68*PS95 + PS72*PS89 + PS74*PS80;
|
||||
nextP(2,5) = PS104*PS72 + PS106*PS74 - PS111*PS60 + PS113*PS62 + PS116*PS68 - PS117*PS65 - PS120*PS66 + PS121;
|
||||
nextP(3,5) = -PS124*PS60 + PS125*PS74 + PS128*PS62 + PS129*PS72 + PS132*PS68 - PS133*PS65 - PS136*PS66 + PS137;
|
||||
nextP(4,5) = -PS140*PS161 + PS142*PS160 + PS145*PS72 - PS146*PS65 + PS149*PS74 + PS152*PS62 - PS155*PS60 - PS157*PS46*PS68 - PS159*PS66 + PS162*PS163 + PS164;
|
||||
nextP(5,5) = PS157*ecl::powf(PS68, 2) + PS160*PS173 - PS162*PS170 - PS169*PS65 - PS172*PS60 + PS175*PS72 + PS177*PS74 + PS179*PS62 + PS180*ecl::powf(PS66, 2) + PS181 + ecl::powf(PS65, 2)*dvyVar;
|
||||
nextP(0,6) = PS23*PS74 - PS26*PS72 - PS47*PS70 + PS53*PS61 - PS56*PS71 + PS58*PS59 + PS67*PS73 + PS75;
|
||||
nextP(1,6) = PS101 + PS60*PS80 + PS62*PS89 - PS70*PS94 - PS71*PS97 - PS72*PS82 + PS73*PS99 + PS74*PS92;
|
||||
nextP(2,6) = PS104*PS62 + PS106*PS60 + PS111*PS74 - PS113*PS72 - PS115*PS70 - PS118*PS71 + PS120*PS73 + PS122;
|
||||
nextP(3,6) = PS124*PS74 + PS125*PS60 - PS128*PS72 + PS129*PS62 - PS131*PS70 - PS134*PS71 + PS136*PS73 + PS138;
|
||||
nextP(4,6) = PS139*PS167 - PS142*PS70 + PS145*PS62 - PS146*PS165 + PS149*PS60 - PS152*PS72 + PS155*PS74 - PS156*PS54*PS71 + PS159*PS73 - PS163*PS166 + PS168;
|
||||
nextP(5,6) = -PS160*PS167 + PS161*PS165 - PS165*PS169 + PS166*PS170 + PS172*PS74 - PS173*PS70 + PS175*PS62 + PS177*PS60 - PS179*PS72 - PS180*PS66*PS73 + PS182;
|
||||
nextP(6,6) = PS156*ecl::powf(PS71, 2) - PS165*PS184 + PS166*PS185 + PS180*ecl::powf(PS73, 2) - PS183*PS70 + PS186 + PS60*(P(0,0)*PS60 + P(0,13)*PS166 - P(0,14)*PS165 - P(0,15)*PS70 + P(0,3)*PS62 + P(0,6) - PS151 + PS171) + PS62*(P(0,3)*PS60 + P(3,13)*PS166 - P(3,14)*PS165 - P(3,15)*PS70 + P(3,3)*PS62 + P(3,6) + PS154 - PS178) + ecl::powf(PS70, 2)*dvzVar - PS72*(P(1,2)*PS74 + P(2,13)*PS166 - P(2,14)*PS165 - P(2,15)*PS70 - P(2,2)*PS72 + P(2,6) + PS147 + PS174) + PS74*(P(1,1)*PS74 + P(1,13)*PS166 - P(1,14)*PS165 - P(1,15)*PS70 - P(1,2)*PS72 + P(1,6) + PS143 + PS176);
|
||||
nextP(0,7) = P(0,7) - P(1,7)*PS11 - P(2,7)*PS12 - P(3,7)*PS13 + P(7,10)*PS6 + P(7,11)*PS7 + P(7,12)*PS9 + PS63*dt;
|
||||
nextP(1,7) = P(0,7)*PS11 + P(1,7) + P(2,7)*PS13 - P(3,7)*PS12 - P(7,10)*PS34 + P(7,11)*PS9 - P(7,12)*PS7 + PS98*dt;
|
||||
nextP(2,7) = P(0,7)*PS12 - P(1,7)*PS13 + P(2,7) + P(3,7)*PS11 - P(7,10)*PS9 - P(7,11)*PS34 + P(7,12)*PS6 + PS119*dt;
|
||||
nextP(3,7) = P(0,7)*PS13 + P(1,7)*PS12 - P(2,7)*PS11 + P(3,7) + P(7,10)*PS7 - P(7,11)*PS6 - P(7,12)*PS34 + PS135*dt;
|
||||
nextP(4,7) = P(0,7)*PS72 + P(1,7)*PS62 + P(2,7)*PS60 - P(3,7)*PS74 + P(4,7) - P(7,13)*PS44 + P(7,14)*PS140 - P(7,15)*PS139 + PS158*dt;
|
||||
nextP(5,7) = P(0,7)*PS74 - P(1,7)*PS60 + P(2,7)*PS62 + P(3,7)*PS72 + P(5,7) - P(7,13)*PS162 - P(7,14)*PS65 + P(7,15)*PS160 + dt*(P(0,4)*PS74 - P(1,4)*PS60 + P(2,4)*PS62 + P(3,4)*PS72 - P(4,13)*PS162 - P(4,14)*PS65 + P(4,15)*PS160 + P(4,5));
|
||||
nextP(6,7) = P(0,7)*PS60 + P(1,7)*PS74 - P(2,7)*PS72 + P(3,7)*PS62 + P(6,7) + P(7,13)*PS166 - P(7,14)*PS165 - P(7,15)*PS70 + dt*(P(0,4)*PS60 + P(1,4)*PS74 - P(2,4)*PS72 + P(3,4)*PS62 + P(4,13)*PS166 - P(4,14)*PS165 - P(4,15)*PS70 + P(4,6));
|
||||
nextP(7,7) = P(4,7)*dt + P(7,7) + dt*(P(4,4)*dt + P(4,7));
|
||||
nextP(0,8) = P(0,8) - P(1,8)*PS11 - P(2,8)*PS12 - P(3,8)*PS13 + P(8,10)*PS6 + P(8,11)*PS7 + P(8,12)*PS9 + PS69*dt;
|
||||
nextP(1,8) = P(0,8)*PS11 + P(1,8) + P(2,8)*PS13 - P(3,8)*PS12 - P(8,10)*PS34 + P(8,11)*PS9 - P(8,12)*PS7 + PS100*dt;
|
||||
nextP(2,8) = P(0,8)*PS12 - P(1,8)*PS13 + P(2,8) + P(3,8)*PS11 - P(8,10)*PS9 - P(8,11)*PS34 + P(8,12)*PS6 + PS121*dt;
|
||||
nextP(3,8) = P(0,8)*PS13 + P(1,8)*PS12 - P(2,8)*PS11 + P(3,8) + P(8,10)*PS7 - P(8,11)*PS6 - P(8,12)*PS34 + PS137*dt;
|
||||
nextP(4,8) = P(0,8)*PS72 + P(1,8)*PS62 + P(2,8)*PS60 - P(3,8)*PS74 + P(4,8) - P(8,13)*PS44 + P(8,14)*PS140 - P(8,15)*PS139 + PS164*dt;
|
||||
nextP(5,8) = P(0,8)*PS74 - P(1,8)*PS60 + P(2,8)*PS62 + P(3,8)*PS72 + P(5,8) - P(8,13)*PS162 - P(8,14)*PS65 + P(8,15)*PS160 + PS181*dt;
|
||||
nextP(6,8) = P(0,8)*PS60 + P(1,8)*PS74 - P(2,8)*PS72 + P(3,8)*PS62 + P(6,8) + P(8,13)*PS166 - P(8,14)*PS165 - P(8,15)*PS70 + dt*(P(0,5)*PS60 + P(1,5)*PS74 - P(2,5)*PS72 + P(3,5)*PS62 + P(5,13)*PS166 - P(5,14)*PS165 - P(5,15)*PS70 + P(5,6));
|
||||
nextP(7,8) = P(4,8)*dt + P(7,8) + dt*(P(4,5)*dt + P(5,7));
|
||||
nextP(8,8) = P(5,8)*dt + P(8,8) + dt*(P(5,5)*dt + P(5,8));
|
||||
nextP(0,9) = P(0,9) - P(1,9)*PS11 - P(2,9)*PS12 - P(3,9)*PS13 + P(9,10)*PS6 + P(9,11)*PS7 + P(9,12)*PS9 + PS75*dt;
|
||||
nextP(1,9) = P(0,9)*PS11 + P(1,9) + P(2,9)*PS13 - P(3,9)*PS12 - P(9,10)*PS34 + P(9,11)*PS9 - P(9,12)*PS7 + PS101*dt;
|
||||
nextP(2,9) = P(0,9)*PS12 - P(1,9)*PS13 + P(2,9) + P(3,9)*PS11 - P(9,10)*PS9 - P(9,11)*PS34 + P(9,12)*PS6 + PS122*dt;
|
||||
nextP(3,9) = P(0,9)*PS13 + P(1,9)*PS12 - P(2,9)*PS11 + P(3,9) + P(9,10)*PS7 - P(9,11)*PS6 - P(9,12)*PS34 + PS138*dt;
|
||||
nextP(4,9) = P(0,9)*PS72 + P(1,9)*PS62 + P(2,9)*PS60 - P(3,9)*PS74 + P(4,9) - P(9,13)*PS44 + P(9,14)*PS140 - P(9,15)*PS139 + PS168*dt;
|
||||
nextP(5,9) = P(0,9)*PS74 - P(1,9)*PS60 + P(2,9)*PS62 + P(3,9)*PS72 + P(5,9) - P(9,13)*PS162 - P(9,14)*PS65 + P(9,15)*PS160 + PS182*dt;
|
||||
nextP(6,9) = P(0,9)*PS60 + P(1,9)*PS74 - P(2,9)*PS72 + P(3,9)*PS62 + P(6,9) + P(9,13)*PS166 - P(9,14)*PS165 - P(9,15)*PS70 + PS186*dt;
|
||||
nextP(7,9) = P(4,9)*dt + P(7,9) + dt*(P(4,6)*dt + P(6,7));
|
||||
nextP(8,9) = P(5,9)*dt + P(8,9) + dt*(P(5,6)*dt + P(6,8));
|
||||
nextP(9,9) = P(6,9)*dt + P(9,9) + dt*(P(6,6)*dt + P(6,9));
|
||||
nextP(0,10) = PS14;
|
||||
nextP(1,10) = PS85;
|
||||
nextP(2,10) = PS109;
|
||||
nextP(3,10) = PS123;
|
||||
nextP(4,10) = P(0,10)*PS72 + P(1,10)*PS62 - P(10,13)*PS44 + P(10,14)*PS140 - P(10,15)*PS139 + P(2,10)*PS60 - P(3,10)*PS74 + P(4,10);
|
||||
nextP(5,10) = P(0,10)*PS74 - P(1,10)*PS60 - P(10,13)*PS162 - P(10,14)*PS65 + P(10,15)*PS160 + P(2,10)*PS62 + P(3,10)*PS72 + P(5,10);
|
||||
nextP(6,10) = P(0,10)*PS60 + P(1,10)*PS74 + P(10,13)*PS166 - P(10,14)*PS165 - P(10,15)*PS70 - P(2,10)*PS72 + P(3,10)*PS62 + P(6,10);
|
||||
nextP(7,10) = P(4,10)*dt + P(7,10);
|
||||
nextP(8,10) = P(5,10)*dt + P(8,10);
|
||||
nextP(9,10) = P(6,10)*dt + P(9,10);
|
||||
nextP(10,10) = P(10,10);
|
||||
nextP(0,11) = P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10];
|
||||
nextP(1,11) = P(1,11) + P(0,11)*SF[8] + P(2,11)*SF[7] + P(3,11)*SF[11] - P(12,11)*SF[15] + P(11,11)*SPP[10] - (P(10,11)*q0)*0.5f;
|
||||
nextP(2,11) = P(2,11) + P(0,11)*SF[6] + P(1,11)*SF[10] + P(3,11)*SF[8] + P(12,11)*SF[14] - P(10,11)*SPP[10] - (P(11,11)*q0)*0.5f;
|
||||
nextP(3,11) = P(3,11) + P(0,11)*SF[7] + P(1,11)*SF[6] + P(2,11)*SF[9] + P(10,11)*SF[15] - P(11,11)*SF[14] - (P(12,11)*q0)*0.5f;
|
||||
nextP(4,11) = P(4,11) + P(0,11)*SF[5] + P(1,11)*SF[3] - P(3,11)*SF[4] + P(2,11)*SPP[0] + P(13,11)*SPP[3] + P(14,11)*SPP[6] - P(15,11)*SPP[9];
|
||||
nextP(5,11) = P(5,11) + P(0,11)*SF[4] + P(2,11)*SF[3] + P(3,11)*SF[5] - P(1,11)*SPP[0] - P(13,11)*SPP[8] + P(14,11)*SPP[2] + P(15,11)*SPP[5];
|
||||
nextP(6,11) = P(6,11) + P(1,11)*SF[4] - P(2,11)*SF[5] + P(3,11)*SF[3] + P(0,11)*SPP[0] + P(13,11)*SPP[4] - P(14,11)*SPP[7] - P(15,11)*SPP[1];
|
||||
nextP(7,11) = P(7,11) + P(4,11)*dt;
|
||||
nextP(8,11) = P(8,11) + P(5,11)*dt;
|
||||
nextP(9,11) = P(9,11) + P(6,11)*dt;
|
||||
nextP(0,11) = PS17;
|
||||
nextP(1,11) = PS77;
|
||||
nextP(2,11) = PS108;
|
||||
nextP(3,11) = PS127;
|
||||
nextP(4,11) = P(0,11)*PS72 + P(1,11)*PS62 - P(11,13)*PS44 + P(11,14)*PS140 - P(11,15)*PS139 + P(2,11)*PS60 - P(3,11)*PS74 + P(4,11);
|
||||
nextP(5,11) = P(0,11)*PS74 - P(1,11)*PS60 - P(11,13)*PS162 - P(11,14)*PS65 + P(11,15)*PS160 + P(2,11)*PS62 + P(3,11)*PS72 + P(5,11);
|
||||
nextP(6,11) = P(0,11)*PS60 + P(1,11)*PS74 + P(11,13)*PS166 - P(11,14)*PS165 - P(11,15)*PS70 - P(2,11)*PS72 + P(3,11)*PS62 + P(6,11);
|
||||
nextP(7,11) = P(4,11)*dt + P(7,11);
|
||||
nextP(8,11) = P(5,11)*dt + P(8,11);
|
||||
nextP(9,11) = P(6,11)*dt + P(9,11);
|
||||
nextP(10,11) = P(10,11);
|
||||
nextP(11,11) = P(11,11);
|
||||
nextP(0,12) = P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10];
|
||||
nextP(1,12) = P(1,12) + P(0,12)*SF[8] + P(2,12)*SF[7] + P(3,12)*SF[11] - P(12,12)*SF[15] + P(11,12)*SPP[10] - (P(10,12)*q0)*0.5f;
|
||||
nextP(2,12) = P(2,12) + P(0,12)*SF[6] + P(1,12)*SF[10] + P(3,12)*SF[8] + P(12,12)*SF[14] - P(10,12)*SPP[10] - (P(11,12)*q0)*0.5f;
|
||||
nextP(3,12) = P(3,12) + P(0,12)*SF[7] + P(1,12)*SF[6] + P(2,12)*SF[9] + P(10,12)*SF[15] - P(11,12)*SF[14] - (P(12,12)*q0)*0.5f;
|
||||
nextP(4,12) = P(4,12) + P(0,12)*SF[5] + P(1,12)*SF[3] - P(3,12)*SF[4] + P(2,12)*SPP[0] + P(13,12)*SPP[3] + P(14,12)*SPP[6] - P(15,12)*SPP[9];
|
||||
nextP(5,12) = P(5,12) + P(0,12)*SF[4] + P(2,12)*SF[3] + P(3,12)*SF[5] - P(1,12)*SPP[0] - P(13,12)*SPP[8] + P(14,12)*SPP[2] + P(15,12)*SPP[5];
|
||||
nextP(6,12) = P(6,12) + P(1,12)*SF[4] - P(2,12)*SF[5] + P(3,12)*SF[3] + P(0,12)*SPP[0] + P(13,12)*SPP[4] - P(14,12)*SPP[7] - P(15,12)*SPP[1];
|
||||
nextP(7,12) = P(7,12) + P(4,12)*dt;
|
||||
nextP(8,12) = P(8,12) + P(5,12)*dt;
|
||||
nextP(9,12) = P(9,12) + P(6,12)*dt;
|
||||
nextP(0,12) = PS20;
|
||||
nextP(1,12) = PS87;
|
||||
nextP(2,12) = PS103;
|
||||
nextP(3,12) = PS126;
|
||||
nextP(4,12) = P(0,12)*PS72 + P(1,12)*PS62 - P(12,13)*PS44 + P(12,14)*PS140 - P(12,15)*PS139 + P(2,12)*PS60 - P(3,12)*PS74 + P(4,12);
|
||||
nextP(5,12) = P(0,12)*PS74 - P(1,12)*PS60 - P(12,13)*PS162 - P(12,14)*PS65 + P(12,15)*PS160 + P(2,12)*PS62 + P(3,12)*PS72 + P(5,12);
|
||||
nextP(6,12) = P(0,12)*PS60 + P(1,12)*PS74 + P(12,13)*PS166 - P(12,14)*PS165 - P(12,15)*PS70 - P(2,12)*PS72 + P(3,12)*PS62 + P(6,12);
|
||||
nextP(7,12) = P(4,12)*dt + P(7,12);
|
||||
nextP(8,12) = P(5,12)*dt + P(8,12);
|
||||
nextP(9,12) = P(6,12)*dt + P(9,12);
|
||||
nextP(10,12) = P(10,12);
|
||||
nextP(11,12) = P(11,12);
|
||||
nextP(12,12) = P(12,12);
|
||||
@@ -429,58 +563,106 @@ void Ekf::predictCovariance()
|
||||
nextP(i,i) = kahanSummation(nextP(i,i), process_noise(i), _delta_angle_bias_var_accum(index));
|
||||
}
|
||||
|
||||
for (unsigned i = 13; i <= 15; i++) {
|
||||
const unsigned index = i - 13;
|
||||
if (!_accel_bias_inhibit[0]) {
|
||||
// calculate variances and upper diagonal covariances for IMU X axis delta velocity bias state
|
||||
nextP(0,13) = PS45;
|
||||
nextP(1,13) = PS93;
|
||||
nextP(2,13) = PS114;
|
||||
nextP(3,13) = PS130;
|
||||
nextP(4,13) = PS141;
|
||||
nextP(5,13) = PS170;
|
||||
nextP(6,13) = PS185;
|
||||
nextP(7,13) = P(4,13)*dt + P(7,13);
|
||||
nextP(8,13) = P(5,13)*dt + P(8,13);
|
||||
nextP(9,13) = P(6,13)*dt + P(9,13);
|
||||
nextP(10,13) = P(10,13);
|
||||
nextP(11,13) = P(11,13);
|
||||
nextP(12,13) = P(12,13);
|
||||
nextP(13,13) = P(13,13);
|
||||
|
||||
if (!_accel_bias_inhibit[index]) {
|
||||
// calculate variances and upper diagonal covariances for IMU delta velocity bias states
|
||||
nextP(0,i) = P(0,i) + P(1,i)*SF[9] + P(2,i)*SF[11] + P(3,i)*SF[10] + P(10,i)*SF[14] + P(11,i)*SF[15] + P(12,i)*SPP[10];
|
||||
nextP(1,i) = P(1,i) + P(0,i)*SF[8] + P(2,i)*SF[7] + P(3,i)*SF[11] - P(12,i)*SF[15] + P(11,i)*SPP[10] - (P(10,i)*q0)*0.5f;
|
||||
nextP(2,i) = P(2,i) + P(0,i)*SF[6] + P(1,i)*SF[10] + P(3,i)*SF[8] + P(12,i)*SF[14] - P(10,i)*SPP[10] - (P(11,i)*q0)*0.5f;
|
||||
nextP(3,i) = P(3,i) + P(0,i)*SF[7] + P(1,i)*SF[6] + P(2,i)*SF[9] + P(10,i)*SF[15] - P(11,i)*SF[14] - (P(12,i)*q0)*0.5f;
|
||||
nextP(4,i) = P(4,i) + P(0,i)*SF[5] + P(1,i)*SF[3] - P(3,i)*SF[4] + P(2,i)*SPP[0] + P(13,i)*SPP[3] + P(14,i)*SPP[6] - P(15,i)*SPP[9];
|
||||
nextP(5,i) = P(5,i) + P(0,i)*SF[4] + P(2,i)*SF[3] + P(3,i)*SF[5] - P(1,i)*SPP[0] - P(13,i)*SPP[8] + P(14,i)*SPP[2] + P(15,i)*SPP[5];
|
||||
nextP(6,i) = P(6,i) + P(1,i)*SF[4] - P(2,i)*SF[5] + P(3,i)*SF[3] + P(0,i)*SPP[0] + P(13,i)*SPP[4] - P(14,i)*SPP[7] - P(15,i)*SPP[1];
|
||||
nextP(7,i) = P(7,i) + P(4,i)*dt;
|
||||
nextP(8,i) = P(8,i) + P(5,i)*dt;
|
||||
nextP(9,i) = P(9,i) + P(6,i)*dt;
|
||||
nextP(10,i) = P(10,i);
|
||||
nextP(11,i) = P(11,i);
|
||||
nextP(12,i) = P(12,i);
|
||||
nextP(13,i) = P(13,i);
|
||||
// add process noise that is not from the IMU
|
||||
// process noise contribution for delta velocity states can be very small compared to
|
||||
// the variances, therefore use algorithm to minimise numerical error
|
||||
nextP(13,13) = kahanSummation(nextP(13,13), process_noise(13), _delta_vel_bias_var_accum(0));
|
||||
|
||||
if (i > 13) {
|
||||
nextP(14,i) = P(14,i);
|
||||
}
|
||||
} else {
|
||||
nextP.uncorrelateCovarianceSetVariance<1>(13, 0.f);
|
||||
_delta_vel_bias_var_accum(0) = 0.f;
|
||||
|
||||
if (i > 14) {
|
||||
nextP(15,i) = P(15,i);
|
||||
}
|
||||
}
|
||||
|
||||
// add process noise that is not from the IMU
|
||||
// process noise contributiton for delta velocity states can be very small compared to
|
||||
// the variances, therefore use algorithm to minimise numerical error
|
||||
nextP(i,i) = kahanSummation(nextP(i,i), process_noise(i), _delta_vel_bias_var_accum(index));
|
||||
if (!_accel_bias_inhibit[1]) {
|
||||
// calculate variances and upper diagonal covariances for IMU Y axis delta velocity bias state
|
||||
nextP(0,14) = PS55;
|
||||
nextP(1,14) = PS96;
|
||||
nextP(2,14) = PS117;
|
||||
nextP(3,14) = PS133;
|
||||
nextP(4,14) = PS146;
|
||||
nextP(5,14) = PS169;
|
||||
nextP(6,14) = PS184;
|
||||
nextP(7,14) = P(4,14)*dt + P(7,14);
|
||||
nextP(8,14) = P(5,14)*dt + P(8,14);
|
||||
nextP(9,14) = P(6,14)*dt + P(9,14);
|
||||
nextP(10,14) = P(10,14);
|
||||
nextP(11,14) = P(11,14);
|
||||
nextP(12,14) = P(12,14);
|
||||
nextP(13,14) = P(13,14);
|
||||
nextP(14,14) = P(14,14);
|
||||
|
||||
// add process noise that is not from the IMU
|
||||
// process noise contribution for delta velocity states can be very small compared to
|
||||
// the variances, therefore use algorithm to minimise numerical error
|
||||
nextP(14,14) = kahanSummation(nextP(14,14), process_noise(14), _delta_vel_bias_var_accum(1));
|
||||
|
||||
} else {
|
||||
nextP.uncorrelateCovarianceSetVariance<1>(14, 0.f);
|
||||
_delta_vel_bias_var_accum(1) = 0.f;
|
||||
|
||||
}
|
||||
|
||||
if (!_accel_bias_inhibit[2]) {
|
||||
// calculate variances and upper diagonal covariances for IMU Z axis delta velocity bias state
|
||||
nextP(0,15) = PS47;
|
||||
nextP(1,15) = PS94;
|
||||
nextP(2,15) = PS115;
|
||||
nextP(3,15) = PS131;
|
||||
nextP(4,15) = PS142;
|
||||
nextP(5,15) = PS173;
|
||||
nextP(6,15) = PS183;
|
||||
nextP(7,15) = P(4,15)*dt + P(7,15);
|
||||
nextP(8,15) = P(5,15)*dt + P(8,15);
|
||||
nextP(9,15) = P(6,15)*dt + P(9,15);
|
||||
nextP(10,15) = P(10,15);
|
||||
nextP(11,15) = P(11,15);
|
||||
nextP(12,15) = P(12,15);
|
||||
nextP(13,15) = P(13,15);
|
||||
nextP(14,15) = P(14,15);
|
||||
nextP(15,15) = P(15,15);
|
||||
|
||||
// add process noise that is not from the IMU
|
||||
// process noise contribution for delta velocity states can be very small compared to
|
||||
// the variances, therefore use algorithm to minimise numerical error
|
||||
nextP(15,15) = kahanSummation(nextP(15,15), process_noise(15), _delta_vel_bias_var_accum(2));
|
||||
|
||||
} else {
|
||||
nextP.uncorrelateCovarianceSetVariance<1>(15, 0.f);
|
||||
_delta_vel_bias_var_accum(2) = 0.f;
|
||||
|
||||
} else {
|
||||
nextP.uncorrelateCovarianceSetVariance<1>(i, 0.f);
|
||||
_delta_vel_bias_var_accum(index) = 0.f;
|
||||
}
|
||||
}
|
||||
|
||||
// Don't do covariance prediction on magnetic field states unless we are using 3-axis fusion
|
||||
if (_control_status.flags.mag_3D) {
|
||||
// calculate variances and upper diagonal covariances for earth and body magnetic field states
|
||||
nextP(0,16) = P(0,16) + P(1,16)*SF[9] + P(2,16)*SF[11] + P(3,16)*SF[10] + P(10,16)*SF[14] + P(11,16)*SF[15] + P(12,16)*SPP[10];
|
||||
nextP(1,16) = P(1,16) + P(0,16)*SF[8] + P(2,16)*SF[7] + P(3,16)*SF[11] - P(12,16)*SF[15] + P(11,16)*SPP[10] - (P(10,16)*q0)*0.5f;
|
||||
nextP(2,16) = P(2,16) + P(0,16)*SF[6] + P(1,16)*SF[10] + P(3,16)*SF[8] + P(12,16)*SF[14] - P(10,16)*SPP[10] - (P(11,16)*q0)*0.5f;
|
||||
nextP(3,16) = P(3,16) + P(0,16)*SF[7] + P(1,16)*SF[6] + P(2,16)*SF[9] + P(10,16)*SF[15] - P(11,16)*SF[14] - (P(12,16)*q0)*0.5f;
|
||||
nextP(4,16) = P(4,16) + P(0,16)*SF[5] + P(1,16)*SF[3] - P(3,16)*SF[4] + P(2,16)*SPP[0] + P(13,16)*SPP[3] + P(14,16)*SPP[6] - P(15,16)*SPP[9];
|
||||
nextP(5,16) = P(5,16) + P(0,16)*SF[4] + P(2,16)*SF[3] + P(3,16)*SF[5] - P(1,16)*SPP[0] - P(13,16)*SPP[8] + P(14,16)*SPP[2] + P(15,16)*SPP[5];
|
||||
nextP(6,16) = P(6,16) + P(1,16)*SF[4] - P(2,16)*SF[5] + P(3,16)*SF[3] + P(0,16)*SPP[0] + P(13,16)*SPP[4] - P(14,16)*SPP[7] - P(15,16)*SPP[1];
|
||||
nextP(7,16) = P(7,16) + P(4,16)*dt;
|
||||
nextP(8,16) = P(8,16) + P(5,16)*dt;
|
||||
nextP(9,16) = P(9,16) + P(6,16)*dt;
|
||||
nextP(0,16) = P(0,16) - P(1,16)*PS11 + P(10,16)*PS6 + P(11,16)*PS7 + P(12,16)*PS9 - P(2,16)*PS12 - P(3,16)*PS13;
|
||||
nextP(1,16) = P(0,16)*PS11 + P(1,16) - P(10,16)*PS34 + P(11,16)*PS9 - P(12,16)*PS7 + P(2,16)*PS13 - P(3,16)*PS12;
|
||||
nextP(2,16) = P(0,16)*PS12 - P(1,16)*PS13 - P(10,16)*PS9 - P(11,16)*PS34 + P(12,16)*PS6 + P(2,16) + P(3,16)*PS11;
|
||||
nextP(3,16) = P(0,16)*PS13 + P(1,16)*PS12 + P(10,16)*PS7 - P(11,16)*PS6 - P(12,16)*PS34 - P(2,16)*PS11 + P(3,16);
|
||||
nextP(4,16) = P(0,16)*PS72 + P(1,16)*PS62 - P(13,16)*PS44 + P(14,16)*PS140 - P(15,16)*PS139 + P(2,16)*PS60 - P(3,16)*PS74 + P(4,16);
|
||||
nextP(5,16) = P(0,16)*PS74 - P(1,16)*PS60 - P(13,16)*PS162 - P(14,16)*PS65 + P(15,16)*PS160 + P(2,16)*PS62 + P(3,16)*PS72 + P(5,16);
|
||||
nextP(6,16) = P(0,16)*PS60 + P(1,16)*PS74 + P(13,16)*PS166 - P(14,16)*PS165 - P(15,16)*PS70 - P(2,16)*PS72 + P(3,16)*PS62 + P(6,16);
|
||||
nextP(7,16) = P(4,16)*dt + P(7,16);
|
||||
nextP(8,16) = P(5,16)*dt + P(8,16);
|
||||
nextP(9,16) = P(6,16)*dt + P(9,16);
|
||||
nextP(10,16) = P(10,16);
|
||||
nextP(11,16) = P(11,16);
|
||||
nextP(12,16) = P(12,16);
|
||||
@@ -488,16 +670,16 @@ void Ekf::predictCovariance()
|
||||
nextP(14,16) = P(14,16);
|
||||
nextP(15,16) = P(15,16);
|
||||
nextP(16,16) = P(16,16);
|
||||
nextP(0,17) = P(0,17) + P(1,17)*SF[9] + P(2,17)*SF[11] + P(3,17)*SF[10] + P(10,17)*SF[14] + P(11,17)*SF[15] + P(12,17)*SPP[10];
|
||||
nextP(1,17) = P(1,17) + P(0,17)*SF[8] + P(2,17)*SF[7] + P(3,17)*SF[11] - P(12,17)*SF[15] + P(11,17)*SPP[10] - (P(10,17)*q0)*0.5f;
|
||||
nextP(2,17) = P(2,17) + P(0,17)*SF[6] + P(1,17)*SF[10] + P(3,17)*SF[8] + P(12,17)*SF[14] - P(10,17)*SPP[10] - (P(11,17)*q0)*0.5f;
|
||||
nextP(3,17) = P(3,17) + P(0,17)*SF[7] + P(1,17)*SF[6] + P(2,17)*SF[9] + P(10,17)*SF[15] - P(11,17)*SF[14] - (P(12,17)*q0)*0.5f;
|
||||
nextP(4,17) = P(4,17) + P(0,17)*SF[5] + P(1,17)*SF[3] - P(3,17)*SF[4] + P(2,17)*SPP[0] + P(13,17)*SPP[3] + P(14,17)*SPP[6] - P(15,17)*SPP[9];
|
||||
nextP(5,17) = P(5,17) + P(0,17)*SF[4] + P(2,17)*SF[3] + P(3,17)*SF[5] - P(1,17)*SPP[0] - P(13,17)*SPP[8] + P(14,17)*SPP[2] + P(15,17)*SPP[5];
|
||||
nextP(6,17) = P(6,17) + P(1,17)*SF[4] - P(2,17)*SF[5] + P(3,17)*SF[3] + P(0,17)*SPP[0] + P(13,17)*SPP[4] - P(14,17)*SPP[7] - P(15,17)*SPP[1];
|
||||
nextP(7,17) = P(7,17) + P(4,17)*dt;
|
||||
nextP(8,17) = P(8,17) + P(5,17)*dt;
|
||||
nextP(9,17) = P(9,17) + P(6,17)*dt;
|
||||
nextP(0,17) = P(0,17) - P(1,17)*PS11 + P(10,17)*PS6 + P(11,17)*PS7 + P(12,17)*PS9 - P(2,17)*PS12 - P(3,17)*PS13;
|
||||
nextP(1,17) = P(0,17)*PS11 + P(1,17) - P(10,17)*PS34 + P(11,17)*PS9 - P(12,17)*PS7 + P(2,17)*PS13 - P(3,17)*PS12;
|
||||
nextP(2,17) = P(0,17)*PS12 - P(1,17)*PS13 - P(10,17)*PS9 - P(11,17)*PS34 + P(12,17)*PS6 + P(2,17) + P(3,17)*PS11;
|
||||
nextP(3,17) = P(0,17)*PS13 + P(1,17)*PS12 + P(10,17)*PS7 - P(11,17)*PS6 - P(12,17)*PS34 - P(2,17)*PS11 + P(3,17);
|
||||
nextP(4,17) = P(0,17)*PS72 + P(1,17)*PS62 - P(13,17)*PS44 + P(14,17)*PS140 - P(15,17)*PS139 + P(2,17)*PS60 - P(3,17)*PS74 + P(4,17);
|
||||
nextP(5,17) = P(0,17)*PS74 - P(1,17)*PS60 - P(13,17)*PS162 - P(14,17)*PS65 + P(15,17)*PS160 + P(2,17)*PS62 + P(3,17)*PS72 + P(5,17);
|
||||
nextP(6,17) = P(0,17)*PS60 + P(1,17)*PS74 + P(13,17)*PS166 - P(14,17)*PS165 - P(15,17)*PS70 - P(2,17)*PS72 + P(3,17)*PS62 + P(6,17);
|
||||
nextP(7,17) = P(4,17)*dt + P(7,17);
|
||||
nextP(8,17) = P(5,17)*dt + P(8,17);
|
||||
nextP(9,17) = P(6,17)*dt + P(9,17);
|
||||
nextP(10,17) = P(10,17);
|
||||
nextP(11,17) = P(11,17);
|
||||
nextP(12,17) = P(12,17);
|
||||
@@ -506,16 +688,16 @@ void Ekf::predictCovariance()
|
||||
nextP(15,17) = P(15,17);
|
||||
nextP(16,17) = P(16,17);
|
||||
nextP(17,17) = P(17,17);
|
||||
nextP(0,18) = P(0,18) + P(1,18)*SF[9] + P(2,18)*SF[11] + P(3,18)*SF[10] + P(10,18)*SF[14] + P(11,18)*SF[15] + P(12,18)*SPP[10];
|
||||
nextP(1,18) = P(1,18) + P(0,18)*SF[8] + P(2,18)*SF[7] + P(3,18)*SF[11] - P(12,18)*SF[15] + P(11,18)*SPP[10] - (P(10,18)*q0)*0.5f;
|
||||
nextP(2,18) = P(2,18) + P(0,18)*SF[6] + P(1,18)*SF[10] + P(3,18)*SF[8] + P(12,18)*SF[14] - P(10,18)*SPP[10] - (P(11,18)*q0)*0.5f;
|
||||
nextP(3,18) = P(3,18) + P(0,18)*SF[7] + P(1,18)*SF[6] + P(2,18)*SF[9] + P(10,18)*SF[15] - P(11,18)*SF[14] - (P(12,18)*q0)*0.5f;
|
||||
nextP(4,18) = P(4,18) + P(0,18)*SF[5] + P(1,18)*SF[3] - P(3,18)*SF[4] + P(2,18)*SPP[0] + P(13,18)*SPP[3] + P(14,18)*SPP[6] - P(15,18)*SPP[9];
|
||||
nextP(5,18) = P(5,18) + P(0,18)*SF[4] + P(2,18)*SF[3] + P(3,18)*SF[5] - P(1,18)*SPP[0] - P(13,18)*SPP[8] + P(14,18)*SPP[2] + P(15,18)*SPP[5];
|
||||
nextP(6,18) = P(6,18) + P(1,18)*SF[4] - P(2,18)*SF[5] + P(3,18)*SF[3] + P(0,18)*SPP[0] + P(13,18)*SPP[4] - P(14,18)*SPP[7] - P(15,18)*SPP[1];
|
||||
nextP(7,18) = P(7,18) + P(4,18)*dt;
|
||||
nextP(8,18) = P(8,18) + P(5,18)*dt;
|
||||
nextP(9,18) = P(9,18) + P(6,18)*dt;
|
||||
nextP(0,18) = P(0,18) - P(1,18)*PS11 + P(10,18)*PS6 + P(11,18)*PS7 + P(12,18)*PS9 - P(2,18)*PS12 - P(3,18)*PS13;
|
||||
nextP(1,18) = P(0,18)*PS11 + P(1,18) - P(10,18)*PS34 + P(11,18)*PS9 - P(12,18)*PS7 + P(2,18)*PS13 - P(3,18)*PS12;
|
||||
nextP(2,18) = P(0,18)*PS12 - P(1,18)*PS13 - P(10,18)*PS9 - P(11,18)*PS34 + P(12,18)*PS6 + P(2,18) + P(3,18)*PS11;
|
||||
nextP(3,18) = P(0,18)*PS13 + P(1,18)*PS12 + P(10,18)*PS7 - P(11,18)*PS6 - P(12,18)*PS34 - P(2,18)*PS11 + P(3,18);
|
||||
nextP(4,18) = P(0,18)*PS72 + P(1,18)*PS62 - P(13,18)*PS44 + P(14,18)*PS140 - P(15,18)*PS139 + P(2,18)*PS60 - P(3,18)*PS74 + P(4,18);
|
||||
nextP(5,18) = P(0,18)*PS74 - P(1,18)*PS60 - P(13,18)*PS162 - P(14,18)*PS65 + P(15,18)*PS160 + P(2,18)*PS62 + P(3,18)*PS72 + P(5,18);
|
||||
nextP(6,18) = P(0,18)*PS60 + P(1,18)*PS74 + P(13,18)*PS166 - P(14,18)*PS165 - P(15,18)*PS70 - P(2,18)*PS72 + P(3,18)*PS62 + P(6,18);
|
||||
nextP(7,18) = P(4,18)*dt + P(7,18);
|
||||
nextP(8,18) = P(5,18)*dt + P(8,18);
|
||||
nextP(9,18) = P(6,18)*dt + P(9,18);
|
||||
nextP(10,18) = P(10,18);
|
||||
nextP(11,18) = P(11,18);
|
||||
nextP(12,18) = P(12,18);
|
||||
@@ -525,16 +707,16 @@ void Ekf::predictCovariance()
|
||||
nextP(16,18) = P(16,18);
|
||||
nextP(17,18) = P(17,18);
|
||||
nextP(18,18) = P(18,18);
|
||||
nextP(0,19) = P(0,19) + P(1,19)*SF[9] + P(2,19)*SF[11] + P(3,19)*SF[10] + P(10,19)*SF[14] + P(11,19)*SF[15] + P(12,19)*SPP[10];
|
||||
nextP(1,19) = P(1,19) + P(0,19)*SF[8] + P(2,19)*SF[7] + P(3,19)*SF[11] - P(12,19)*SF[15] + P(11,19)*SPP[10] - (P(10,19)*q0)*0.5f;
|
||||
nextP(2,19) = P(2,19) + P(0,19)*SF[6] + P(1,19)*SF[10] + P(3,19)*SF[8] + P(12,19)*SF[14] - P(10,19)*SPP[10] - (P(11,19)*q0)*0.5f;
|
||||
nextP(3,19) = P(3,19) + P(0,19)*SF[7] + P(1,19)*SF[6] + P(2,19)*SF[9] + P(10,19)*SF[15] - P(11,19)*SF[14] - (P(12,19)*q0)*0.5f;
|
||||
nextP(4,19) = P(4,19) + P(0,19)*SF[5] + P(1,19)*SF[3] - P(3,19)*SF[4] + P(2,19)*SPP[0] + P(13,19)*SPP[3] + P(14,19)*SPP[6] - P(15,19)*SPP[9];
|
||||
nextP(5,19) = P(5,19) + P(0,19)*SF[4] + P(2,19)*SF[3] + P(3,19)*SF[5] - P(1,19)*SPP[0] - P(13,19)*SPP[8] + P(14,19)*SPP[2] + P(15,19)*SPP[5];
|
||||
nextP(6,19) = P(6,19) + P(1,19)*SF[4] - P(2,19)*SF[5] + P(3,19)*SF[3] + P(0,19)*SPP[0] + P(13,19)*SPP[4] - P(14,19)*SPP[7] - P(15,19)*SPP[1];
|
||||
nextP(7,19) = P(7,19) + P(4,19)*dt;
|
||||
nextP(8,19) = P(8,19) + P(5,19)*dt;
|
||||
nextP(9,19) = P(9,19) + P(6,19)*dt;
|
||||
nextP(0,19) = P(0,19) - P(1,19)*PS11 + P(10,19)*PS6 + P(11,19)*PS7 + P(12,19)*PS9 - P(2,19)*PS12 - P(3,19)*PS13;
|
||||
nextP(1,19) = P(0,19)*PS11 + P(1,19) - P(10,19)*PS34 + P(11,19)*PS9 - P(12,19)*PS7 + P(2,19)*PS13 - P(3,19)*PS12;
|
||||
nextP(2,19) = P(0,19)*PS12 - P(1,19)*PS13 - P(10,19)*PS9 - P(11,19)*PS34 + P(12,19)*PS6 + P(2,19) + P(3,19)*PS11;
|
||||
nextP(3,19) = P(0,19)*PS13 + P(1,19)*PS12 + P(10,19)*PS7 - P(11,19)*PS6 - P(12,19)*PS34 - P(2,19)*PS11 + P(3,19);
|
||||
nextP(4,19) = P(0,19)*PS72 + P(1,19)*PS62 - P(13,19)*PS44 + P(14,19)*PS140 - P(15,19)*PS139 + P(2,19)*PS60 - P(3,19)*PS74 + P(4,19);
|
||||
nextP(5,19) = P(0,19)*PS74 - P(1,19)*PS60 - P(13,19)*PS162 - P(14,19)*PS65 + P(15,19)*PS160 + P(2,19)*PS62 + P(3,19)*PS72 + P(5,19);
|
||||
nextP(6,19) = P(0,19)*PS60 + P(1,19)*PS74 + P(13,19)*PS166 - P(14,19)*PS165 - P(15,19)*PS70 - P(2,19)*PS72 + P(3,19)*PS62 + P(6,19);
|
||||
nextP(7,19) = P(4,19)*dt + P(7,19);
|
||||
nextP(8,19) = P(5,19)*dt + P(8,19);
|
||||
nextP(9,19) = P(6,19)*dt + P(9,19);
|
||||
nextP(10,19) = P(10,19);
|
||||
nextP(11,19) = P(11,19);
|
||||
nextP(12,19) = P(12,19);
|
||||
@@ -545,16 +727,16 @@ void Ekf::predictCovariance()
|
||||
nextP(17,19) = P(17,19);
|
||||
nextP(18,19) = P(18,19);
|
||||
nextP(19,19) = P(19,19);
|
||||
nextP(0,20) = P(0,20) + P(1,20)*SF[9] + P(2,20)*SF[11] + P(3,20)*SF[10] + P(10,20)*SF[14] + P(11,20)*SF[15] + P(12,20)*SPP[10];
|
||||
nextP(1,20) = P(1,20) + P(0,20)*SF[8] + P(2,20)*SF[7] + P(3,20)*SF[11] - P(12,20)*SF[15] + P(11,20)*SPP[10] - (P(10,20)*q0)*0.5f;
|
||||
nextP(2,20) = P(2,20) + P(0,20)*SF[6] + P(1,20)*SF[10] + P(3,20)*SF[8] + P(12,20)*SF[14] - P(10,20)*SPP[10] - (P(11,20)*q0)*0.5f;
|
||||
nextP(3,20) = P(3,20) + P(0,20)*SF[7] + P(1,20)*SF[6] + P(2,20)*SF[9] + P(10,20)*SF[15] - P(11,20)*SF[14] - (P(12,20)*q0)*0.5f;
|
||||
nextP(4,20) = P(4,20) + P(0,20)*SF[5] + P(1,20)*SF[3] - P(3,20)*SF[4] + P(2,20)*SPP[0] + P(13,20)*SPP[3] + P(14,20)*SPP[6] - P(15,20)*SPP[9];
|
||||
nextP(5,20) = P(5,20) + P(0,20)*SF[4] + P(2,20)*SF[3] + P(3,20)*SF[5] - P(1,20)*SPP[0] - P(13,20)*SPP[8] + P(14,20)*SPP[2] + P(15,20)*SPP[5];
|
||||
nextP(6,20) = P(6,20) + P(1,20)*SF[4] - P(2,20)*SF[5] + P(3,20)*SF[3] + P(0,20)*SPP[0] + P(13,20)*SPP[4] - P(14,20)*SPP[7] - P(15,20)*SPP[1];
|
||||
nextP(7,20) = P(7,20) + P(4,20)*dt;
|
||||
nextP(8,20) = P(8,20) + P(5,20)*dt;
|
||||
nextP(9,20) = P(9,20) + P(6,20)*dt;
|
||||
nextP(0,20) = P(0,20) - P(1,20)*PS11 + P(10,20)*PS6 + P(11,20)*PS7 + P(12,20)*PS9 - P(2,20)*PS12 - P(3,20)*PS13;
|
||||
nextP(1,20) = P(0,20)*PS11 + P(1,20) - P(10,20)*PS34 + P(11,20)*PS9 - P(12,20)*PS7 + P(2,20)*PS13 - P(3,20)*PS12;
|
||||
nextP(2,20) = P(0,20)*PS12 - P(1,20)*PS13 - P(10,20)*PS9 - P(11,20)*PS34 + P(12,20)*PS6 + P(2,20) + P(3,20)*PS11;
|
||||
nextP(3,20) = P(0,20)*PS13 + P(1,20)*PS12 + P(10,20)*PS7 - P(11,20)*PS6 - P(12,20)*PS34 - P(2,20)*PS11 + P(3,20);
|
||||
nextP(4,20) = P(0,20)*PS72 + P(1,20)*PS62 - P(13,20)*PS44 + P(14,20)*PS140 - P(15,20)*PS139 + P(2,20)*PS60 - P(3,20)*PS74 + P(4,20);
|
||||
nextP(5,20) = P(0,20)*PS74 - P(1,20)*PS60 - P(13,20)*PS162 - P(14,20)*PS65 + P(15,20)*PS160 + P(2,20)*PS62 + P(3,20)*PS72 + P(5,20);
|
||||
nextP(6,20) = P(0,20)*PS60 + P(1,20)*PS74 + P(13,20)*PS166 - P(14,20)*PS165 - P(15,20)*PS70 - P(2,20)*PS72 + P(3,20)*PS62 + P(6,20);
|
||||
nextP(7,20) = P(4,20)*dt + P(7,20);
|
||||
nextP(8,20) = P(5,20)*dt + P(8,20);
|
||||
nextP(9,20) = P(6,20)*dt + P(9,20);
|
||||
nextP(10,20) = P(10,20);
|
||||
nextP(11,20) = P(11,20);
|
||||
nextP(12,20) = P(12,20);
|
||||
@@ -566,16 +748,16 @@ void Ekf::predictCovariance()
|
||||
nextP(18,20) = P(18,20);
|
||||
nextP(19,20) = P(19,20);
|
||||
nextP(20,20) = P(20,20);
|
||||
nextP(0,21) = P(0,21) + P(1,21)*SF[9] + P(2,21)*SF[11] + P(3,21)*SF[10] + P(10,21)*SF[14] + P(11,21)*SF[15] + P(12,21)*SPP[10];
|
||||
nextP(1,21) = P(1,21) + P(0,21)*SF[8] + P(2,21)*SF[7] + P(3,21)*SF[11] - P(12,21)*SF[15] + P(11,21)*SPP[10] - (P(10,21)*q0)*0.5f;
|
||||
nextP(2,21) = P(2,21) + P(0,21)*SF[6] + P(1,21)*SF[10] + P(3,21)*SF[8] + P(12,21)*SF[14] - P(10,21)*SPP[10] - (P(11,21)*q0)*0.5f;
|
||||
nextP(3,21) = P(3,21) + P(0,21)*SF[7] + P(1,21)*SF[6] + P(2,21)*SF[9] + P(10,21)*SF[15] - P(11,21)*SF[14] - (P(12,21)*q0)*0.5f;
|
||||
nextP(4,21) = P(4,21) + P(0,21)*SF[5] + P(1,21)*SF[3] - P(3,21)*SF[4] + P(2,21)*SPP[0] + P(13,21)*SPP[3] + P(14,21)*SPP[6] - P(15,21)*SPP[9];
|
||||
nextP(5,21) = P(5,21) + P(0,21)*SF[4] + P(2,21)*SF[3] + P(3,21)*SF[5] - P(1,21)*SPP[0] - P(13,21)*SPP[8] + P(14,21)*SPP[2] + P(15,21)*SPP[5];
|
||||
nextP(6,21) = P(6,21) + P(1,21)*SF[4] - P(2,21)*SF[5] + P(3,21)*SF[3] + P(0,21)*SPP[0] + P(13,21)*SPP[4] - P(14,21)*SPP[7] - P(15,21)*SPP[1];
|
||||
nextP(7,21) = P(7,21) + P(4,21)*dt;
|
||||
nextP(8,21) = P(8,21) + P(5,21)*dt;
|
||||
nextP(9,21) = P(9,21) + P(6,21)*dt;
|
||||
nextP(0,21) = P(0,21) - P(1,21)*PS11 + P(10,21)*PS6 + P(11,21)*PS7 + P(12,21)*PS9 - P(2,21)*PS12 - P(3,21)*PS13;
|
||||
nextP(1,21) = P(0,21)*PS11 + P(1,21) - P(10,21)*PS34 + P(11,21)*PS9 - P(12,21)*PS7 + P(2,21)*PS13 - P(3,21)*PS12;
|
||||
nextP(2,21) = P(0,21)*PS12 - P(1,21)*PS13 - P(10,21)*PS9 - P(11,21)*PS34 + P(12,21)*PS6 + P(2,21) + P(3,21)*PS11;
|
||||
nextP(3,21) = P(0,21)*PS13 + P(1,21)*PS12 + P(10,21)*PS7 - P(11,21)*PS6 - P(12,21)*PS34 - P(2,21)*PS11 + P(3,21);
|
||||
nextP(4,21) = P(0,21)*PS72 + P(1,21)*PS62 - P(13,21)*PS44 + P(14,21)*PS140 - P(15,21)*PS139 + P(2,21)*PS60 - P(3,21)*PS74 + P(4,21);
|
||||
nextP(5,21) = P(0,21)*PS74 - P(1,21)*PS60 - P(13,21)*PS162 - P(14,21)*PS65 + P(15,21)*PS160 + P(2,21)*PS62 + P(3,21)*PS72 + P(5,21);
|
||||
nextP(6,21) = P(0,21)*PS60 + P(1,21)*PS74 + P(13,21)*PS166 - P(14,21)*PS165 - P(15,21)*PS70 - P(2,21)*PS72 + P(3,21)*PS62 + P(6,21);
|
||||
nextP(7,21) = P(4,21)*dt + P(7,21);
|
||||
nextP(8,21) = P(5,21)*dt + P(8,21);
|
||||
nextP(9,21) = P(6,21)*dt + P(9,21);
|
||||
nextP(10,21) = P(10,21);
|
||||
nextP(11,21) = P(11,21);
|
||||
nextP(12,21) = P(12,21);
|
||||
@@ -600,16 +782,16 @@ void Ekf::predictCovariance()
|
||||
if (_control_status.flags.wind) {
|
||||
|
||||
// calculate variances and upper diagonal covariances for wind states
|
||||
nextP(0,22) = P(0,22) + P(1,22)*SF[9] + P(2,22)*SF[11] + P(3,22)*SF[10] + P(10,22)*SF[14] + P(11,22)*SF[15] + P(12,22)*SPP[10];
|
||||
nextP(1,22) = P(1,22) + P(0,22)*SF[8] + P(2,22)*SF[7] + P(3,22)*SF[11] - P(12,22)*SF[15] + P(11,22)*SPP[10] - (P(10,22)*q0)*0.5f;
|
||||
nextP(2,22) = P(2,22) + P(0,22)*SF[6] + P(1,22)*SF[10] + P(3,22)*SF[8] + P(12,22)*SF[14] - P(10,22)*SPP[10] - (P(11,22)*q0)*0.5f;
|
||||
nextP(3,22) = P(3,22) + P(0,22)*SF[7] + P(1,22)*SF[6] + P(2,22)*SF[9] + P(10,22)*SF[15] - P(11,22)*SF[14] - (P(12,22)*q0)*0.5f;
|
||||
nextP(4,22) = P(4,22) + P(0,22)*SF[5] + P(1,22)*SF[3] - P(3,22)*SF[4] + P(2,22)*SPP[0] + P(13,22)*SPP[3] + P(14,22)*SPP[6] - P(15,22)*SPP[9];
|
||||
nextP(5,22) = P(5,22) + P(0,22)*SF[4] + P(2,22)*SF[3] + P(3,22)*SF[5] - P(1,22)*SPP[0] - P(13,22)*SPP[8] + P(14,22)*SPP[2] + P(15,22)*SPP[5];
|
||||
nextP(6,22) = P(6,22) + P(1,22)*SF[4] - P(2,22)*SF[5] + P(3,22)*SF[3] + P(0,22)*SPP[0] + P(13,22)*SPP[4] - P(14,22)*SPP[7] - P(15,22)*SPP[1];
|
||||
nextP(7,22) = P(7,22) + P(4,22)*dt;
|
||||
nextP(8,22) = P(8,22) + P(5,22)*dt;
|
||||
nextP(9,22) = P(9,22) + P(6,22)*dt;
|
||||
nextP(0,22) = P(0,22) - P(1,22)*PS11 + P(10,22)*PS6 + P(11,22)*PS7 + P(12,22)*PS9 - P(2,22)*PS12 - P(3,22)*PS13;
|
||||
nextP(1,22) = P(0,22)*PS11 + P(1,22) - P(10,22)*PS34 + P(11,22)*PS9 - P(12,22)*PS7 + P(2,22)*PS13 - P(3,22)*PS12;
|
||||
nextP(2,22) = P(0,22)*PS12 - P(1,22)*PS13 - P(10,22)*PS9 - P(11,22)*PS34 + P(12,22)*PS6 + P(2,22) + P(3,22)*PS11;
|
||||
nextP(3,22) = P(0,22)*PS13 + P(1,22)*PS12 + P(10,22)*PS7 - P(11,22)*PS6 - P(12,22)*PS34 - P(2,22)*PS11 + P(3,22);
|
||||
nextP(4,22) = P(0,22)*PS72 + P(1,22)*PS62 - P(13,22)*PS44 + P(14,22)*PS140 - P(15,22)*PS139 + P(2,22)*PS60 - P(3,22)*PS74 + P(4,22);
|
||||
nextP(5,22) = P(0,22)*PS74 - P(1,22)*PS60 - P(13,22)*PS162 - P(14,22)*PS65 + P(15,22)*PS160 + P(2,22)*PS62 + P(3,22)*PS72 + P(5,22);
|
||||
nextP(6,22) = P(0,22)*PS60 + P(1,22)*PS74 + P(13,22)*PS166 - P(14,22)*PS165 - P(15,22)*PS70 - P(2,22)*PS72 + P(3,22)*PS62 + P(6,22);
|
||||
nextP(7,22) = P(4,22)*dt + P(7,22);
|
||||
nextP(8,22) = P(5,22)*dt + P(8,22);
|
||||
nextP(9,22) = P(6,22)*dt + P(9,22);
|
||||
nextP(10,22) = P(10,22);
|
||||
nextP(11,22) = P(11,22);
|
||||
nextP(12,22) = P(12,22);
|
||||
@@ -623,16 +805,16 @@ void Ekf::predictCovariance()
|
||||
nextP(20,22) = P(20,22);
|
||||
nextP(21,22) = P(21,22);
|
||||
nextP(22,22) = P(22,22);
|
||||
nextP(0,23) = P(0,23) + P(1,23)*SF[9] + P(2,23)*SF[11] + P(3,23)*SF[10] + P(10,23)*SF[14] + P(11,23)*SF[15] + P(12,23)*SPP[10];
|
||||
nextP(1,23) = P(1,23) + P(0,23)*SF[8] + P(2,23)*SF[7] + P(3,23)*SF[11] - P(12,23)*SF[15] + P(11,23)*SPP[10] - (P(10,23)*q0)*0.5f;
|
||||
nextP(2,23) = P(2,23) + P(0,23)*SF[6] + P(1,23)*SF[10] + P(3,23)*SF[8] + P(12,23)*SF[14] - P(10,23)*SPP[10] - (P(11,23)*q0)*0.5f;
|
||||
nextP(3,23) = P(3,23) + P(0,23)*SF[7] + P(1,23)*SF[6] + P(2,23)*SF[9] + P(10,23)*SF[15] - P(11,23)*SF[14] - (P(12,23)*q0)*0.5f;
|
||||
nextP(4,23) = P(4,23) + P(0,23)*SF[5] + P(1,23)*SF[3] - P(3,23)*SF[4] + P(2,23)*SPP[0] + P(13,23)*SPP[3] + P(14,23)*SPP[6] - P(15,23)*SPP[9];
|
||||
nextP(5,23) = P(5,23) + P(0,23)*SF[4] + P(2,23)*SF[3] + P(3,23)*SF[5] - P(1,23)*SPP[0] - P(13,23)*SPP[8] + P(14,23)*SPP[2] + P(15,23)*SPP[5];
|
||||
nextP(6,23) = P(6,23) + P(1,23)*SF[4] - P(2,23)*SF[5] + P(3,23)*SF[3] + P(0,23)*SPP[0] + P(13,23)*SPP[4] - P(14,23)*SPP[7] - P(15,23)*SPP[1];
|
||||
nextP(7,23) = P(7,23) + P(4,23)*dt;
|
||||
nextP(8,23) = P(8,23) + P(5,23)*dt;
|
||||
nextP(9,23) = P(9,23) + P(6,23)*dt;
|
||||
nextP(0,23) = P(0,23) - P(1,23)*PS11 + P(10,23)*PS6 + P(11,23)*PS7 + P(12,23)*PS9 - P(2,23)*PS12 - P(3,23)*PS13;
|
||||
nextP(1,23) = P(0,23)*PS11 + P(1,23) - P(10,23)*PS34 + P(11,23)*PS9 - P(12,23)*PS7 + P(2,23)*PS13 - P(3,23)*PS12;
|
||||
nextP(2,23) = P(0,23)*PS12 - P(1,23)*PS13 - P(10,23)*PS9 - P(11,23)*PS34 + P(12,23)*PS6 + P(2,23) + P(3,23)*PS11;
|
||||
nextP(3,23) = P(0,23)*PS13 + P(1,23)*PS12 + P(10,23)*PS7 - P(11,23)*PS6 - P(12,23)*PS34 - P(2,23)*PS11 + P(3,23);
|
||||
nextP(4,23) = P(0,23)*PS72 + P(1,23)*PS62 - P(13,23)*PS44 + P(14,23)*PS140 - P(15,23)*PS139 + P(2,23)*PS60 - P(3,23)*PS74 + P(4,23);
|
||||
nextP(5,23) = P(0,23)*PS74 - P(1,23)*PS60 - P(13,23)*PS162 - P(14,23)*PS65 + P(15,23)*PS160 + P(2,23)*PS62 + P(3,23)*PS72 + P(5,23);
|
||||
nextP(6,23) = P(0,23)*PS60 + P(1,23)*PS74 + P(13,23)*PS166 - P(14,23)*PS165 - P(15,23)*PS70 - P(2,23)*PS72 + P(3,23)*PS62 + P(6,23);
|
||||
nextP(7,23) = P(4,23)*dt + P(7,23);
|
||||
nextP(8,23) = P(5,23)*dt + P(8,23);
|
||||
nextP(9,23) = P(6,23)*dt + P(9,23);
|
||||
nextP(10,23) = P(10,23);
|
||||
nextP(11,23) = P(11,23);
|
||||
nextP(12,23) = P(12,23);
|
||||
|
||||
@@ -0,0 +1,8 @@
|
||||
#!/usr/bin/env python3
|
||||
# -*- coding: utf-8 -*-
|
||||
"""
|
||||
Created on Sat Mar 14 13:02:26 2020
|
||||
|
||||
@author: roman
|
||||
"""
|
||||
|
||||
@@ -0,0 +1,55 @@
|
||||
#!/usr/bin/env python3
|
||||
# -*- coding: utf-8 -*-
|
||||
"""
|
||||
Created on Sat Mar 14 12:47:24 2020
|
||||
|
||||
@author: roman
|
||||
"""
|
||||
from sympy import ccode
|
||||
from sympy.codegen.ast import float32, real
|
||||
|
||||
class CodeGenerator:
|
||||
def __init__(self, file_name):
|
||||
self.file_name = file_name
|
||||
self.file = open(self.file_name, 'w')
|
||||
|
||||
def print_string(self, string):
|
||||
self.file.write("// " + string + "\n")
|
||||
|
||||
def get_ccode(self, expression):
|
||||
return ccode(expression, type_aliases={real:float32})
|
||||
|
||||
def write_subexpressions(self,subexpressions):
|
||||
write_string = ""
|
||||
for item in subexpressions:
|
||||
write_string = write_string + "const float " + str(item[0]) + " = " + self.get_ccode(item[1]) + ";\n"
|
||||
|
||||
write_string = write_string + "\n\n"
|
||||
self.file.write(write_string)
|
||||
|
||||
def write_matrix(self, matrix, identifier, is_symmetric=False):
|
||||
write_string = ""
|
||||
|
||||
if matrix.shape[0] * matrix.shape[1] == 1:
|
||||
write_string = write_string + identifier + " = " + self.get_ccode(matrix[0]) + ";\n"
|
||||
elif matrix.shape[0] == 1 or matrix.shape[1] == 1:
|
||||
for i in range(0,len(matrix)):
|
||||
if (identifier == "Kfusion"):
|
||||
# Vector f format used by Kfusion
|
||||
write_string = write_string + identifier + "(" + str(i) + ") = " + self.get_ccode(matrix[i]) + ";\n"
|
||||
else:
|
||||
# legacy array format used by Hfusion
|
||||
write_string = write_string + identifier + "[" + str(i) + "] = " + self.get_ccode(matrix[i]) + ";\n"
|
||||
else:
|
||||
for j in range(0, matrix.shape[1]):
|
||||
for i in range(0, matrix.shape[0]):
|
||||
if j >= i or not is_symmetric:
|
||||
write_string = write_string + identifier + "(" + str(i) + "," + str(j) + ") = " + self.get_ccode(matrix[i,j]) + ";\n"
|
||||
# legacy array format
|
||||
# write_string = write_string + identifier + "[" + str(i) + "][" + str(j) + "] = " + self.get_ccode(matrix[i,j]) + ";\n"
|
||||
|
||||
write_string = write_string + "\n\n"
|
||||
self.file.write(write_string)
|
||||
|
||||
def close(self):
|
||||
self.file.close()
|
||||
@@ -0,0 +1,492 @@
|
||||
// Equations for covariance matrix prediction, without process noise!
|
||||
const float PS0 = powf(q1, 2);
|
||||
const float PS1 = 0.25F*daxVar;
|
||||
const float PS2 = powf(q2, 2);
|
||||
const float PS3 = 0.25F*dayVar;
|
||||
const float PS4 = powf(q3, 2);
|
||||
const float PS5 = 0.25F*dazVar;
|
||||
const float PS6 = 0.5F*q1;
|
||||
const float PS7 = 0.5F*q2;
|
||||
const float PS8 = P(10,11)*PS7;
|
||||
const float PS9 = 0.5F*q3;
|
||||
const float PS10 = P(10,12)*PS9;
|
||||
const float PS11 = 0.5F*dax - 0.5F*dax_b;
|
||||
const float PS12 = 0.5F*day - 0.5F*day_b;
|
||||
const float PS13 = 0.5F*daz - 0.5F*daz_b;
|
||||
const float PS14 = P(0,10) - P(1,10)*PS11 + P(10,10)*PS6 - P(2,10)*PS12 - P(3,10)*PS13 + PS10 + PS8;
|
||||
const float PS15 = P(10,11)*PS6;
|
||||
const float PS16 = P(11,12)*PS9;
|
||||
const float PS17 = P(0,11) - P(1,11)*PS11 + P(11,11)*PS7 - P(2,11)*PS12 - P(3,11)*PS13 + PS15 + PS16;
|
||||
const float PS18 = P(10,12)*PS6;
|
||||
const float PS19 = P(11,12)*PS7;
|
||||
const float PS20 = P(0,12) - P(1,12)*PS11 + P(12,12)*PS9 - P(2,12)*PS12 - P(3,12)*PS13 + PS18 + PS19;
|
||||
const float PS21 = P(1,2)*PS12;
|
||||
const float PS22 = -P(1,3)*PS13;
|
||||
const float PS23 = P(0,1) - P(1,1)*PS11 + P(1,10)*PS6 + P(1,11)*PS7 + P(1,12)*PS9 - PS21 + PS22;
|
||||
const float PS24 = -P(1,2)*PS11;
|
||||
const float PS25 = P(2,3)*PS13;
|
||||
const float PS26 = P(0,2) + P(2,10)*PS6 + P(2,11)*PS7 + P(2,12)*PS9 - P(2,2)*PS12 + PS24 - PS25;
|
||||
const float PS27 = P(1,3)*PS11;
|
||||
const float PS28 = -P(2,3)*PS12;
|
||||
const float PS29 = P(0,3) + P(3,10)*PS6 + P(3,11)*PS7 + P(3,12)*PS9 - P(3,3)*PS13 - PS27 + PS28;
|
||||
const float PS30 = P(0,1)*PS11;
|
||||
const float PS31 = P(0,2)*PS12;
|
||||
const float PS32 = P(0,3)*PS13;
|
||||
const float PS33 = P(0,0) + P(0,10)*PS6 + P(0,11)*PS7 + P(0,12)*PS9 - PS30 - PS31 - PS32;
|
||||
const float PS34 = 0.5F*q0;
|
||||
const float PS35 = q2*q3;
|
||||
const float PS36 = q0*q1;
|
||||
const float PS37 = q1*q3;
|
||||
const float PS38 = q0*q2;
|
||||
const float PS39 = q1*q2;
|
||||
const float PS40 = q0*q3;
|
||||
const float PS41 = -PS2;
|
||||
const float PS42 = powf(q0, 2);
|
||||
const float PS43 = -PS4 + PS42;
|
||||
const float PS44 = PS0 + PS41 + PS43;
|
||||
const float PS45 = P(0,13) - P(1,13)*PS11 + P(10,13)*PS6 + P(11,13)*PS7 + P(12,13)*PS9 - P(2,13)*PS12 - P(3,13)*PS13;
|
||||
const float PS46 = PS37 + PS38;
|
||||
const float PS47 = P(0,15) - P(1,15)*PS11 + P(10,15)*PS6 + P(11,15)*PS7 + P(12,15)*PS9 - P(2,15)*PS12 - P(3,15)*PS13;
|
||||
const float PS48 = 2*PS47;
|
||||
const float PS49 = dvy - dvy_b;
|
||||
const float PS50 = dvx - dvx_b;
|
||||
const float PS51 = dvz - dvz_b;
|
||||
const float PS52 = PS49*q0 + PS50*q3 - PS51*q1;
|
||||
const float PS53 = 2*PS29;
|
||||
const float PS54 = -PS39 + PS40;
|
||||
const float PS55 = P(0,14) - P(1,14)*PS11 + P(10,14)*PS6 + P(11,14)*PS7 + P(12,14)*PS9 - P(2,14)*PS12 - P(3,14)*PS13;
|
||||
const float PS56 = 2*PS55;
|
||||
const float PS57 = -PS49*q3 + PS50*q0 + PS51*q2;
|
||||
const float PS58 = 2*PS33;
|
||||
const float PS59 = PS49*q1 - PS50*q2 + PS51*q0;
|
||||
const float PS60 = 2*PS59;
|
||||
const float PS61 = PS49*q2 + PS50*q1 + PS51*q3;
|
||||
const float PS62 = 2*PS61;
|
||||
const float PS63 = P(0,4) - P(1,4)*PS11 - P(2,4)*PS12 - P(3,4)*PS13 + P(4,10)*PS6 + P(4,11)*PS7 + P(4,12)*PS9;
|
||||
const float PS64 = -PS0;
|
||||
const float PS65 = PS2 + PS43 + PS64;
|
||||
const float PS66 = PS39 + PS40;
|
||||
const float PS67 = 2*PS45;
|
||||
const float PS68 = -PS35 + PS36;
|
||||
const float PS69 = P(0,5) - P(1,5)*PS11 - P(2,5)*PS12 - P(3,5)*PS13 + P(5,10)*PS6 + P(5,11)*PS7 + P(5,12)*PS9;
|
||||
const float PS70 = PS4 + PS41 + PS42 + PS64;
|
||||
const float PS71 = PS35 + PS36;
|
||||
const float PS72 = 2*PS57;
|
||||
const float PS73 = -PS37 + PS38;
|
||||
const float PS74 = 2*PS52;
|
||||
const float PS75 = P(0,6) - P(1,6)*PS11 - P(2,6)*PS12 - P(3,6)*PS13 + P(6,10)*PS6 + P(6,11)*PS7 + P(6,12)*PS9;
|
||||
const float PS76 = -P(10,11)*PS34;
|
||||
const float PS77 = P(0,11)*PS11 + P(1,11) + P(11,11)*PS9 + P(2,11)*PS13 - P(3,11)*PS12 - PS19 + PS76;
|
||||
const float PS78 = P(0,2)*PS13;
|
||||
const float PS79 = P(0,3)*PS12;
|
||||
const float PS80 = P(0,0)*PS11 + P(0,1) - P(0,10)*PS34 + P(0,11)*PS9 - P(0,12)*PS7 + PS78 - PS79;
|
||||
const float PS81 = P(0,2)*PS11;
|
||||
const float PS82 = P(1,2) - P(2,10)*PS34 + P(2,11)*PS9 - P(2,12)*PS7 + P(2,2)*PS13 + PS28 + PS81;
|
||||
const float PS83 = P(10,11)*PS9;
|
||||
const float PS84 = P(10,12)*PS7;
|
||||
const float PS85 = P(0,10)*PS11 + P(1,10) - P(10,10)*PS34 + P(2,10)*PS13 - P(3,10)*PS12 + PS83 - PS84;
|
||||
const float PS86 = -P(10,12)*PS34;
|
||||
const float PS87 = P(0,12)*PS11 + P(1,12) - P(12,12)*PS7 + P(2,12)*PS13 - P(3,12)*PS12 + PS16 + PS86;
|
||||
const float PS88 = P(0,3)*PS11;
|
||||
const float PS89 = P(1,3) - P(3,10)*PS34 + P(3,11)*PS9 - P(3,12)*PS7 - P(3,3)*PS12 + PS25 + PS88;
|
||||
const float PS90 = P(1,2)*PS13;
|
||||
const float PS91 = P(1,3)*PS12;
|
||||
const float PS92 = P(1,1) - P(1,10)*PS34 + P(1,11)*PS9 - P(1,12)*PS7 + PS30 + PS90 - PS91;
|
||||
const float PS93 = P(0,13)*PS11 + P(1,13) - P(10,13)*PS34 + P(11,13)*PS9 - P(12,13)*PS7 + P(2,13)*PS13 - P(3,13)*PS12;
|
||||
const float PS94 = P(0,15)*PS11 + P(1,15) - P(10,15)*PS34 + P(11,15)*PS9 - P(12,15)*PS7 + P(2,15)*PS13 - P(3,15)*PS12;
|
||||
const float PS95 = 2*PS94;
|
||||
const float PS96 = P(0,14)*PS11 + P(1,14) - P(10,14)*PS34 + P(11,14)*PS9 - P(12,14)*PS7 + P(2,14)*PS13 - P(3,14)*PS12;
|
||||
const float PS97 = 2*PS96;
|
||||
const float PS98 = P(0,4)*PS11 + P(1,4) + P(2,4)*PS13 - P(3,4)*PS12 - P(4,10)*PS34 + P(4,11)*PS9 - P(4,12)*PS7;
|
||||
const float PS99 = 2*PS93;
|
||||
const float PS100 = P(0,5)*PS11 + P(1,5) + P(2,5)*PS13 - P(3,5)*PS12 - P(5,10)*PS34 + P(5,11)*PS9 - P(5,12)*PS7;
|
||||
const float PS101 = P(0,6)*PS11 + P(1,6) + P(2,6)*PS13 - P(3,6)*PS12 - P(6,10)*PS34 + P(6,11)*PS9 - P(6,12)*PS7;
|
||||
const float PS102 = -P(11,12)*PS34;
|
||||
const float PS103 = P(0,12)*PS12 - P(1,12)*PS13 + P(12,12)*PS6 + P(2,12) + P(3,12)*PS11 - PS10 + PS102;
|
||||
const float PS104 = P(2,3) - P(3,10)*PS9 - P(3,11)*PS34 + P(3,12)*PS6 + P(3,3)*PS11 + PS22 + PS79;
|
||||
const float PS105 = P(0,1)*PS13;
|
||||
const float PS106 = P(0,0)*PS12 - P(0,10)*PS9 - P(0,11)*PS34 + P(0,12)*PS6 + P(0,2) - PS105 + PS88;
|
||||
const float PS107 = P(11,12)*PS6;
|
||||
const float PS108 = P(0,11)*PS12 - P(1,11)*PS13 - P(11,11)*PS34 + P(2,11) + P(3,11)*PS11 + PS107 - PS83;
|
||||
const float PS109 = P(0,10)*PS12 - P(1,10)*PS13 - P(10,10)*PS9 + P(2,10) + P(3,10)*PS11 + PS18 + PS76;
|
||||
const float PS110 = P(0,1)*PS12;
|
||||
const float PS111 = -P(1,1)*PS13 - P(1,10)*PS9 - P(1,11)*PS34 + P(1,12)*PS6 + P(1,2) + PS110 + PS27;
|
||||
const float PS112 = P(2,3)*PS11;
|
||||
const float PS113 = -P(2,10)*PS9 - P(2,11)*PS34 + P(2,12)*PS6 + P(2,2) + PS112 + PS31 - PS90;
|
||||
const float PS114 = P(0,13)*PS12 - P(1,13)*PS13 - P(10,13)*PS9 - P(11,13)*PS34 + P(12,13)*PS6 + P(2,13) + P(3,13)*PS11;
|
||||
const float PS115 = P(0,15)*PS12 - P(1,15)*PS13 - P(10,15)*PS9 - P(11,15)*PS34 + P(12,15)*PS6 + P(2,15) + P(3,15)*PS11;
|
||||
const float PS116 = 2*PS115;
|
||||
const float PS117 = P(0,14)*PS12 - P(1,14)*PS13 - P(10,14)*PS9 - P(11,14)*PS34 + P(12,14)*PS6 + P(2,14) + P(3,14)*PS11;
|
||||
const float PS118 = 2*PS117;
|
||||
const float PS119 = P(0,4)*PS12 - P(1,4)*PS13 + P(2,4) + P(3,4)*PS11 - P(4,10)*PS9 - P(4,11)*PS34 + P(4,12)*PS6;
|
||||
const float PS120 = 2*PS114;
|
||||
const float PS121 = P(0,5)*PS12 - P(1,5)*PS13 + P(2,5) + P(3,5)*PS11 - P(5,10)*PS9 - P(5,11)*PS34 + P(5,12)*PS6;
|
||||
const float PS122 = P(0,6)*PS12 - P(1,6)*PS13 + P(2,6) + P(3,6)*PS11 - P(6,10)*PS9 - P(6,11)*PS34 + P(6,12)*PS6;
|
||||
const float PS123 = P(0,10)*PS13 + P(1,10)*PS12 + P(10,10)*PS7 - P(2,10)*PS11 + P(3,10) - PS15 + PS86;
|
||||
const float PS124 = P(1,1)*PS12 + P(1,10)*PS7 - P(1,11)*PS6 - P(1,12)*PS34 + P(1,3) + PS105 + PS24;
|
||||
const float PS125 = P(0,0)*PS13 + P(0,10)*PS7 - P(0,11)*PS6 - P(0,12)*PS34 + P(0,3) + PS110 - PS81;
|
||||
const float PS126 = P(0,12)*PS13 + P(1,12)*PS12 - P(12,12)*PS34 - P(2,12)*PS11 + P(3,12) - PS107 + PS84;
|
||||
const float PS127 = P(0,11)*PS13 + P(1,11)*PS12 - P(11,11)*PS6 - P(2,11)*PS11 + P(3,11) + PS102 + PS8;
|
||||
const float PS128 = P(2,10)*PS7 - P(2,11)*PS6 - P(2,12)*PS34 - P(2,2)*PS11 + P(2,3) + PS21 + PS78;
|
||||
const float PS129 = P(3,10)*PS7 - P(3,11)*PS6 - P(3,12)*PS34 + P(3,3) - PS112 + PS32 + PS91;
|
||||
const float PS130 = P(0,13)*PS13 + P(1,13)*PS12 + P(10,13)*PS7 - P(11,13)*PS6 - P(12,13)*PS34 - P(2,13)*PS11 + P(3,13);
|
||||
const float PS131 = P(0,15)*PS13 + P(1,15)*PS12 + P(10,15)*PS7 - P(11,15)*PS6 - P(12,15)*PS34 - P(2,15)*PS11 + P(3,15);
|
||||
const float PS132 = 2*PS131;
|
||||
const float PS133 = P(0,14)*PS13 + P(1,14)*PS12 + P(10,14)*PS7 - P(11,14)*PS6 - P(12,14)*PS34 - P(2,14)*PS11 + P(3,14);
|
||||
const float PS134 = 2*PS133;
|
||||
const float PS135 = P(0,4)*PS13 + P(1,4)*PS12 - P(2,4)*PS11 + P(3,4) + P(4,10)*PS7 - P(4,11)*PS6 - P(4,12)*PS34;
|
||||
const float PS136 = 2*PS130;
|
||||
const float PS137 = P(0,5)*PS13 + P(1,5)*PS12 - P(2,5)*PS11 + P(3,5) + P(5,10)*PS7 - P(5,11)*PS6 - P(5,12)*PS34;
|
||||
const float PS138 = P(0,6)*PS13 + P(1,6)*PS12 - P(2,6)*PS11 + P(3,6) + P(6,10)*PS7 - P(6,11)*PS6 - P(6,12)*PS34;
|
||||
const float PS139 = 2*PS46;
|
||||
const float PS140 = 2*PS54;
|
||||
const float PS141 = P(0,13)*PS72 + P(1,13)*PS62 - P(13,13)*PS44 + P(13,14)*PS140 - P(13,15)*PS139 + P(2,13)*PS60 - P(3,13)*PS74 + P(4,13);
|
||||
const float PS142 = P(0,15)*PS72 + P(1,15)*PS62 - P(13,15)*PS44 + P(14,15)*PS140 - P(15,15)*PS139 + P(2,15)*PS60 - P(3,15)*PS74 + P(4,15);
|
||||
const float PS143 = P(1,3)*PS62;
|
||||
const float PS144 = P(0,3)*PS72;
|
||||
const float PS145 = P(2,3)*PS60 - P(3,13)*PS44 + P(3,14)*PS140 - P(3,15)*PS139 - P(3,3)*PS74 + P(3,4) + PS143 + PS144;
|
||||
const float PS146 = P(0,14)*PS72 + P(1,14)*PS62 - P(13,14)*PS44 + P(14,14)*PS140 - P(14,15)*PS139 + P(2,14)*PS60 - P(3,14)*PS74 + P(4,14);
|
||||
const float PS147 = P(0,2)*PS60;
|
||||
const float PS148 = P(0,3)*PS74;
|
||||
const float PS149 = P(0,0)*PS72 + P(0,1)*PS62 - P(0,13)*PS44 + P(0,14)*PS140 - P(0,15)*PS139 + P(0,4) + PS147 - PS148;
|
||||
const float PS150 = P(1,2)*PS62;
|
||||
const float PS151 = P(0,2)*PS72;
|
||||
const float PS152 = -P(2,13)*PS44 + P(2,14)*PS140 - P(2,15)*PS139 + P(2,2)*PS60 - P(2,3)*PS74 + P(2,4) + PS150 + PS151;
|
||||
const float PS153 = P(1,2)*PS60;
|
||||
const float PS154 = P(1,3)*PS74;
|
||||
const float PS155 = P(0,1)*PS72 + P(1,1)*PS62 - P(1,13)*PS44 + P(1,14)*PS140 - P(1,15)*PS139 + P(1,4) + PS153 - PS154;
|
||||
const float PS156 = 4*dvyVar;
|
||||
const float PS157 = 4*dvzVar;
|
||||
const float PS158 = P(0,4)*PS72 + P(1,4)*PS62 + P(2,4)*PS60 - P(3,4)*PS74 - P(4,13)*PS44 + P(4,14)*PS140 - P(4,15)*PS139 + P(4,4);
|
||||
const float PS159 = 2*PS141;
|
||||
const float PS160 = 2*PS68;
|
||||
const float PS161 = PS65*dvyVar;
|
||||
const float PS162 = 2*PS66;
|
||||
const float PS163 = PS44*dvxVar;
|
||||
const float PS164 = P(0,5)*PS72 + P(1,5)*PS62 + P(2,5)*PS60 - P(3,5)*PS74 + P(4,5) - P(5,13)*PS44 + P(5,14)*PS140 - P(5,15)*PS139;
|
||||
const float PS165 = 2*PS71;
|
||||
const float PS166 = 2*PS73;
|
||||
const float PS167 = PS70*dvzVar;
|
||||
const float PS168 = P(0,6)*PS72 + P(1,6)*PS62 + P(2,6)*PS60 - P(3,6)*PS74 + P(4,6) - P(6,13)*PS44 + P(6,14)*PS140 - P(6,15)*PS139;
|
||||
const float PS169 = P(0,14)*PS74 - P(1,14)*PS60 - P(13,14)*PS162 - P(14,14)*PS65 + P(14,15)*PS160 + P(2,14)*PS62 + P(3,14)*PS72 + P(5,14);
|
||||
const float PS170 = P(0,13)*PS74 - P(1,13)*PS60 - P(13,13)*PS162 - P(13,14)*PS65 + P(13,15)*PS160 + P(2,13)*PS62 + P(3,13)*PS72 + P(5,13);
|
||||
const float PS171 = P(0,1)*PS74;
|
||||
const float PS172 = -P(1,1)*PS60 - P(1,13)*PS162 - P(1,14)*PS65 + P(1,15)*PS160 + P(1,3)*PS72 + P(1,5) + PS150 + PS171;
|
||||
const float PS173 = P(0,15)*PS74 - P(1,15)*PS60 - P(13,15)*PS162 - P(14,15)*PS65 + P(15,15)*PS160 + P(2,15)*PS62 + P(3,15)*PS72 + P(5,15);
|
||||
const float PS174 = P(2,3)*PS62;
|
||||
const float PS175 = -P(1,3)*PS60 - P(3,13)*PS162 - P(3,14)*PS65 + P(3,15)*PS160 + P(3,3)*PS72 + P(3,5) + PS148 + PS174;
|
||||
const float PS176 = P(0,1)*PS60;
|
||||
const float PS177 = P(0,0)*PS74 - P(0,13)*PS162 - P(0,14)*PS65 + P(0,15)*PS160 + P(0,2)*PS62 + P(0,5) + PS144 - PS176;
|
||||
const float PS178 = P(2,3)*PS72;
|
||||
const float PS179 = P(0,2)*PS74 - P(2,13)*PS162 - P(2,14)*PS65 + P(2,15)*PS160 + P(2,2)*PS62 + P(2,5) - PS153 + PS178;
|
||||
const float PS180 = 4*dvxVar;
|
||||
const float PS181 = P(0,5)*PS74 - P(1,5)*PS60 + P(2,5)*PS62 + P(3,5)*PS72 - P(5,13)*PS162 - P(5,14)*PS65 + P(5,15)*PS160 + P(5,5);
|
||||
const float PS182 = P(0,6)*PS74 - P(1,6)*PS60 + P(2,6)*PS62 + P(3,6)*PS72 + P(5,6) - P(6,13)*PS162 - P(6,14)*PS65 + P(6,15)*PS160;
|
||||
const float PS183 = P(0,15)*PS60 + P(1,15)*PS74 + P(13,15)*PS166 - P(14,15)*PS165 - P(15,15)*PS70 - P(2,15)*PS72 + P(3,15)*PS62 + P(6,15);
|
||||
const float PS184 = P(0,14)*PS60 + P(1,14)*PS74 + P(13,14)*PS166 - P(14,14)*PS165 - P(14,15)*PS70 - P(2,14)*PS72 + P(3,14)*PS62 + P(6,14);
|
||||
const float PS185 = P(0,13)*PS60 + P(1,13)*PS74 + P(13,13)*PS166 - P(13,14)*PS165 - P(13,15)*PS70 - P(2,13)*PS72 + P(3,13)*PS62 + P(6,13);
|
||||
const float PS186 = P(0,6)*PS60 + P(1,6)*PS74 - P(2,6)*PS72 + P(3,6)*PS62 + P(6,13)*PS166 - P(6,14)*PS165 - P(6,15)*PS70 + P(6,6);
|
||||
|
||||
|
||||
nextP(0,0) = PS0*PS1 - PS11*PS23 - PS12*PS26 - PS13*PS29 + PS14*PS6 + PS17*PS7 + PS2*PS3 + PS20*PS9 + PS33 + PS4*PS5;
|
||||
nextP(0,1) = -PS1*PS36 + PS11*PS33 - PS12*PS29 + PS13*PS26 - PS14*PS34 + PS17*PS9 - PS20*PS7 + PS23 + PS3*PS35 - PS35*PS5;
|
||||
nextP(1,1) = PS1*PS42 + PS11*PS80 - PS12*PS89 + PS13*PS82 + PS2*PS5 + PS3*PS4 - PS34*PS85 - PS7*PS87 + PS77*PS9 + PS92;
|
||||
nextP(0,2) = -PS1*PS37 + PS11*PS29 + PS12*PS33 - PS13*PS23 - PS14*PS9 - PS17*PS34 + PS20*PS6 + PS26 - PS3*PS38 + PS37*PS5;
|
||||
nextP(1,2) = PS1*PS40 + PS11*PS89 + PS12*PS80 - PS13*PS92 - PS3*PS40 - PS34*PS77 - PS39*PS5 + PS6*PS87 + PS82 - PS85*PS9;
|
||||
nextP(2,2) = PS0*PS5 + PS1*PS4 + PS103*PS6 + PS104*PS11 + PS106*PS12 - PS108*PS34 - PS109*PS9 - PS111*PS13 + PS113 + PS3*PS42;
|
||||
nextP(0,3) = PS1*PS39 - PS11*PS26 + PS12*PS23 + PS13*PS33 + PS14*PS7 - PS17*PS6 - PS20*PS34 + PS29 - PS3*PS39 - PS40*PS5;
|
||||
nextP(1,3) = -PS1*PS38 - PS11*PS82 + PS12*PS92 + PS13*PS80 - PS3*PS37 - PS34*PS87 + PS38*PS5 - PS6*PS77 + PS7*PS85 + PS89;
|
||||
nextP(2,3) = -PS1*PS35 - PS103*PS34 + PS104 + PS106*PS13 - PS108*PS6 + PS109*PS7 - PS11*PS113 + PS111*PS12 + PS3*PS36 - PS36*PS5;
|
||||
nextP(3,3) = PS0*PS3 + PS1*PS2 - PS11*PS128 + PS12*PS124 + PS123*PS7 + PS125*PS13 - PS126*PS34 - PS127*PS6 + PS129 + PS42*PS5;
|
||||
nextP(0,4) = PS23*PS62 + PS26*PS60 - PS44*PS45 - PS46*PS48 - PS52*PS53 + PS54*PS56 + PS57*PS58 + PS63;
|
||||
nextP(1,4) = -PS44*PS93 - PS46*PS95 + PS54*PS97 + PS60*PS82 + PS62*PS92 + PS72*PS80 - PS74*PS89 + PS98;
|
||||
nextP(2,4) = -PS104*PS74 + PS106*PS72 + PS111*PS62 + PS113*PS60 - PS114*PS44 - PS116*PS46 + PS118*PS54 + PS119;
|
||||
nextP(3,4) = PS124*PS62 + PS125*PS72 + PS128*PS60 - PS129*PS74 - PS130*PS44 - PS132*PS46 + PS134*PS54 + PS135;
|
||||
nextP(4,4) = -PS139*PS142 + PS140*PS146 - PS141*PS44 - PS145*PS74 + PS149*PS72 + PS152*PS60 + PS155*PS62 + PS156*powf(PS54, 2) + PS157*powf(PS46, 2) + PS158 + powf(PS44, 2)*dvxVar;
|
||||
nextP(0,5) = -PS23*PS60 + PS26*PS62 + PS48*PS68 + PS52*PS58 + PS53*PS57 - PS55*PS65 - PS66*PS67 + PS69;
|
||||
nextP(1,5) = PS100 - PS60*PS92 + PS62*PS82 - PS65*PS96 - PS66*PS99 + PS68*PS95 + PS72*PS89 + PS74*PS80;
|
||||
nextP(2,5) = PS104*PS72 + PS106*PS74 - PS111*PS60 + PS113*PS62 + PS116*PS68 - PS117*PS65 - PS120*PS66 + PS121;
|
||||
nextP(3,5) = -PS124*PS60 + PS125*PS74 + PS128*PS62 + PS129*PS72 + PS132*PS68 - PS133*PS65 - PS136*PS66 + PS137;
|
||||
nextP(4,5) = -PS140*PS161 + PS142*PS160 + PS145*PS72 - PS146*PS65 + PS149*PS74 + PS152*PS62 - PS155*PS60 - PS157*PS46*PS68 - PS159*PS66 + PS162*PS163 + PS164;
|
||||
nextP(5,5) = PS157*powf(PS68, 2) + PS160*PS173 - PS162*PS170 - PS169*PS65 - PS172*PS60 + PS175*PS72 + PS177*PS74 + PS179*PS62 + PS180*powf(PS66, 2) + PS181 + powf(PS65, 2)*dvyVar;
|
||||
nextP(0,6) = PS23*PS74 - PS26*PS72 - PS47*PS70 + PS53*PS61 - PS56*PS71 + PS58*PS59 + PS67*PS73 + PS75;
|
||||
nextP(1,6) = PS101 + PS60*PS80 + PS62*PS89 - PS70*PS94 - PS71*PS97 - PS72*PS82 + PS73*PS99 + PS74*PS92;
|
||||
nextP(2,6) = PS104*PS62 + PS106*PS60 + PS111*PS74 - PS113*PS72 - PS115*PS70 - PS118*PS71 + PS120*PS73 + PS122;
|
||||
nextP(3,6) = PS124*PS74 + PS125*PS60 - PS128*PS72 + PS129*PS62 - PS131*PS70 - PS134*PS71 + PS136*PS73 + PS138;
|
||||
nextP(4,6) = PS139*PS167 - PS142*PS70 + PS145*PS62 - PS146*PS165 + PS149*PS60 - PS152*PS72 + PS155*PS74 - PS156*PS54*PS71 + PS159*PS73 - PS163*PS166 + PS168;
|
||||
nextP(5,6) = -PS160*PS167 + PS161*PS165 - PS165*PS169 + PS166*PS170 + PS172*PS74 - PS173*PS70 + PS175*PS62 + PS177*PS60 - PS179*PS72 - PS180*PS66*PS73 + PS182;
|
||||
nextP(6,6) = PS156*powf(PS71, 2) - PS165*PS184 + PS166*PS185 + PS180*powf(PS73, 2) - PS183*PS70 + PS186 + PS60*(P(0,0)*PS60 + P(0,13)*PS166 - P(0,14)*PS165 - P(0,15)*PS70 + P(0,3)*PS62 + P(0,6) - PS151 + PS171) + PS62*(P(0,3)*PS60 + P(3,13)*PS166 - P(3,14)*PS165 - P(3,15)*PS70 + P(3,3)*PS62 + P(3,6) + PS154 - PS178) + powf(PS70, 2)*dvzVar - PS72*(P(1,2)*PS74 + P(2,13)*PS166 - P(2,14)*PS165 - P(2,15)*PS70 - P(2,2)*PS72 + P(2,6) + PS147 + PS174) + PS74*(P(1,1)*PS74 + P(1,13)*PS166 - P(1,14)*PS165 - P(1,15)*PS70 - P(1,2)*PS72 + P(1,6) + PS143 + PS176);
|
||||
nextP(0,7) = P(0,7) - P(1,7)*PS11 - P(2,7)*PS12 - P(3,7)*PS13 + P(7,10)*PS6 + P(7,11)*PS7 + P(7,12)*PS9 + PS63*dt;
|
||||
nextP(1,7) = P(0,7)*PS11 + P(1,7) + P(2,7)*PS13 - P(3,7)*PS12 - P(7,10)*PS34 + P(7,11)*PS9 - P(7,12)*PS7 + PS98*dt;
|
||||
nextP(2,7) = P(0,7)*PS12 - P(1,7)*PS13 + P(2,7) + P(3,7)*PS11 - P(7,10)*PS9 - P(7,11)*PS34 + P(7,12)*PS6 + PS119*dt;
|
||||
nextP(3,7) = P(0,7)*PS13 + P(1,7)*PS12 - P(2,7)*PS11 + P(3,7) + P(7,10)*PS7 - P(7,11)*PS6 - P(7,12)*PS34 + PS135*dt;
|
||||
nextP(4,7) = P(0,7)*PS72 + P(1,7)*PS62 + P(2,7)*PS60 - P(3,7)*PS74 + P(4,7) - P(7,13)*PS44 + P(7,14)*PS140 - P(7,15)*PS139 + PS158*dt;
|
||||
nextP(5,7) = P(0,7)*PS74 - P(1,7)*PS60 + P(2,7)*PS62 + P(3,7)*PS72 + P(5,7) - P(7,13)*PS162 - P(7,14)*PS65 + P(7,15)*PS160 + dt*(P(0,4)*PS74 - P(1,4)*PS60 + P(2,4)*PS62 + P(3,4)*PS72 - P(4,13)*PS162 - P(4,14)*PS65 + P(4,15)*PS160 + P(4,5));
|
||||
nextP(6,7) = P(0,7)*PS60 + P(1,7)*PS74 - P(2,7)*PS72 + P(3,7)*PS62 + P(6,7) + P(7,13)*PS166 - P(7,14)*PS165 - P(7,15)*PS70 + dt*(P(0,4)*PS60 + P(1,4)*PS74 - P(2,4)*PS72 + P(3,4)*PS62 + P(4,13)*PS166 - P(4,14)*PS165 - P(4,15)*PS70 + P(4,6));
|
||||
nextP(7,7) = P(4,7)*dt + P(7,7) + dt*(P(4,4)*dt + P(4,7));
|
||||
nextP(0,8) = P(0,8) - P(1,8)*PS11 - P(2,8)*PS12 - P(3,8)*PS13 + P(8,10)*PS6 + P(8,11)*PS7 + P(8,12)*PS9 + PS69*dt;
|
||||
nextP(1,8) = P(0,8)*PS11 + P(1,8) + P(2,8)*PS13 - P(3,8)*PS12 - P(8,10)*PS34 + P(8,11)*PS9 - P(8,12)*PS7 + PS100*dt;
|
||||
nextP(2,8) = P(0,8)*PS12 - P(1,8)*PS13 + P(2,8) + P(3,8)*PS11 - P(8,10)*PS9 - P(8,11)*PS34 + P(8,12)*PS6 + PS121*dt;
|
||||
nextP(3,8) = P(0,8)*PS13 + P(1,8)*PS12 - P(2,8)*PS11 + P(3,8) + P(8,10)*PS7 - P(8,11)*PS6 - P(8,12)*PS34 + PS137*dt;
|
||||
nextP(4,8) = P(0,8)*PS72 + P(1,8)*PS62 + P(2,8)*PS60 - P(3,8)*PS74 + P(4,8) - P(8,13)*PS44 + P(8,14)*PS140 - P(8,15)*PS139 + PS164*dt;
|
||||
nextP(5,8) = P(0,8)*PS74 - P(1,8)*PS60 + P(2,8)*PS62 + P(3,8)*PS72 + P(5,8) - P(8,13)*PS162 - P(8,14)*PS65 + P(8,15)*PS160 + PS181*dt;
|
||||
nextP(6,8) = P(0,8)*PS60 + P(1,8)*PS74 - P(2,8)*PS72 + P(3,8)*PS62 + P(6,8) + P(8,13)*PS166 - P(8,14)*PS165 - P(8,15)*PS70 + dt*(P(0,5)*PS60 + P(1,5)*PS74 - P(2,5)*PS72 + P(3,5)*PS62 + P(5,13)*PS166 - P(5,14)*PS165 - P(5,15)*PS70 + P(5,6));
|
||||
nextP(7,8) = P(4,8)*dt + P(7,8) + dt*(P(4,5)*dt + P(5,7));
|
||||
nextP(8,8) = P(5,8)*dt + P(8,8) + dt*(P(5,5)*dt + P(5,8));
|
||||
nextP(0,9) = P(0,9) - P(1,9)*PS11 - P(2,9)*PS12 - P(3,9)*PS13 + P(9,10)*PS6 + P(9,11)*PS7 + P(9,12)*PS9 + PS75*dt;
|
||||
nextP(1,9) = P(0,9)*PS11 + P(1,9) + P(2,9)*PS13 - P(3,9)*PS12 - P(9,10)*PS34 + P(9,11)*PS9 - P(9,12)*PS7 + PS101*dt;
|
||||
nextP(2,9) = P(0,9)*PS12 - P(1,9)*PS13 + P(2,9) + P(3,9)*PS11 - P(9,10)*PS9 - P(9,11)*PS34 + P(9,12)*PS6 + PS122*dt;
|
||||
nextP(3,9) = P(0,9)*PS13 + P(1,9)*PS12 - P(2,9)*PS11 + P(3,9) + P(9,10)*PS7 - P(9,11)*PS6 - P(9,12)*PS34 + PS138*dt;
|
||||
nextP(4,9) = P(0,9)*PS72 + P(1,9)*PS62 + P(2,9)*PS60 - P(3,9)*PS74 + P(4,9) - P(9,13)*PS44 + P(9,14)*PS140 - P(9,15)*PS139 + PS168*dt;
|
||||
nextP(5,9) = P(0,9)*PS74 - P(1,9)*PS60 + P(2,9)*PS62 + P(3,9)*PS72 + P(5,9) - P(9,13)*PS162 - P(9,14)*PS65 + P(9,15)*PS160 + PS182*dt;
|
||||
nextP(6,9) = P(0,9)*PS60 + P(1,9)*PS74 - P(2,9)*PS72 + P(3,9)*PS62 + P(6,9) + P(9,13)*PS166 - P(9,14)*PS165 - P(9,15)*PS70 + PS186*dt;
|
||||
nextP(7,9) = P(4,9)*dt + P(7,9) + dt*(P(4,6)*dt + P(6,7));
|
||||
nextP(8,9) = P(5,9)*dt + P(8,9) + dt*(P(5,6)*dt + P(6,8));
|
||||
nextP(9,9) = P(6,9)*dt + P(9,9) + dt*(P(6,6)*dt + P(6,9));
|
||||
nextP(0,10) = PS14;
|
||||
nextP(1,10) = PS85;
|
||||
nextP(2,10) = PS109;
|
||||
nextP(3,10) = PS123;
|
||||
nextP(4,10) = P(0,10)*PS72 + P(1,10)*PS62 - P(10,13)*PS44 + P(10,14)*PS140 - P(10,15)*PS139 + P(2,10)*PS60 - P(3,10)*PS74 + P(4,10);
|
||||
nextP(5,10) = P(0,10)*PS74 - P(1,10)*PS60 - P(10,13)*PS162 - P(10,14)*PS65 + P(10,15)*PS160 + P(2,10)*PS62 + P(3,10)*PS72 + P(5,10);
|
||||
nextP(6,10) = P(0,10)*PS60 + P(1,10)*PS74 + P(10,13)*PS166 - P(10,14)*PS165 - P(10,15)*PS70 - P(2,10)*PS72 + P(3,10)*PS62 + P(6,10);
|
||||
nextP(7,10) = P(4,10)*dt + P(7,10);
|
||||
nextP(8,10) = P(5,10)*dt + P(8,10);
|
||||
nextP(9,10) = P(6,10)*dt + P(9,10);
|
||||
nextP(10,10) = P(10,10);
|
||||
nextP(0,11) = PS17;
|
||||
nextP(1,11) = PS77;
|
||||
nextP(2,11) = PS108;
|
||||
nextP(3,11) = PS127;
|
||||
nextP(4,11) = P(0,11)*PS72 + P(1,11)*PS62 - P(11,13)*PS44 + P(11,14)*PS140 - P(11,15)*PS139 + P(2,11)*PS60 - P(3,11)*PS74 + P(4,11);
|
||||
nextP(5,11) = P(0,11)*PS74 - P(1,11)*PS60 - P(11,13)*PS162 - P(11,14)*PS65 + P(11,15)*PS160 + P(2,11)*PS62 + P(3,11)*PS72 + P(5,11);
|
||||
nextP(6,11) = P(0,11)*PS60 + P(1,11)*PS74 + P(11,13)*PS166 - P(11,14)*PS165 - P(11,15)*PS70 - P(2,11)*PS72 + P(3,11)*PS62 + P(6,11);
|
||||
nextP(7,11) = P(4,11)*dt + P(7,11);
|
||||
nextP(8,11) = P(5,11)*dt + P(8,11);
|
||||
nextP(9,11) = P(6,11)*dt + P(9,11);
|
||||
nextP(10,11) = P(10,11);
|
||||
nextP(11,11) = P(11,11);
|
||||
nextP(0,12) = PS20;
|
||||
nextP(1,12) = PS87;
|
||||
nextP(2,12) = PS103;
|
||||
nextP(3,12) = PS126;
|
||||
nextP(4,12) = P(0,12)*PS72 + P(1,12)*PS62 - P(12,13)*PS44 + P(12,14)*PS140 - P(12,15)*PS139 + P(2,12)*PS60 - P(3,12)*PS74 + P(4,12);
|
||||
nextP(5,12) = P(0,12)*PS74 - P(1,12)*PS60 - P(12,13)*PS162 - P(12,14)*PS65 + P(12,15)*PS160 + P(2,12)*PS62 + P(3,12)*PS72 + P(5,12);
|
||||
nextP(6,12) = P(0,12)*PS60 + P(1,12)*PS74 + P(12,13)*PS166 - P(12,14)*PS165 - P(12,15)*PS70 - P(2,12)*PS72 + P(3,12)*PS62 + P(6,12);
|
||||
nextP(7,12) = P(4,12)*dt + P(7,12);
|
||||
nextP(8,12) = P(5,12)*dt + P(8,12);
|
||||
nextP(9,12) = P(6,12)*dt + P(9,12);
|
||||
nextP(10,12) = P(10,12);
|
||||
nextP(11,12) = P(11,12);
|
||||
nextP(12,12) = P(12,12);
|
||||
nextP(0,13) = PS45;
|
||||
nextP(1,13) = PS93;
|
||||
nextP(2,13) = PS114;
|
||||
nextP(3,13) = PS130;
|
||||
nextP(4,13) = PS141;
|
||||
nextP(5,13) = PS170;
|
||||
nextP(6,13) = PS185;
|
||||
nextP(7,13) = P(4,13)*dt + P(7,13);
|
||||
nextP(8,13) = P(5,13)*dt + P(8,13);
|
||||
nextP(9,13) = P(6,13)*dt + P(9,13);
|
||||
nextP(10,13) = P(10,13);
|
||||
nextP(11,13) = P(11,13);
|
||||
nextP(12,13) = P(12,13);
|
||||
nextP(13,13) = P(13,13);
|
||||
nextP(0,14) = PS55;
|
||||
nextP(1,14) = PS96;
|
||||
nextP(2,14) = PS117;
|
||||
nextP(3,14) = PS133;
|
||||
nextP(4,14) = PS146;
|
||||
nextP(5,14) = PS169;
|
||||
nextP(6,14) = PS184;
|
||||
nextP(7,14) = P(4,14)*dt + P(7,14);
|
||||
nextP(8,14) = P(5,14)*dt + P(8,14);
|
||||
nextP(9,14) = P(6,14)*dt + P(9,14);
|
||||
nextP(10,14) = P(10,14);
|
||||
nextP(11,14) = P(11,14);
|
||||
nextP(12,14) = P(12,14);
|
||||
nextP(13,14) = P(13,14);
|
||||
nextP(14,14) = P(14,14);
|
||||
nextP(0,15) = PS47;
|
||||
nextP(1,15) = PS94;
|
||||
nextP(2,15) = PS115;
|
||||
nextP(3,15) = PS131;
|
||||
nextP(4,15) = PS142;
|
||||
nextP(5,15) = PS173;
|
||||
nextP(6,15) = PS183;
|
||||
nextP(7,15) = P(4,15)*dt + P(7,15);
|
||||
nextP(8,15) = P(5,15)*dt + P(8,15);
|
||||
nextP(9,15) = P(6,15)*dt + P(9,15);
|
||||
nextP(10,15) = P(10,15);
|
||||
nextP(11,15) = P(11,15);
|
||||
nextP(12,15) = P(12,15);
|
||||
nextP(13,15) = P(13,15);
|
||||
nextP(14,15) = P(14,15);
|
||||
nextP(15,15) = P(15,15);
|
||||
nextP(0,16) = P(0,16) - P(1,16)*PS11 + P(10,16)*PS6 + P(11,16)*PS7 + P(12,16)*PS9 - P(2,16)*PS12 - P(3,16)*PS13;
|
||||
nextP(1,16) = P(0,16)*PS11 + P(1,16) - P(10,16)*PS34 + P(11,16)*PS9 - P(12,16)*PS7 + P(2,16)*PS13 - P(3,16)*PS12;
|
||||
nextP(2,16) = P(0,16)*PS12 - P(1,16)*PS13 - P(10,16)*PS9 - P(11,16)*PS34 + P(12,16)*PS6 + P(2,16) + P(3,16)*PS11;
|
||||
nextP(3,16) = P(0,16)*PS13 + P(1,16)*PS12 + P(10,16)*PS7 - P(11,16)*PS6 - P(12,16)*PS34 - P(2,16)*PS11 + P(3,16);
|
||||
nextP(4,16) = P(0,16)*PS72 + P(1,16)*PS62 - P(13,16)*PS44 + P(14,16)*PS140 - P(15,16)*PS139 + P(2,16)*PS60 - P(3,16)*PS74 + P(4,16);
|
||||
nextP(5,16) = P(0,16)*PS74 - P(1,16)*PS60 - P(13,16)*PS162 - P(14,16)*PS65 + P(15,16)*PS160 + P(2,16)*PS62 + P(3,16)*PS72 + P(5,16);
|
||||
nextP(6,16) = P(0,16)*PS60 + P(1,16)*PS74 + P(13,16)*PS166 - P(14,16)*PS165 - P(15,16)*PS70 - P(2,16)*PS72 + P(3,16)*PS62 + P(6,16);
|
||||
nextP(7,16) = P(4,16)*dt + P(7,16);
|
||||
nextP(8,16) = P(5,16)*dt + P(8,16);
|
||||
nextP(9,16) = P(6,16)*dt + P(9,16);
|
||||
nextP(10,16) = P(10,16);
|
||||
nextP(11,16) = P(11,16);
|
||||
nextP(12,16) = P(12,16);
|
||||
nextP(13,16) = P(13,16);
|
||||
nextP(14,16) = P(14,16);
|
||||
nextP(15,16) = P(15,16);
|
||||
nextP(16,16) = P(16,16);
|
||||
nextP(0,17) = P(0,17) - P(1,17)*PS11 + P(10,17)*PS6 + P(11,17)*PS7 + P(12,17)*PS9 - P(2,17)*PS12 - P(3,17)*PS13;
|
||||
nextP(1,17) = P(0,17)*PS11 + P(1,17) - P(10,17)*PS34 + P(11,17)*PS9 - P(12,17)*PS7 + P(2,17)*PS13 - P(3,17)*PS12;
|
||||
nextP(2,17) = P(0,17)*PS12 - P(1,17)*PS13 - P(10,17)*PS9 - P(11,17)*PS34 + P(12,17)*PS6 + P(2,17) + P(3,17)*PS11;
|
||||
nextP(3,17) = P(0,17)*PS13 + P(1,17)*PS12 + P(10,17)*PS7 - P(11,17)*PS6 - P(12,17)*PS34 - P(2,17)*PS11 + P(3,17);
|
||||
nextP(4,17) = P(0,17)*PS72 + P(1,17)*PS62 - P(13,17)*PS44 + P(14,17)*PS140 - P(15,17)*PS139 + P(2,17)*PS60 - P(3,17)*PS74 + P(4,17);
|
||||
nextP(5,17) = P(0,17)*PS74 - P(1,17)*PS60 - P(13,17)*PS162 - P(14,17)*PS65 + P(15,17)*PS160 + P(2,17)*PS62 + P(3,17)*PS72 + P(5,17);
|
||||
nextP(6,17) = P(0,17)*PS60 + P(1,17)*PS74 + P(13,17)*PS166 - P(14,17)*PS165 - P(15,17)*PS70 - P(2,17)*PS72 + P(3,17)*PS62 + P(6,17);
|
||||
nextP(7,17) = P(4,17)*dt + P(7,17);
|
||||
nextP(8,17) = P(5,17)*dt + P(8,17);
|
||||
nextP(9,17) = P(6,17)*dt + P(9,17);
|
||||
nextP(10,17) = P(10,17);
|
||||
nextP(11,17) = P(11,17);
|
||||
nextP(12,17) = P(12,17);
|
||||
nextP(13,17) = P(13,17);
|
||||
nextP(14,17) = P(14,17);
|
||||
nextP(15,17) = P(15,17);
|
||||
nextP(16,17) = P(16,17);
|
||||
nextP(17,17) = P(17,17);
|
||||
nextP(0,18) = P(0,18) - P(1,18)*PS11 + P(10,18)*PS6 + P(11,18)*PS7 + P(12,18)*PS9 - P(2,18)*PS12 - P(3,18)*PS13;
|
||||
nextP(1,18) = P(0,18)*PS11 + P(1,18) - P(10,18)*PS34 + P(11,18)*PS9 - P(12,18)*PS7 + P(2,18)*PS13 - P(3,18)*PS12;
|
||||
nextP(2,18) = P(0,18)*PS12 - P(1,18)*PS13 - P(10,18)*PS9 - P(11,18)*PS34 + P(12,18)*PS6 + P(2,18) + P(3,18)*PS11;
|
||||
nextP(3,18) = P(0,18)*PS13 + P(1,18)*PS12 + P(10,18)*PS7 - P(11,18)*PS6 - P(12,18)*PS34 - P(2,18)*PS11 + P(3,18);
|
||||
nextP(4,18) = P(0,18)*PS72 + P(1,18)*PS62 - P(13,18)*PS44 + P(14,18)*PS140 - P(15,18)*PS139 + P(2,18)*PS60 - P(3,18)*PS74 + P(4,18);
|
||||
nextP(5,18) = P(0,18)*PS74 - P(1,18)*PS60 - P(13,18)*PS162 - P(14,18)*PS65 + P(15,18)*PS160 + P(2,18)*PS62 + P(3,18)*PS72 + P(5,18);
|
||||
nextP(6,18) = P(0,18)*PS60 + P(1,18)*PS74 + P(13,18)*PS166 - P(14,18)*PS165 - P(15,18)*PS70 - P(2,18)*PS72 + P(3,18)*PS62 + P(6,18);
|
||||
nextP(7,18) = P(4,18)*dt + P(7,18);
|
||||
nextP(8,18) = P(5,18)*dt + P(8,18);
|
||||
nextP(9,18) = P(6,18)*dt + P(9,18);
|
||||
nextP(10,18) = P(10,18);
|
||||
nextP(11,18) = P(11,18);
|
||||
nextP(12,18) = P(12,18);
|
||||
nextP(13,18) = P(13,18);
|
||||
nextP(14,18) = P(14,18);
|
||||
nextP(15,18) = P(15,18);
|
||||
nextP(16,18) = P(16,18);
|
||||
nextP(17,18) = P(17,18);
|
||||
nextP(18,18) = P(18,18);
|
||||
nextP(0,19) = P(0,19) - P(1,19)*PS11 + P(10,19)*PS6 + P(11,19)*PS7 + P(12,19)*PS9 - P(2,19)*PS12 - P(3,19)*PS13;
|
||||
nextP(1,19) = P(0,19)*PS11 + P(1,19) - P(10,19)*PS34 + P(11,19)*PS9 - P(12,19)*PS7 + P(2,19)*PS13 - P(3,19)*PS12;
|
||||
nextP(2,19) = P(0,19)*PS12 - P(1,19)*PS13 - P(10,19)*PS9 - P(11,19)*PS34 + P(12,19)*PS6 + P(2,19) + P(3,19)*PS11;
|
||||
nextP(3,19) = P(0,19)*PS13 + P(1,19)*PS12 + P(10,19)*PS7 - P(11,19)*PS6 - P(12,19)*PS34 - P(2,19)*PS11 + P(3,19);
|
||||
nextP(4,19) = P(0,19)*PS72 + P(1,19)*PS62 - P(13,19)*PS44 + P(14,19)*PS140 - P(15,19)*PS139 + P(2,19)*PS60 - P(3,19)*PS74 + P(4,19);
|
||||
nextP(5,19) = P(0,19)*PS74 - P(1,19)*PS60 - P(13,19)*PS162 - P(14,19)*PS65 + P(15,19)*PS160 + P(2,19)*PS62 + P(3,19)*PS72 + P(5,19);
|
||||
nextP(6,19) = P(0,19)*PS60 + P(1,19)*PS74 + P(13,19)*PS166 - P(14,19)*PS165 - P(15,19)*PS70 - P(2,19)*PS72 + P(3,19)*PS62 + P(6,19);
|
||||
nextP(7,19) = P(4,19)*dt + P(7,19);
|
||||
nextP(8,19) = P(5,19)*dt + P(8,19);
|
||||
nextP(9,19) = P(6,19)*dt + P(9,19);
|
||||
nextP(10,19) = P(10,19);
|
||||
nextP(11,19) = P(11,19);
|
||||
nextP(12,19) = P(12,19);
|
||||
nextP(13,19) = P(13,19);
|
||||
nextP(14,19) = P(14,19);
|
||||
nextP(15,19) = P(15,19);
|
||||
nextP(16,19) = P(16,19);
|
||||
nextP(17,19) = P(17,19);
|
||||
nextP(18,19) = P(18,19);
|
||||
nextP(19,19) = P(19,19);
|
||||
nextP(0,20) = P(0,20) - P(1,20)*PS11 + P(10,20)*PS6 + P(11,20)*PS7 + P(12,20)*PS9 - P(2,20)*PS12 - P(3,20)*PS13;
|
||||
nextP(1,20) = P(0,20)*PS11 + P(1,20) - P(10,20)*PS34 + P(11,20)*PS9 - P(12,20)*PS7 + P(2,20)*PS13 - P(3,20)*PS12;
|
||||
nextP(2,20) = P(0,20)*PS12 - P(1,20)*PS13 - P(10,20)*PS9 - P(11,20)*PS34 + P(12,20)*PS6 + P(2,20) + P(3,20)*PS11;
|
||||
nextP(3,20) = P(0,20)*PS13 + P(1,20)*PS12 + P(10,20)*PS7 - P(11,20)*PS6 - P(12,20)*PS34 - P(2,20)*PS11 + P(3,20);
|
||||
nextP(4,20) = P(0,20)*PS72 + P(1,20)*PS62 - P(13,20)*PS44 + P(14,20)*PS140 - P(15,20)*PS139 + P(2,20)*PS60 - P(3,20)*PS74 + P(4,20);
|
||||
nextP(5,20) = P(0,20)*PS74 - P(1,20)*PS60 - P(13,20)*PS162 - P(14,20)*PS65 + P(15,20)*PS160 + P(2,20)*PS62 + P(3,20)*PS72 + P(5,20);
|
||||
nextP(6,20) = P(0,20)*PS60 + P(1,20)*PS74 + P(13,20)*PS166 - P(14,20)*PS165 - P(15,20)*PS70 - P(2,20)*PS72 + P(3,20)*PS62 + P(6,20);
|
||||
nextP(7,20) = P(4,20)*dt + P(7,20);
|
||||
nextP(8,20) = P(5,20)*dt + P(8,20);
|
||||
nextP(9,20) = P(6,20)*dt + P(9,20);
|
||||
nextP(10,20) = P(10,20);
|
||||
nextP(11,20) = P(11,20);
|
||||
nextP(12,20) = P(12,20);
|
||||
nextP(13,20) = P(13,20);
|
||||
nextP(14,20) = P(14,20);
|
||||
nextP(15,20) = P(15,20);
|
||||
nextP(16,20) = P(16,20);
|
||||
nextP(17,20) = P(17,20);
|
||||
nextP(18,20) = P(18,20);
|
||||
nextP(19,20) = P(19,20);
|
||||
nextP(20,20) = P(20,20);
|
||||
nextP(0,21) = P(0,21) - P(1,21)*PS11 + P(10,21)*PS6 + P(11,21)*PS7 + P(12,21)*PS9 - P(2,21)*PS12 - P(3,21)*PS13;
|
||||
nextP(1,21) = P(0,21)*PS11 + P(1,21) - P(10,21)*PS34 + P(11,21)*PS9 - P(12,21)*PS7 + P(2,21)*PS13 - P(3,21)*PS12;
|
||||
nextP(2,21) = P(0,21)*PS12 - P(1,21)*PS13 - P(10,21)*PS9 - P(11,21)*PS34 + P(12,21)*PS6 + P(2,21) + P(3,21)*PS11;
|
||||
nextP(3,21) = P(0,21)*PS13 + P(1,21)*PS12 + P(10,21)*PS7 - P(11,21)*PS6 - P(12,21)*PS34 - P(2,21)*PS11 + P(3,21);
|
||||
nextP(4,21) = P(0,21)*PS72 + P(1,21)*PS62 - P(13,21)*PS44 + P(14,21)*PS140 - P(15,21)*PS139 + P(2,21)*PS60 - P(3,21)*PS74 + P(4,21);
|
||||
nextP(5,21) = P(0,21)*PS74 - P(1,21)*PS60 - P(13,21)*PS162 - P(14,21)*PS65 + P(15,21)*PS160 + P(2,21)*PS62 + P(3,21)*PS72 + P(5,21);
|
||||
nextP(6,21) = P(0,21)*PS60 + P(1,21)*PS74 + P(13,21)*PS166 - P(14,21)*PS165 - P(15,21)*PS70 - P(2,21)*PS72 + P(3,21)*PS62 + P(6,21);
|
||||
nextP(7,21) = P(4,21)*dt + P(7,21);
|
||||
nextP(8,21) = P(5,21)*dt + P(8,21);
|
||||
nextP(9,21) = P(6,21)*dt + P(9,21);
|
||||
nextP(10,21) = P(10,21);
|
||||
nextP(11,21) = P(11,21);
|
||||
nextP(12,21) = P(12,21);
|
||||
nextP(13,21) = P(13,21);
|
||||
nextP(14,21) = P(14,21);
|
||||
nextP(15,21) = P(15,21);
|
||||
nextP(16,21) = P(16,21);
|
||||
nextP(17,21) = P(17,21);
|
||||
nextP(18,21) = P(18,21);
|
||||
nextP(19,21) = P(19,21);
|
||||
nextP(20,21) = P(20,21);
|
||||
nextP(21,21) = P(21,21);
|
||||
nextP(0,22) = P(0,22) - P(1,22)*PS11 + P(10,22)*PS6 + P(11,22)*PS7 + P(12,22)*PS9 - P(2,22)*PS12 - P(3,22)*PS13;
|
||||
nextP(1,22) = P(0,22)*PS11 + P(1,22) - P(10,22)*PS34 + P(11,22)*PS9 - P(12,22)*PS7 + P(2,22)*PS13 - P(3,22)*PS12;
|
||||
nextP(2,22) = P(0,22)*PS12 - P(1,22)*PS13 - P(10,22)*PS9 - P(11,22)*PS34 + P(12,22)*PS6 + P(2,22) + P(3,22)*PS11;
|
||||
nextP(3,22) = P(0,22)*PS13 + P(1,22)*PS12 + P(10,22)*PS7 - P(11,22)*PS6 - P(12,22)*PS34 - P(2,22)*PS11 + P(3,22);
|
||||
nextP(4,22) = P(0,22)*PS72 + P(1,22)*PS62 - P(13,22)*PS44 + P(14,22)*PS140 - P(15,22)*PS139 + P(2,22)*PS60 - P(3,22)*PS74 + P(4,22);
|
||||
nextP(5,22) = P(0,22)*PS74 - P(1,22)*PS60 - P(13,22)*PS162 - P(14,22)*PS65 + P(15,22)*PS160 + P(2,22)*PS62 + P(3,22)*PS72 + P(5,22);
|
||||
nextP(6,22) = P(0,22)*PS60 + P(1,22)*PS74 + P(13,22)*PS166 - P(14,22)*PS165 - P(15,22)*PS70 - P(2,22)*PS72 + P(3,22)*PS62 + P(6,22);
|
||||
nextP(7,22) = P(4,22)*dt + P(7,22);
|
||||
nextP(8,22) = P(5,22)*dt + P(8,22);
|
||||
nextP(9,22) = P(6,22)*dt + P(9,22);
|
||||
nextP(10,22) = P(10,22);
|
||||
nextP(11,22) = P(11,22);
|
||||
nextP(12,22) = P(12,22);
|
||||
nextP(13,22) = P(13,22);
|
||||
nextP(14,22) = P(14,22);
|
||||
nextP(15,22) = P(15,22);
|
||||
nextP(16,22) = P(16,22);
|
||||
nextP(17,22) = P(17,22);
|
||||
nextP(18,22) = P(18,22);
|
||||
nextP(19,22) = P(19,22);
|
||||
nextP(20,22) = P(20,22);
|
||||
nextP(21,22) = P(21,22);
|
||||
nextP(22,22) = P(22,22);
|
||||
nextP(0,23) = P(0,23) - P(1,23)*PS11 + P(10,23)*PS6 + P(11,23)*PS7 + P(12,23)*PS9 - P(2,23)*PS12 - P(3,23)*PS13;
|
||||
nextP(1,23) = P(0,23)*PS11 + P(1,23) - P(10,23)*PS34 + P(11,23)*PS9 - P(12,23)*PS7 + P(2,23)*PS13 - P(3,23)*PS12;
|
||||
nextP(2,23) = P(0,23)*PS12 - P(1,23)*PS13 - P(10,23)*PS9 - P(11,23)*PS34 + P(12,23)*PS6 + P(2,23) + P(3,23)*PS11;
|
||||
nextP(3,23) = P(0,23)*PS13 + P(1,23)*PS12 + P(10,23)*PS7 - P(11,23)*PS6 - P(12,23)*PS34 - P(2,23)*PS11 + P(3,23);
|
||||
nextP(4,23) = P(0,23)*PS72 + P(1,23)*PS62 - P(13,23)*PS44 + P(14,23)*PS140 - P(15,23)*PS139 + P(2,23)*PS60 - P(3,23)*PS74 + P(4,23);
|
||||
nextP(5,23) = P(0,23)*PS74 - P(1,23)*PS60 - P(13,23)*PS162 - P(14,23)*PS65 + P(15,23)*PS160 + P(2,23)*PS62 + P(3,23)*PS72 + P(5,23);
|
||||
nextP(6,23) = P(0,23)*PS60 + P(1,23)*PS74 + P(13,23)*PS166 - P(14,23)*PS165 - P(15,23)*PS70 - P(2,23)*PS72 + P(3,23)*PS62 + P(6,23);
|
||||
nextP(7,23) = P(4,23)*dt + P(7,23);
|
||||
nextP(8,23) = P(5,23)*dt + P(8,23);
|
||||
nextP(9,23) = P(6,23)*dt + P(9,23);
|
||||
nextP(10,23) = P(10,23);
|
||||
nextP(11,23) = P(11,23);
|
||||
nextP(12,23) = P(12,23);
|
||||
nextP(13,23) = P(13,23);
|
||||
nextP(14,23) = P(14,23);
|
||||
nextP(15,23) = P(15,23);
|
||||
nextP(16,23) = P(16,23);
|
||||
nextP(17,23) = P(17,23);
|
||||
nextP(18,23) = P(18,23);
|
||||
nextP(19,23) = P(19,23);
|
||||
nextP(20,23) = P(20,23);
|
||||
nextP(21,23) = P(21,23);
|
||||
nextP(22,23) = P(22,23);
|
||||
nextP(23,23) = P(23,23);
|
||||
|
||||
|
||||
@@ -0,0 +1,955 @@
|
||||
#include <math.h>
|
||||
#include <stdio.h>
|
||||
#include <cstdlib>
|
||||
#include "../../../../../matrix/matrix/math.hpp"
|
||||
|
||||
typedef matrix::SquareMatrix<float, 24> SquareMatrix24f;
|
||||
|
||||
inline float sq(float in) {
|
||||
return in * in;
|
||||
}
|
||||
|
||||
namespace ecl{
|
||||
inline float powf(float x, int exp)
|
||||
{
|
||||
float ret;
|
||||
if (exp > 0) {
|
||||
ret = x;
|
||||
for (int count = 1; count < exp; count++) {
|
||||
ret *= x;
|
||||
}
|
||||
return ret;
|
||||
} else if (exp < 0) {
|
||||
return 1.0f / ecl::powf(x, -exp);
|
||||
}
|
||||
return 1.0f;
|
||||
}
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
// create input data
|
||||
const float dt = 0.01f;
|
||||
|
||||
for (uint8_t iteration=0; iteration<100; iteration++) {
|
||||
// quaternion states must be normalised
|
||||
float q0 = 2.0f * ((float)rand() - 0.5f);
|
||||
float q1 = 2.0f * ((float)rand() - 0.5f);
|
||||
float q2 = 2.0f * ((float)rand() - 0.5f);
|
||||
float q3 = 2.0f * ((float)rand() - 0.5f);
|
||||
const float length = sqrtf(sq(q0) + sq(q1) + sq(q2) + sq(q3));
|
||||
q0 /= length;
|
||||
q1 /= length;
|
||||
q2 /= length;
|
||||
q3 /= length;
|
||||
|
||||
// up to 1 rad/sec of rate
|
||||
const float dax = 2.0f * dt * ((float)rand() - 0.5f);
|
||||
const float day = 2.0f * dt * ((float)rand() - 0.5f);
|
||||
const float daz = 2.0f * dt * ((float)rand() - 0.5f);
|
||||
|
||||
// up to 2g of accel
|
||||
const float dvx = 2.0f * 20.0f * dt * ((float)rand() - 0.5f);
|
||||
const float dvy = 2.0f * 20.0f * dt * ((float)rand() - 0.5f);
|
||||
const float dvz = 2.0f * 20.0f * dt * ((float)rand() - 0.5f);
|
||||
|
||||
// up to 0.1 rad/sec of gyro bias
|
||||
const float dax_b = 2.0f * 0.1f * dt * ((float)rand() - 0.5f);
|
||||
const float day_b = 2.0f * 0.1f * dt * ((float)rand() - 0.5f);
|
||||
const float daz_b = 2.0f * 0.1f * dt * ((float)rand() - 0.5f);
|
||||
|
||||
// up to 0.5 m/s/s of accel bias
|
||||
const float dvx_b = 2.0f * 0.5f * dt * ((float)rand() - 0.5f);
|
||||
const float dvy_b = 2.0f * 0.5f * dt * ((float)rand() - 0.5f);
|
||||
const float dvz_b = 2.0f * 0.5f * dt * ((float)rand() - 0.5f);
|
||||
|
||||
|
||||
const float daxVar = sq(dt * 0.015f);
|
||||
const float dayVar = daxVar;
|
||||
const float dazVar = daxVar;
|
||||
|
||||
const float dvxVar = sq(dt * 0.3f);
|
||||
const float dvyVar = dvxVar;
|
||||
const float dvzVar = dvxVar;
|
||||
|
||||
// create a symmetrical positive dfinite matrix with off diagonals between -1 and 1 and diagonals between 0 and 1
|
||||
SquareMatrix24f P;
|
||||
for (int col=0; col<=23; col++) {
|
||||
for (int row=0; row<=col; row++) {
|
||||
if (row == col) {
|
||||
P(row,col) = (float)rand();
|
||||
} else {
|
||||
P(col,row) = P(row,col) = 0.01f * 2.0f * ((float)rand() - 0.5f);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Equations for covariance matrix prediction, without process noise!
|
||||
const float PS0 = ecl::powf(q1, 2);
|
||||
const float PS1 = 0.25F*daxVar;
|
||||
const float PS2 = ecl::powf(q2, 2);
|
||||
const float PS3 = 0.25F*dayVar;
|
||||
const float PS4 = ecl::powf(q3, 2);
|
||||
const float PS5 = 0.25F*dazVar;
|
||||
const float PS6 = 0.5F*q1;
|
||||
const float PS7 = 0.5F*q2;
|
||||
const float PS8 = P(10,11)*PS7;
|
||||
const float PS9 = 0.5F*q3;
|
||||
const float PS10 = P(10,12)*PS9;
|
||||
const float PS11 = 0.5F*dax - 0.5F*dax_b;
|
||||
const float PS12 = 0.5F*day - 0.5F*day_b;
|
||||
const float PS13 = 0.5F*daz - 0.5F*daz_b;
|
||||
const float PS14 = P(0,10) - P(1,10)*PS11 + P(10,10)*PS6 - P(2,10)*PS12 - P(3,10)*PS13 + PS10 + PS8;
|
||||
const float PS15 = P(10,11)*PS6;
|
||||
const float PS16 = P(11,12)*PS9;
|
||||
const float PS17 = P(0,11) - P(1,11)*PS11 + P(11,11)*PS7 - P(2,11)*PS12 - P(3,11)*PS13 + PS15 + PS16;
|
||||
const float PS18 = P(10,12)*PS6;
|
||||
const float PS19 = P(11,12)*PS7;
|
||||
const float PS20 = P(0,12) - P(1,12)*PS11 + P(12,12)*PS9 - P(2,12)*PS12 - P(3,12)*PS13 + PS18 + PS19;
|
||||
const float PS21 = P(1,2)*PS12;
|
||||
const float PS22 = -P(1,3)*PS13;
|
||||
const float PS23 = P(0,1) - P(1,1)*PS11 + P(1,10)*PS6 + P(1,11)*PS7 + P(1,12)*PS9 - PS21 + PS22;
|
||||
const float PS24 = -P(1,2)*PS11;
|
||||
const float PS25 = P(2,3)*PS13;
|
||||
const float PS26 = P(0,2) + P(2,10)*PS6 + P(2,11)*PS7 + P(2,12)*PS9 - P(2,2)*PS12 + PS24 - PS25;
|
||||
const float PS27 = P(1,3)*PS11;
|
||||
const float PS28 = -P(2,3)*PS12;
|
||||
const float PS29 = P(0,3) + P(3,10)*PS6 + P(3,11)*PS7 + P(3,12)*PS9 - P(3,3)*PS13 - PS27 + PS28;
|
||||
const float PS30 = P(0,1)*PS11;
|
||||
const float PS31 = P(0,2)*PS12;
|
||||
const float PS32 = P(0,3)*PS13;
|
||||
const float PS33 = P(0,0) + P(0,10)*PS6 + P(0,11)*PS7 + P(0,12)*PS9 - PS30 - PS31 - PS32;
|
||||
const float PS34 = 0.5F*q0;
|
||||
const float PS35 = q2*q3;
|
||||
const float PS36 = q0*q1;
|
||||
const float PS37 = q1*q3;
|
||||
const float PS38 = q0*q2;
|
||||
const float PS39 = q1*q2;
|
||||
const float PS40 = q0*q3;
|
||||
const float PS41 = -PS2;
|
||||
const float PS42 = ecl::powf(q0, 2);
|
||||
const float PS43 = -PS4 + PS42;
|
||||
const float PS44 = PS0 + PS41 + PS43;
|
||||
const float PS45 = P(0,13) - P(1,13)*PS11 + P(10,13)*PS6 + P(11,13)*PS7 + P(12,13)*PS9 - P(2,13)*PS12 - P(3,13)*PS13;
|
||||
const float PS46 = PS37 + PS38;
|
||||
const float PS47 = P(0,15) - P(1,15)*PS11 + P(10,15)*PS6 + P(11,15)*PS7 + P(12,15)*PS9 - P(2,15)*PS12 - P(3,15)*PS13;
|
||||
const float PS48 = 2*PS47;
|
||||
const float PS49 = dvy - dvy_b;
|
||||
const float PS50 = dvx - dvx_b;
|
||||
const float PS51 = dvz - dvz_b;
|
||||
const float PS52 = PS49*q0 + PS50*q3 - PS51*q1;
|
||||
const float PS53 = 2*PS29;
|
||||
const float PS54 = -PS39 + PS40;
|
||||
const float PS55 = P(0,14) - P(1,14)*PS11 + P(10,14)*PS6 + P(11,14)*PS7 + P(12,14)*PS9 - P(2,14)*PS12 - P(3,14)*PS13;
|
||||
const float PS56 = 2*PS55;
|
||||
const float PS57 = -PS49*q3 + PS50*q0 + PS51*q2;
|
||||
const float PS58 = 2*PS33;
|
||||
const float PS59 = PS49*q1 - PS50*q2 + PS51*q0;
|
||||
const float PS60 = 2*PS59;
|
||||
const float PS61 = PS49*q2 + PS50*q1 + PS51*q3;
|
||||
const float PS62 = 2*PS61;
|
||||
const float PS63 = P(0,4) - P(1,4)*PS11 - P(2,4)*PS12 - P(3,4)*PS13 + P(4,10)*PS6 + P(4,11)*PS7 + P(4,12)*PS9;
|
||||
const float PS64 = -PS0;
|
||||
const float PS65 = PS2 + PS43 + PS64;
|
||||
const float PS66 = PS39 + PS40;
|
||||
const float PS67 = 2*PS45;
|
||||
const float PS68 = -PS35 + PS36;
|
||||
const float PS69 = P(0,5) - P(1,5)*PS11 - P(2,5)*PS12 - P(3,5)*PS13 + P(5,10)*PS6 + P(5,11)*PS7 + P(5,12)*PS9;
|
||||
const float PS70 = PS4 + PS41 + PS42 + PS64;
|
||||
const float PS71 = PS35 + PS36;
|
||||
const float PS72 = 2*PS57;
|
||||
const float PS73 = -PS37 + PS38;
|
||||
const float PS74 = 2*PS52;
|
||||
const float PS75 = P(0,6) - P(1,6)*PS11 - P(2,6)*PS12 - P(3,6)*PS13 + P(6,10)*PS6 + P(6,11)*PS7 + P(6,12)*PS9;
|
||||
const float PS76 = -P(10,11)*PS34;
|
||||
const float PS77 = P(0,11)*PS11 + P(1,11) + P(11,11)*PS9 + P(2,11)*PS13 - P(3,11)*PS12 - PS19 + PS76;
|
||||
const float PS78 = P(0,2)*PS13;
|
||||
const float PS79 = P(0,3)*PS12;
|
||||
const float PS80 = P(0,0)*PS11 + P(0,1) - P(0,10)*PS34 + P(0,11)*PS9 - P(0,12)*PS7 + PS78 - PS79;
|
||||
const float PS81 = P(0,2)*PS11;
|
||||
const float PS82 = P(1,2) - P(2,10)*PS34 + P(2,11)*PS9 - P(2,12)*PS7 + P(2,2)*PS13 + PS28 + PS81;
|
||||
const float PS83 = P(10,11)*PS9;
|
||||
const float PS84 = P(10,12)*PS7;
|
||||
const float PS85 = P(0,10)*PS11 + P(1,10) - P(10,10)*PS34 + P(2,10)*PS13 - P(3,10)*PS12 + PS83 - PS84;
|
||||
const float PS86 = -P(10,12)*PS34;
|
||||
const float PS87 = P(0,12)*PS11 + P(1,12) - P(12,12)*PS7 + P(2,12)*PS13 - P(3,12)*PS12 + PS16 + PS86;
|
||||
const float PS88 = P(0,3)*PS11;
|
||||
const float PS89 = P(1,3) - P(3,10)*PS34 + P(3,11)*PS9 - P(3,12)*PS7 - P(3,3)*PS12 + PS25 + PS88;
|
||||
const float PS90 = P(1,2)*PS13;
|
||||
const float PS91 = P(1,3)*PS12;
|
||||
const float PS92 = P(1,1) - P(1,10)*PS34 + P(1,11)*PS9 - P(1,12)*PS7 + PS30 + PS90 - PS91;
|
||||
const float PS93 = P(0,13)*PS11 + P(1,13) - P(10,13)*PS34 + P(11,13)*PS9 - P(12,13)*PS7 + P(2,13)*PS13 - P(3,13)*PS12;
|
||||
const float PS94 = P(0,15)*PS11 + P(1,15) - P(10,15)*PS34 + P(11,15)*PS9 - P(12,15)*PS7 + P(2,15)*PS13 - P(3,15)*PS12;
|
||||
const float PS95 = 2*PS94;
|
||||
const float PS96 = P(0,14)*PS11 + P(1,14) - P(10,14)*PS34 + P(11,14)*PS9 - P(12,14)*PS7 + P(2,14)*PS13 - P(3,14)*PS12;
|
||||
const float PS97 = 2*PS96;
|
||||
const float PS98 = P(0,4)*PS11 + P(1,4) + P(2,4)*PS13 - P(3,4)*PS12 - P(4,10)*PS34 + P(4,11)*PS9 - P(4,12)*PS7;
|
||||
const float PS99 = 2*PS93;
|
||||
const float PS100 = P(0,5)*PS11 + P(1,5) + P(2,5)*PS13 - P(3,5)*PS12 - P(5,10)*PS34 + P(5,11)*PS9 - P(5,12)*PS7;
|
||||
const float PS101 = P(0,6)*PS11 + P(1,6) + P(2,6)*PS13 - P(3,6)*PS12 - P(6,10)*PS34 + P(6,11)*PS9 - P(6,12)*PS7;
|
||||
const float PS102 = -P(11,12)*PS34;
|
||||
const float PS103 = P(0,12)*PS12 - P(1,12)*PS13 + P(12,12)*PS6 + P(2,12) + P(3,12)*PS11 - PS10 + PS102;
|
||||
const float PS104 = P(2,3) - P(3,10)*PS9 - P(3,11)*PS34 + P(3,12)*PS6 + P(3,3)*PS11 + PS22 + PS79;
|
||||
const float PS105 = P(0,1)*PS13;
|
||||
const float PS106 = P(0,0)*PS12 - P(0,10)*PS9 - P(0,11)*PS34 + P(0,12)*PS6 + P(0,2) - PS105 + PS88;
|
||||
const float PS107 = P(11,12)*PS6;
|
||||
const float PS108 = P(0,11)*PS12 - P(1,11)*PS13 - P(11,11)*PS34 + P(2,11) + P(3,11)*PS11 + PS107 - PS83;
|
||||
const float PS109 = P(0,10)*PS12 - P(1,10)*PS13 - P(10,10)*PS9 + P(2,10) + P(3,10)*PS11 + PS18 + PS76;
|
||||
const float PS110 = P(0,1)*PS12;
|
||||
const float PS111 = -P(1,1)*PS13 - P(1,10)*PS9 - P(1,11)*PS34 + P(1,12)*PS6 + P(1,2) + PS110 + PS27;
|
||||
const float PS112 = P(2,3)*PS11;
|
||||
const float PS113 = -P(2,10)*PS9 - P(2,11)*PS34 + P(2,12)*PS6 + P(2,2) + PS112 + PS31 - PS90;
|
||||
const float PS114 = P(0,13)*PS12 - P(1,13)*PS13 - P(10,13)*PS9 - P(11,13)*PS34 + P(12,13)*PS6 + P(2,13) + P(3,13)*PS11;
|
||||
const float PS115 = P(0,15)*PS12 - P(1,15)*PS13 - P(10,15)*PS9 - P(11,15)*PS34 + P(12,15)*PS6 + P(2,15) + P(3,15)*PS11;
|
||||
const float PS116 = 2*PS115;
|
||||
const float PS117 = P(0,14)*PS12 - P(1,14)*PS13 - P(10,14)*PS9 - P(11,14)*PS34 + P(12,14)*PS6 + P(2,14) + P(3,14)*PS11;
|
||||
const float PS118 = 2*PS117;
|
||||
const float PS119 = P(0,4)*PS12 - P(1,4)*PS13 + P(2,4) + P(3,4)*PS11 - P(4,10)*PS9 - P(4,11)*PS34 + P(4,12)*PS6;
|
||||
const float PS120 = 2*PS114;
|
||||
const float PS121 = P(0,5)*PS12 - P(1,5)*PS13 + P(2,5) + P(3,5)*PS11 - P(5,10)*PS9 - P(5,11)*PS34 + P(5,12)*PS6;
|
||||
const float PS122 = P(0,6)*PS12 - P(1,6)*PS13 + P(2,6) + P(3,6)*PS11 - P(6,10)*PS9 - P(6,11)*PS34 + P(6,12)*PS6;
|
||||
const float PS123 = P(0,10)*PS13 + P(1,10)*PS12 + P(10,10)*PS7 - P(2,10)*PS11 + P(3,10) - PS15 + PS86;
|
||||
const float PS124 = P(1,1)*PS12 + P(1,10)*PS7 - P(1,11)*PS6 - P(1,12)*PS34 + P(1,3) + PS105 + PS24;
|
||||
const float PS125 = P(0,0)*PS13 + P(0,10)*PS7 - P(0,11)*PS6 - P(0,12)*PS34 + P(0,3) + PS110 - PS81;
|
||||
const float PS126 = P(0,12)*PS13 + P(1,12)*PS12 - P(12,12)*PS34 - P(2,12)*PS11 + P(3,12) - PS107 + PS84;
|
||||
const float PS127 = P(0,11)*PS13 + P(1,11)*PS12 - P(11,11)*PS6 - P(2,11)*PS11 + P(3,11) + PS102 + PS8;
|
||||
const float PS128 = P(2,10)*PS7 - P(2,11)*PS6 - P(2,12)*PS34 - P(2,2)*PS11 + P(2,3) + PS21 + PS78;
|
||||
const float PS129 = P(3,10)*PS7 - P(3,11)*PS6 - P(3,12)*PS34 + P(3,3) - PS112 + PS32 + PS91;
|
||||
const float PS130 = P(0,13)*PS13 + P(1,13)*PS12 + P(10,13)*PS7 - P(11,13)*PS6 - P(12,13)*PS34 - P(2,13)*PS11 + P(3,13);
|
||||
const float PS131 = P(0,15)*PS13 + P(1,15)*PS12 + P(10,15)*PS7 - P(11,15)*PS6 - P(12,15)*PS34 - P(2,15)*PS11 + P(3,15);
|
||||
const float PS132 = 2*PS131;
|
||||
const float PS133 = P(0,14)*PS13 + P(1,14)*PS12 + P(10,14)*PS7 - P(11,14)*PS6 - P(12,14)*PS34 - P(2,14)*PS11 + P(3,14);
|
||||
const float PS134 = 2*PS133;
|
||||
const float PS135 = P(0,4)*PS13 + P(1,4)*PS12 - P(2,4)*PS11 + P(3,4) + P(4,10)*PS7 - P(4,11)*PS6 - P(4,12)*PS34;
|
||||
const float PS136 = 2*PS130;
|
||||
const float PS137 = P(0,5)*PS13 + P(1,5)*PS12 - P(2,5)*PS11 + P(3,5) + P(5,10)*PS7 - P(5,11)*PS6 - P(5,12)*PS34;
|
||||
const float PS138 = P(0,6)*PS13 + P(1,6)*PS12 - P(2,6)*PS11 + P(3,6) + P(6,10)*PS7 - P(6,11)*PS6 - P(6,12)*PS34;
|
||||
const float PS139 = 2*PS46;
|
||||
const float PS140 = 2*PS54;
|
||||
const float PS141 = P(0,13)*PS72 + P(1,13)*PS62 - P(13,13)*PS44 + P(13,14)*PS140 - P(13,15)*PS139 + P(2,13)*PS60 - P(3,13)*PS74 + P(4,13);
|
||||
const float PS142 = P(0,15)*PS72 + P(1,15)*PS62 - P(13,15)*PS44 + P(14,15)*PS140 - P(15,15)*PS139 + P(2,15)*PS60 - P(3,15)*PS74 + P(4,15);
|
||||
const float PS143 = P(1,3)*PS62;
|
||||
const float PS144 = P(0,3)*PS72;
|
||||
const float PS145 = P(2,3)*PS60 - P(3,13)*PS44 + P(3,14)*PS140 - P(3,15)*PS139 - P(3,3)*PS74 + P(3,4) + PS143 + PS144;
|
||||
const float PS146 = P(0,14)*PS72 + P(1,14)*PS62 - P(13,14)*PS44 + P(14,14)*PS140 - P(14,15)*PS139 + P(2,14)*PS60 - P(3,14)*PS74 + P(4,14);
|
||||
const float PS147 = P(0,2)*PS60;
|
||||
const float PS148 = P(0,3)*PS74;
|
||||
const float PS149 = P(0,0)*PS72 + P(0,1)*PS62 - P(0,13)*PS44 + P(0,14)*PS140 - P(0,15)*PS139 + P(0,4) + PS147 - PS148;
|
||||
const float PS150 = P(1,2)*PS62;
|
||||
const float PS151 = P(0,2)*PS72;
|
||||
const float PS152 = -P(2,13)*PS44 + P(2,14)*PS140 - P(2,15)*PS139 + P(2,2)*PS60 - P(2,3)*PS74 + P(2,4) + PS150 + PS151;
|
||||
const float PS153 = P(1,2)*PS60;
|
||||
const float PS154 = P(1,3)*PS74;
|
||||
const float PS155 = P(0,1)*PS72 + P(1,1)*PS62 - P(1,13)*PS44 + P(1,14)*PS140 - P(1,15)*PS139 + P(1,4) + PS153 - PS154;
|
||||
const float PS156 = 4*dvyVar;
|
||||
const float PS157 = 4*dvzVar;
|
||||
const float PS158 = P(0,4)*PS72 + P(1,4)*PS62 + P(2,4)*PS60 - P(3,4)*PS74 - P(4,13)*PS44 + P(4,14)*PS140 - P(4,15)*PS139 + P(4,4);
|
||||
const float PS159 = 2*PS141;
|
||||
const float PS160 = 2*PS68;
|
||||
const float PS161 = PS65*dvyVar;
|
||||
const float PS162 = 2*PS66;
|
||||
const float PS163 = PS44*dvxVar;
|
||||
const float PS164 = P(0,5)*PS72 + P(1,5)*PS62 + P(2,5)*PS60 - P(3,5)*PS74 + P(4,5) - P(5,13)*PS44 + P(5,14)*PS140 - P(5,15)*PS139;
|
||||
const float PS165 = 2*PS71;
|
||||
const float PS166 = 2*PS73;
|
||||
const float PS167 = PS70*dvzVar;
|
||||
const float PS168 = P(0,6)*PS72 + P(1,6)*PS62 + P(2,6)*PS60 - P(3,6)*PS74 + P(4,6) - P(6,13)*PS44 + P(6,14)*PS140 - P(6,15)*PS139;
|
||||
const float PS169 = P(0,14)*PS74 - P(1,14)*PS60 - P(13,14)*PS162 - P(14,14)*PS65 + P(14,15)*PS160 + P(2,14)*PS62 + P(3,14)*PS72 + P(5,14);
|
||||
const float PS170 = P(0,13)*PS74 - P(1,13)*PS60 - P(13,13)*PS162 - P(13,14)*PS65 + P(13,15)*PS160 + P(2,13)*PS62 + P(3,13)*PS72 + P(5,13);
|
||||
const float PS171 = P(0,1)*PS74;
|
||||
const float PS172 = -P(1,1)*PS60 - P(1,13)*PS162 - P(1,14)*PS65 + P(1,15)*PS160 + P(1,3)*PS72 + P(1,5) + PS150 + PS171;
|
||||
const float PS173 = P(0,15)*PS74 - P(1,15)*PS60 - P(13,15)*PS162 - P(14,15)*PS65 + P(15,15)*PS160 + P(2,15)*PS62 + P(3,15)*PS72 + P(5,15);
|
||||
const float PS174 = P(2,3)*PS62;
|
||||
const float PS175 = -P(1,3)*PS60 - P(3,13)*PS162 - P(3,14)*PS65 + P(3,15)*PS160 + P(3,3)*PS72 + P(3,5) + PS148 + PS174;
|
||||
const float PS176 = P(0,1)*PS60;
|
||||
const float PS177 = P(0,0)*PS74 - P(0,13)*PS162 - P(0,14)*PS65 + P(0,15)*PS160 + P(0,2)*PS62 + P(0,5) + PS144 - PS176;
|
||||
const float PS178 = P(2,3)*PS72;
|
||||
const float PS179 = P(0,2)*PS74 - P(2,13)*PS162 - P(2,14)*PS65 + P(2,15)*PS160 + P(2,2)*PS62 + P(2,5) - PS153 + PS178;
|
||||
const float PS180 = 4*dvxVar;
|
||||
const float PS181 = P(0,5)*PS74 - P(1,5)*PS60 + P(2,5)*PS62 + P(3,5)*PS72 - P(5,13)*PS162 - P(5,14)*PS65 + P(5,15)*PS160 + P(5,5);
|
||||
const float PS182 = P(0,6)*PS74 - P(1,6)*PS60 + P(2,6)*PS62 + P(3,6)*PS72 + P(5,6) - P(6,13)*PS162 - P(6,14)*PS65 + P(6,15)*PS160;
|
||||
const float PS183 = P(0,15)*PS60 + P(1,15)*PS74 + P(13,15)*PS166 - P(14,15)*PS165 - P(15,15)*PS70 - P(2,15)*PS72 + P(3,15)*PS62 + P(6,15);
|
||||
const float PS184 = P(0,14)*PS60 + P(1,14)*PS74 + P(13,14)*PS166 - P(14,14)*PS165 - P(14,15)*PS70 - P(2,14)*PS72 + P(3,14)*PS62 + P(6,14);
|
||||
const float PS185 = P(0,13)*PS60 + P(1,13)*PS74 + P(13,13)*PS166 - P(13,14)*PS165 - P(13,15)*PS70 - P(2,13)*PS72 + P(3,13)*PS62 + P(6,13);
|
||||
const float PS186 = P(0,6)*PS60 + P(1,6)*PS74 - P(2,6)*PS72 + P(3,6)*PS62 + P(6,13)*PS166 - P(6,14)*PS165 - P(6,15)*PS70 + P(6,6);
|
||||
|
||||
SquareMatrix24f nextP;
|
||||
|
||||
nextP(0,0) = PS0*PS1 - PS11*PS23 - PS12*PS26 - PS13*PS29 + PS14*PS6 + PS17*PS7 + PS2*PS3 + PS20*PS9 + PS33 + PS4*PS5;
|
||||
nextP(0,1) = -PS1*PS36 + PS11*PS33 - PS12*PS29 + PS13*PS26 - PS14*PS34 + PS17*PS9 - PS20*PS7 + PS23 + PS3*PS35 - PS35*PS5;
|
||||
nextP(1,1) = PS1*PS42 + PS11*PS80 - PS12*PS89 + PS13*PS82 + PS2*PS5 + PS3*PS4 - PS34*PS85 - PS7*PS87 + PS77*PS9 + PS92;
|
||||
nextP(0,2) = -PS1*PS37 + PS11*PS29 + PS12*PS33 - PS13*PS23 - PS14*PS9 - PS17*PS34 + PS20*PS6 + PS26 - PS3*PS38 + PS37*PS5;
|
||||
nextP(1,2) = PS1*PS40 + PS11*PS89 + PS12*PS80 - PS13*PS92 - PS3*PS40 - PS34*PS77 - PS39*PS5 + PS6*PS87 + PS82 - PS85*PS9;
|
||||
nextP(2,2) = PS0*PS5 + PS1*PS4 + PS103*PS6 + PS104*PS11 + PS106*PS12 - PS108*PS34 - PS109*PS9 - PS111*PS13 + PS113 + PS3*PS42;
|
||||
nextP(0,3) = PS1*PS39 - PS11*PS26 + PS12*PS23 + PS13*PS33 + PS14*PS7 - PS17*PS6 - PS20*PS34 + PS29 - PS3*PS39 - PS40*PS5;
|
||||
nextP(1,3) = -PS1*PS38 - PS11*PS82 + PS12*PS92 + PS13*PS80 - PS3*PS37 - PS34*PS87 + PS38*PS5 - PS6*PS77 + PS7*PS85 + PS89;
|
||||
nextP(2,3) = -PS1*PS35 - PS103*PS34 + PS104 + PS106*PS13 - PS108*PS6 + PS109*PS7 - PS11*PS113 + PS111*PS12 + PS3*PS36 - PS36*PS5;
|
||||
nextP(3,3) = PS0*PS3 + PS1*PS2 - PS11*PS128 + PS12*PS124 + PS123*PS7 + PS125*PS13 - PS126*PS34 - PS127*PS6 + PS129 + PS42*PS5;
|
||||
nextP(0,4) = PS23*PS62 + PS26*PS60 - PS44*PS45 - PS46*PS48 - PS52*PS53 + PS54*PS56 + PS57*PS58 + PS63;
|
||||
nextP(1,4) = -PS44*PS93 - PS46*PS95 + PS54*PS97 + PS60*PS82 + PS62*PS92 + PS72*PS80 - PS74*PS89 + PS98;
|
||||
nextP(2,4) = -PS104*PS74 + PS106*PS72 + PS111*PS62 + PS113*PS60 - PS114*PS44 - PS116*PS46 + PS118*PS54 + PS119;
|
||||
nextP(3,4) = PS124*PS62 + PS125*PS72 + PS128*PS60 - PS129*PS74 - PS130*PS44 - PS132*PS46 + PS134*PS54 + PS135;
|
||||
nextP(4,4) = -PS139*PS142 + PS140*PS146 - PS141*PS44 - PS145*PS74 + PS149*PS72 + PS152*PS60 + PS155*PS62 + PS156*ecl::powf(PS54, 2) + PS157*ecl::powf(PS46, 2) + PS158 + ecl::powf(PS44, 2)*dvxVar;
|
||||
nextP(0,5) = -PS23*PS60 + PS26*PS62 + PS48*PS68 + PS52*PS58 + PS53*PS57 - PS55*PS65 - PS66*PS67 + PS69;
|
||||
nextP(1,5) = PS100 - PS60*PS92 + PS62*PS82 - PS65*PS96 - PS66*PS99 + PS68*PS95 + PS72*PS89 + PS74*PS80;
|
||||
nextP(2,5) = PS104*PS72 + PS106*PS74 - PS111*PS60 + PS113*PS62 + PS116*PS68 - PS117*PS65 - PS120*PS66 + PS121;
|
||||
nextP(3,5) = -PS124*PS60 + PS125*PS74 + PS128*PS62 + PS129*PS72 + PS132*PS68 - PS133*PS65 - PS136*PS66 + PS137;
|
||||
nextP(4,5) = -PS140*PS161 + PS142*PS160 + PS145*PS72 - PS146*PS65 + PS149*PS74 + PS152*PS62 - PS155*PS60 - PS157*PS46*PS68 - PS159*PS66 + PS162*PS163 + PS164;
|
||||
nextP(5,5) = PS157*ecl::powf(PS68, 2) + PS160*PS173 - PS162*PS170 - PS169*PS65 - PS172*PS60 + PS175*PS72 + PS177*PS74 + PS179*PS62 + PS180*ecl::powf(PS66, 2) + PS181 + ecl::powf(PS65, 2)*dvyVar;
|
||||
nextP(0,6) = PS23*PS74 - PS26*PS72 - PS47*PS70 + PS53*PS61 - PS56*PS71 + PS58*PS59 + PS67*PS73 + PS75;
|
||||
nextP(1,6) = PS101 + PS60*PS80 + PS62*PS89 - PS70*PS94 - PS71*PS97 - PS72*PS82 + PS73*PS99 + PS74*PS92;
|
||||
nextP(2,6) = PS104*PS62 + PS106*PS60 + PS111*PS74 - PS113*PS72 - PS115*PS70 - PS118*PS71 + PS120*PS73 + PS122;
|
||||
nextP(3,6) = PS124*PS74 + PS125*PS60 - PS128*PS72 + PS129*PS62 - PS131*PS70 - PS134*PS71 + PS136*PS73 + PS138;
|
||||
nextP(4,6) = PS139*PS167 - PS142*PS70 + PS145*PS62 - PS146*PS165 + PS149*PS60 - PS152*PS72 + PS155*PS74 - PS156*PS54*PS71 + PS159*PS73 - PS163*PS166 + PS168;
|
||||
nextP(5,6) = -PS160*PS167 + PS161*PS165 - PS165*PS169 + PS166*PS170 + PS172*PS74 - PS173*PS70 + PS175*PS62 + PS177*PS60 - PS179*PS72 - PS180*PS66*PS73 + PS182;
|
||||
nextP(6,6) = PS156*ecl::powf(PS71, 2) - PS165*PS184 + PS166*PS185 + PS180*ecl::powf(PS73, 2) - PS183*PS70 + PS186 + PS60*(P(0,0)*PS60 + P(0,13)*PS166 - P(0,14)*PS165 - P(0,15)*PS70 + P(0,3)*PS62 + P(0,6) - PS151 + PS171) + PS62*(P(0,3)*PS60 + P(3,13)*PS166 - P(3,14)*PS165 - P(3,15)*PS70 + P(3,3)*PS62 + P(3,6) + PS154 - PS178) + ecl::powf(PS70, 2)*dvzVar - PS72*(P(1,2)*PS74 + P(2,13)*PS166 - P(2,14)*PS165 - P(2,15)*PS70 - P(2,2)*PS72 + P(2,6) + PS147 + PS174) + PS74*(P(1,1)*PS74 + P(1,13)*PS166 - P(1,14)*PS165 - P(1,15)*PS70 - P(1,2)*PS72 + P(1,6) + PS143 + PS176);
|
||||
nextP(0,7) = P(0,7) - P(1,7)*PS11 - P(2,7)*PS12 - P(3,7)*PS13 + P(7,10)*PS6 + P(7,11)*PS7 + P(7,12)*PS9 + PS63*dt;
|
||||
nextP(1,7) = P(0,7)*PS11 + P(1,7) + P(2,7)*PS13 - P(3,7)*PS12 - P(7,10)*PS34 + P(7,11)*PS9 - P(7,12)*PS7 + PS98*dt;
|
||||
nextP(2,7) = P(0,7)*PS12 - P(1,7)*PS13 + P(2,7) + P(3,7)*PS11 - P(7,10)*PS9 - P(7,11)*PS34 + P(7,12)*PS6 + PS119*dt;
|
||||
nextP(3,7) = P(0,7)*PS13 + P(1,7)*PS12 - P(2,7)*PS11 + P(3,7) + P(7,10)*PS7 - P(7,11)*PS6 - P(7,12)*PS34 + PS135*dt;
|
||||
nextP(4,7) = P(0,7)*PS72 + P(1,7)*PS62 + P(2,7)*PS60 - P(3,7)*PS74 + P(4,7) - P(7,13)*PS44 + P(7,14)*PS140 - P(7,15)*PS139 + PS158*dt;
|
||||
nextP(5,7) = P(0,7)*PS74 - P(1,7)*PS60 + P(2,7)*PS62 + P(3,7)*PS72 + P(5,7) - P(7,13)*PS162 - P(7,14)*PS65 + P(7,15)*PS160 + dt*(P(0,4)*PS74 - P(1,4)*PS60 + P(2,4)*PS62 + P(3,4)*PS72 - P(4,13)*PS162 - P(4,14)*PS65 + P(4,15)*PS160 + P(4,5));
|
||||
nextP(6,7) = P(0,7)*PS60 + P(1,7)*PS74 - P(2,7)*PS72 + P(3,7)*PS62 + P(6,7) + P(7,13)*PS166 - P(7,14)*PS165 - P(7,15)*PS70 + dt*(P(0,4)*PS60 + P(1,4)*PS74 - P(2,4)*PS72 + P(3,4)*PS62 + P(4,13)*PS166 - P(4,14)*PS165 - P(4,15)*PS70 + P(4,6));
|
||||
nextP(7,7) = P(4,7)*dt + P(7,7) + dt*(P(4,4)*dt + P(4,7));
|
||||
nextP(0,8) = P(0,8) - P(1,8)*PS11 - P(2,8)*PS12 - P(3,8)*PS13 + P(8,10)*PS6 + P(8,11)*PS7 + P(8,12)*PS9 + PS69*dt;
|
||||
nextP(1,8) = P(0,8)*PS11 + P(1,8) + P(2,8)*PS13 - P(3,8)*PS12 - P(8,10)*PS34 + P(8,11)*PS9 - P(8,12)*PS7 + PS100*dt;
|
||||
nextP(2,8) = P(0,8)*PS12 - P(1,8)*PS13 + P(2,8) + P(3,8)*PS11 - P(8,10)*PS9 - P(8,11)*PS34 + P(8,12)*PS6 + PS121*dt;
|
||||
nextP(3,8) = P(0,8)*PS13 + P(1,8)*PS12 - P(2,8)*PS11 + P(3,8) + P(8,10)*PS7 - P(8,11)*PS6 - P(8,12)*PS34 + PS137*dt;
|
||||
nextP(4,8) = P(0,8)*PS72 + P(1,8)*PS62 + P(2,8)*PS60 - P(3,8)*PS74 + P(4,8) - P(8,13)*PS44 + P(8,14)*PS140 - P(8,15)*PS139 + PS164*dt;
|
||||
nextP(5,8) = P(0,8)*PS74 - P(1,8)*PS60 + P(2,8)*PS62 + P(3,8)*PS72 + P(5,8) - P(8,13)*PS162 - P(8,14)*PS65 + P(8,15)*PS160 + PS181*dt;
|
||||
nextP(6,8) = P(0,8)*PS60 + P(1,8)*PS74 - P(2,8)*PS72 + P(3,8)*PS62 + P(6,8) + P(8,13)*PS166 - P(8,14)*PS165 - P(8,15)*PS70 + dt*(P(0,5)*PS60 + P(1,5)*PS74 - P(2,5)*PS72 + P(3,5)*PS62 + P(5,13)*PS166 - P(5,14)*PS165 - P(5,15)*PS70 + P(5,6));
|
||||
nextP(7,8) = P(4,8)*dt + P(7,8) + dt*(P(4,5)*dt + P(5,7));
|
||||
nextP(8,8) = P(5,8)*dt + P(8,8) + dt*(P(5,5)*dt + P(5,8));
|
||||
nextP(0,9) = P(0,9) - P(1,9)*PS11 - P(2,9)*PS12 - P(3,9)*PS13 + P(9,10)*PS6 + P(9,11)*PS7 + P(9,12)*PS9 + PS75*dt;
|
||||
nextP(1,9) = P(0,9)*PS11 + P(1,9) + P(2,9)*PS13 - P(3,9)*PS12 - P(9,10)*PS34 + P(9,11)*PS9 - P(9,12)*PS7 + PS101*dt;
|
||||
nextP(2,9) = P(0,9)*PS12 - P(1,9)*PS13 + P(2,9) + P(3,9)*PS11 - P(9,10)*PS9 - P(9,11)*PS34 + P(9,12)*PS6 + PS122*dt;
|
||||
nextP(3,9) = P(0,9)*PS13 + P(1,9)*PS12 - P(2,9)*PS11 + P(3,9) + P(9,10)*PS7 - P(9,11)*PS6 - P(9,12)*PS34 + PS138*dt;
|
||||
nextP(4,9) = P(0,9)*PS72 + P(1,9)*PS62 + P(2,9)*PS60 - P(3,9)*PS74 + P(4,9) - P(9,13)*PS44 + P(9,14)*PS140 - P(9,15)*PS139 + PS168*dt;
|
||||
nextP(5,9) = P(0,9)*PS74 - P(1,9)*PS60 + P(2,9)*PS62 + P(3,9)*PS72 + P(5,9) - P(9,13)*PS162 - P(9,14)*PS65 + P(9,15)*PS160 + PS182*dt;
|
||||
nextP(6,9) = P(0,9)*PS60 + P(1,9)*PS74 - P(2,9)*PS72 + P(3,9)*PS62 + P(6,9) + P(9,13)*PS166 - P(9,14)*PS165 - P(9,15)*PS70 + PS186*dt;
|
||||
nextP(7,9) = P(4,9)*dt + P(7,9) + dt*(P(4,6)*dt + P(6,7));
|
||||
nextP(8,9) = P(5,9)*dt + P(8,9) + dt*(P(5,6)*dt + P(6,8));
|
||||
nextP(9,9) = P(6,9)*dt + P(9,9) + dt*(P(6,6)*dt + P(6,9));
|
||||
nextP(0,10) = PS14;
|
||||
nextP(1,10) = PS85;
|
||||
nextP(2,10) = PS109;
|
||||
nextP(3,10) = PS123;
|
||||
nextP(4,10) = P(0,10)*PS72 + P(1,10)*PS62 - P(10,13)*PS44 + P(10,14)*PS140 - P(10,15)*PS139 + P(2,10)*PS60 - P(3,10)*PS74 + P(4,10);
|
||||
nextP(5,10) = P(0,10)*PS74 - P(1,10)*PS60 - P(10,13)*PS162 - P(10,14)*PS65 + P(10,15)*PS160 + P(2,10)*PS62 + P(3,10)*PS72 + P(5,10);
|
||||
nextP(6,10) = P(0,10)*PS60 + P(1,10)*PS74 + P(10,13)*PS166 - P(10,14)*PS165 - P(10,15)*PS70 - P(2,10)*PS72 + P(3,10)*PS62 + P(6,10);
|
||||
nextP(7,10) = P(4,10)*dt + P(7,10);
|
||||
nextP(8,10) = P(5,10)*dt + P(8,10);
|
||||
nextP(9,10) = P(6,10)*dt + P(9,10);
|
||||
nextP(10,10) = P(10,10);
|
||||
nextP(0,11) = PS17;
|
||||
nextP(1,11) = PS77;
|
||||
nextP(2,11) = PS108;
|
||||
nextP(3,11) = PS127;
|
||||
nextP(4,11) = P(0,11)*PS72 + P(1,11)*PS62 - P(11,13)*PS44 + P(11,14)*PS140 - P(11,15)*PS139 + P(2,11)*PS60 - P(3,11)*PS74 + P(4,11);
|
||||
nextP(5,11) = P(0,11)*PS74 - P(1,11)*PS60 - P(11,13)*PS162 - P(11,14)*PS65 + P(11,15)*PS160 + P(2,11)*PS62 + P(3,11)*PS72 + P(5,11);
|
||||
nextP(6,11) = P(0,11)*PS60 + P(1,11)*PS74 + P(11,13)*PS166 - P(11,14)*PS165 - P(11,15)*PS70 - P(2,11)*PS72 + P(3,11)*PS62 + P(6,11);
|
||||
nextP(7,11) = P(4,11)*dt + P(7,11);
|
||||
nextP(8,11) = P(5,11)*dt + P(8,11);
|
||||
nextP(9,11) = P(6,11)*dt + P(9,11);
|
||||
nextP(10,11) = P(10,11);
|
||||
nextP(11,11) = P(11,11);
|
||||
nextP(0,12) = PS20;
|
||||
nextP(1,12) = PS87;
|
||||
nextP(2,12) = PS103;
|
||||
nextP(3,12) = PS126;
|
||||
nextP(4,12) = P(0,12)*PS72 + P(1,12)*PS62 - P(12,13)*PS44 + P(12,14)*PS140 - P(12,15)*PS139 + P(2,12)*PS60 - P(3,12)*PS74 + P(4,12);
|
||||
nextP(5,12) = P(0,12)*PS74 - P(1,12)*PS60 - P(12,13)*PS162 - P(12,14)*PS65 + P(12,15)*PS160 + P(2,12)*PS62 + P(3,12)*PS72 + P(5,12);
|
||||
nextP(6,12) = P(0,12)*PS60 + P(1,12)*PS74 + P(12,13)*PS166 - P(12,14)*PS165 - P(12,15)*PS70 - P(2,12)*PS72 + P(3,12)*PS62 + P(6,12);
|
||||
nextP(7,12) = P(4,12)*dt + P(7,12);
|
||||
nextP(8,12) = P(5,12)*dt + P(8,12);
|
||||
nextP(9,12) = P(6,12)*dt + P(9,12);
|
||||
nextP(10,12) = P(10,12);
|
||||
nextP(11,12) = P(11,12);
|
||||
nextP(12,12) = P(12,12);
|
||||
nextP(0,13) = PS45;
|
||||
nextP(1,13) = PS93;
|
||||
nextP(2,13) = PS114;
|
||||
nextP(3,13) = PS130;
|
||||
nextP(4,13) = PS141;
|
||||
nextP(5,13) = PS170;
|
||||
nextP(6,13) = PS185;
|
||||
nextP(7,13) = P(4,13)*dt + P(7,13);
|
||||
nextP(8,13) = P(5,13)*dt + P(8,13);
|
||||
nextP(9,13) = P(6,13)*dt + P(9,13);
|
||||
nextP(10,13) = P(10,13);
|
||||
nextP(11,13) = P(11,13);
|
||||
nextP(12,13) = P(12,13);
|
||||
nextP(13,13) = P(13,13);
|
||||
nextP(0,14) = PS55;
|
||||
nextP(1,14) = PS96;
|
||||
nextP(2,14) = PS117;
|
||||
nextP(3,14) = PS133;
|
||||
nextP(4,14) = PS146;
|
||||
nextP(5,14) = PS169;
|
||||
nextP(6,14) = PS184;
|
||||
nextP(7,14) = P(4,14)*dt + P(7,14);
|
||||
nextP(8,14) = P(5,14)*dt + P(8,14);
|
||||
nextP(9,14) = P(6,14)*dt + P(9,14);
|
||||
nextP(10,14) = P(10,14);
|
||||
nextP(11,14) = P(11,14);
|
||||
nextP(12,14) = P(12,14);
|
||||
nextP(13,14) = P(13,14);
|
||||
nextP(14,14) = P(14,14);
|
||||
nextP(0,15) = PS47;
|
||||
nextP(1,15) = PS94;
|
||||
nextP(2,15) = PS115;
|
||||
nextP(3,15) = PS131;
|
||||
nextP(4,15) = PS142;
|
||||
nextP(5,15) = PS173;
|
||||
nextP(6,15) = PS183;
|
||||
nextP(7,15) = P(4,15)*dt + P(7,15);
|
||||
nextP(8,15) = P(5,15)*dt + P(8,15);
|
||||
nextP(9,15) = P(6,15)*dt + P(9,15);
|
||||
nextP(10,15) = P(10,15);
|
||||
nextP(11,15) = P(11,15);
|
||||
nextP(12,15) = P(12,15);
|
||||
nextP(13,15) = P(13,15);
|
||||
nextP(14,15) = P(14,15);
|
||||
nextP(15,15) = P(15,15);
|
||||
nextP(0,16) = P(0,16) - P(1,16)*PS11 + P(10,16)*PS6 + P(11,16)*PS7 + P(12,16)*PS9 - P(2,16)*PS12 - P(3,16)*PS13;
|
||||
nextP(1,16) = P(0,16)*PS11 + P(1,16) - P(10,16)*PS34 + P(11,16)*PS9 - P(12,16)*PS7 + P(2,16)*PS13 - P(3,16)*PS12;
|
||||
nextP(2,16) = P(0,16)*PS12 - P(1,16)*PS13 - P(10,16)*PS9 - P(11,16)*PS34 + P(12,16)*PS6 + P(2,16) + P(3,16)*PS11;
|
||||
nextP(3,16) = P(0,16)*PS13 + P(1,16)*PS12 + P(10,16)*PS7 - P(11,16)*PS6 - P(12,16)*PS34 - P(2,16)*PS11 + P(3,16);
|
||||
nextP(4,16) = P(0,16)*PS72 + P(1,16)*PS62 - P(13,16)*PS44 + P(14,16)*PS140 - P(15,16)*PS139 + P(2,16)*PS60 - P(3,16)*PS74 + P(4,16);
|
||||
nextP(5,16) = P(0,16)*PS74 - P(1,16)*PS60 - P(13,16)*PS162 - P(14,16)*PS65 + P(15,16)*PS160 + P(2,16)*PS62 + P(3,16)*PS72 + P(5,16);
|
||||
nextP(6,16) = P(0,16)*PS60 + P(1,16)*PS74 + P(13,16)*PS166 - P(14,16)*PS165 - P(15,16)*PS70 - P(2,16)*PS72 + P(3,16)*PS62 + P(6,16);
|
||||
nextP(7,16) = P(4,16)*dt + P(7,16);
|
||||
nextP(8,16) = P(5,16)*dt + P(8,16);
|
||||
nextP(9,16) = P(6,16)*dt + P(9,16);
|
||||
nextP(10,16) = P(10,16);
|
||||
nextP(11,16) = P(11,16);
|
||||
nextP(12,16) = P(12,16);
|
||||
nextP(13,16) = P(13,16);
|
||||
nextP(14,16) = P(14,16);
|
||||
nextP(15,16) = P(15,16);
|
||||
nextP(16,16) = P(16,16);
|
||||
nextP(0,17) = P(0,17) - P(1,17)*PS11 + P(10,17)*PS6 + P(11,17)*PS7 + P(12,17)*PS9 - P(2,17)*PS12 - P(3,17)*PS13;
|
||||
nextP(1,17) = P(0,17)*PS11 + P(1,17) - P(10,17)*PS34 + P(11,17)*PS9 - P(12,17)*PS7 + P(2,17)*PS13 - P(3,17)*PS12;
|
||||
nextP(2,17) = P(0,17)*PS12 - P(1,17)*PS13 - P(10,17)*PS9 - P(11,17)*PS34 + P(12,17)*PS6 + P(2,17) + P(3,17)*PS11;
|
||||
nextP(3,17) = P(0,17)*PS13 + P(1,17)*PS12 + P(10,17)*PS7 - P(11,17)*PS6 - P(12,17)*PS34 - P(2,17)*PS11 + P(3,17);
|
||||
nextP(4,17) = P(0,17)*PS72 + P(1,17)*PS62 - P(13,17)*PS44 + P(14,17)*PS140 - P(15,17)*PS139 + P(2,17)*PS60 - P(3,17)*PS74 + P(4,17);
|
||||
nextP(5,17) = P(0,17)*PS74 - P(1,17)*PS60 - P(13,17)*PS162 - P(14,17)*PS65 + P(15,17)*PS160 + P(2,17)*PS62 + P(3,17)*PS72 + P(5,17);
|
||||
nextP(6,17) = P(0,17)*PS60 + P(1,17)*PS74 + P(13,17)*PS166 - P(14,17)*PS165 - P(15,17)*PS70 - P(2,17)*PS72 + P(3,17)*PS62 + P(6,17);
|
||||
nextP(7,17) = P(4,17)*dt + P(7,17);
|
||||
nextP(8,17) = P(5,17)*dt + P(8,17);
|
||||
nextP(9,17) = P(6,17)*dt + P(9,17);
|
||||
nextP(10,17) = P(10,17);
|
||||
nextP(11,17) = P(11,17);
|
||||
nextP(12,17) = P(12,17);
|
||||
nextP(13,17) = P(13,17);
|
||||
nextP(14,17) = P(14,17);
|
||||
nextP(15,17) = P(15,17);
|
||||
nextP(16,17) = P(16,17);
|
||||
nextP(17,17) = P(17,17);
|
||||
nextP(0,18) = P(0,18) - P(1,18)*PS11 + P(10,18)*PS6 + P(11,18)*PS7 + P(12,18)*PS9 - P(2,18)*PS12 - P(3,18)*PS13;
|
||||
nextP(1,18) = P(0,18)*PS11 + P(1,18) - P(10,18)*PS34 + P(11,18)*PS9 - P(12,18)*PS7 + P(2,18)*PS13 - P(3,18)*PS12;
|
||||
nextP(2,18) = P(0,18)*PS12 - P(1,18)*PS13 - P(10,18)*PS9 - P(11,18)*PS34 + P(12,18)*PS6 + P(2,18) + P(3,18)*PS11;
|
||||
nextP(3,18) = P(0,18)*PS13 + P(1,18)*PS12 + P(10,18)*PS7 - P(11,18)*PS6 - P(12,18)*PS34 - P(2,18)*PS11 + P(3,18);
|
||||
nextP(4,18) = P(0,18)*PS72 + P(1,18)*PS62 - P(13,18)*PS44 + P(14,18)*PS140 - P(15,18)*PS139 + P(2,18)*PS60 - P(3,18)*PS74 + P(4,18);
|
||||
nextP(5,18) = P(0,18)*PS74 - P(1,18)*PS60 - P(13,18)*PS162 - P(14,18)*PS65 + P(15,18)*PS160 + P(2,18)*PS62 + P(3,18)*PS72 + P(5,18);
|
||||
nextP(6,18) = P(0,18)*PS60 + P(1,18)*PS74 + P(13,18)*PS166 - P(14,18)*PS165 - P(15,18)*PS70 - P(2,18)*PS72 + P(3,18)*PS62 + P(6,18);
|
||||
nextP(7,18) = P(4,18)*dt + P(7,18);
|
||||
nextP(8,18) = P(5,18)*dt + P(8,18);
|
||||
nextP(9,18) = P(6,18)*dt + P(9,18);
|
||||
nextP(10,18) = P(10,18);
|
||||
nextP(11,18) = P(11,18);
|
||||
nextP(12,18) = P(12,18);
|
||||
nextP(13,18) = P(13,18);
|
||||
nextP(14,18) = P(14,18);
|
||||
nextP(15,18) = P(15,18);
|
||||
nextP(16,18) = P(16,18);
|
||||
nextP(17,18) = P(17,18);
|
||||
nextP(18,18) = P(18,18);
|
||||
nextP(0,19) = P(0,19) - P(1,19)*PS11 + P(10,19)*PS6 + P(11,19)*PS7 + P(12,19)*PS9 - P(2,19)*PS12 - P(3,19)*PS13;
|
||||
nextP(1,19) = P(0,19)*PS11 + P(1,19) - P(10,19)*PS34 + P(11,19)*PS9 - P(12,19)*PS7 + P(2,19)*PS13 - P(3,19)*PS12;
|
||||
nextP(2,19) = P(0,19)*PS12 - P(1,19)*PS13 - P(10,19)*PS9 - P(11,19)*PS34 + P(12,19)*PS6 + P(2,19) + P(3,19)*PS11;
|
||||
nextP(3,19) = P(0,19)*PS13 + P(1,19)*PS12 + P(10,19)*PS7 - P(11,19)*PS6 - P(12,19)*PS34 - P(2,19)*PS11 + P(3,19);
|
||||
nextP(4,19) = P(0,19)*PS72 + P(1,19)*PS62 - P(13,19)*PS44 + P(14,19)*PS140 - P(15,19)*PS139 + P(2,19)*PS60 - P(3,19)*PS74 + P(4,19);
|
||||
nextP(5,19) = P(0,19)*PS74 - P(1,19)*PS60 - P(13,19)*PS162 - P(14,19)*PS65 + P(15,19)*PS160 + P(2,19)*PS62 + P(3,19)*PS72 + P(5,19);
|
||||
nextP(6,19) = P(0,19)*PS60 + P(1,19)*PS74 + P(13,19)*PS166 - P(14,19)*PS165 - P(15,19)*PS70 - P(2,19)*PS72 + P(3,19)*PS62 + P(6,19);
|
||||
nextP(7,19) = P(4,19)*dt + P(7,19);
|
||||
nextP(8,19) = P(5,19)*dt + P(8,19);
|
||||
nextP(9,19) = P(6,19)*dt + P(9,19);
|
||||
nextP(10,19) = P(10,19);
|
||||
nextP(11,19) = P(11,19);
|
||||
nextP(12,19) = P(12,19);
|
||||
nextP(13,19) = P(13,19);
|
||||
nextP(14,19) = P(14,19);
|
||||
nextP(15,19) = P(15,19);
|
||||
nextP(16,19) = P(16,19);
|
||||
nextP(17,19) = P(17,19);
|
||||
nextP(18,19) = P(18,19);
|
||||
nextP(19,19) = P(19,19);
|
||||
nextP(0,20) = P(0,20) - P(1,20)*PS11 + P(10,20)*PS6 + P(11,20)*PS7 + P(12,20)*PS9 - P(2,20)*PS12 - P(3,20)*PS13;
|
||||
nextP(1,20) = P(0,20)*PS11 + P(1,20) - P(10,20)*PS34 + P(11,20)*PS9 - P(12,20)*PS7 + P(2,20)*PS13 - P(3,20)*PS12;
|
||||
nextP(2,20) = P(0,20)*PS12 - P(1,20)*PS13 - P(10,20)*PS9 - P(11,20)*PS34 + P(12,20)*PS6 + P(2,20) + P(3,20)*PS11;
|
||||
nextP(3,20) = P(0,20)*PS13 + P(1,20)*PS12 + P(10,20)*PS7 - P(11,20)*PS6 - P(12,20)*PS34 - P(2,20)*PS11 + P(3,20);
|
||||
nextP(4,20) = P(0,20)*PS72 + P(1,20)*PS62 - P(13,20)*PS44 + P(14,20)*PS140 - P(15,20)*PS139 + P(2,20)*PS60 - P(3,20)*PS74 + P(4,20);
|
||||
nextP(5,20) = P(0,20)*PS74 - P(1,20)*PS60 - P(13,20)*PS162 - P(14,20)*PS65 + P(15,20)*PS160 + P(2,20)*PS62 + P(3,20)*PS72 + P(5,20);
|
||||
nextP(6,20) = P(0,20)*PS60 + P(1,20)*PS74 + P(13,20)*PS166 - P(14,20)*PS165 - P(15,20)*PS70 - P(2,20)*PS72 + P(3,20)*PS62 + P(6,20);
|
||||
nextP(7,20) = P(4,20)*dt + P(7,20);
|
||||
nextP(8,20) = P(5,20)*dt + P(8,20);
|
||||
nextP(9,20) = P(6,20)*dt + P(9,20);
|
||||
nextP(10,20) = P(10,20);
|
||||
nextP(11,20) = P(11,20);
|
||||
nextP(12,20) = P(12,20);
|
||||
nextP(13,20) = P(13,20);
|
||||
nextP(14,20) = P(14,20);
|
||||
nextP(15,20) = P(15,20);
|
||||
nextP(16,20) = P(16,20);
|
||||
nextP(17,20) = P(17,20);
|
||||
nextP(18,20) = P(18,20);
|
||||
nextP(19,20) = P(19,20);
|
||||
nextP(20,20) = P(20,20);
|
||||
nextP(0,21) = P(0,21) - P(1,21)*PS11 + P(10,21)*PS6 + P(11,21)*PS7 + P(12,21)*PS9 - P(2,21)*PS12 - P(3,21)*PS13;
|
||||
nextP(1,21) = P(0,21)*PS11 + P(1,21) - P(10,21)*PS34 + P(11,21)*PS9 - P(12,21)*PS7 + P(2,21)*PS13 - P(3,21)*PS12;
|
||||
nextP(2,21) = P(0,21)*PS12 - P(1,21)*PS13 - P(10,21)*PS9 - P(11,21)*PS34 + P(12,21)*PS6 + P(2,21) + P(3,21)*PS11;
|
||||
nextP(3,21) = P(0,21)*PS13 + P(1,21)*PS12 + P(10,21)*PS7 - P(11,21)*PS6 - P(12,21)*PS34 - P(2,21)*PS11 + P(3,21);
|
||||
nextP(4,21) = P(0,21)*PS72 + P(1,21)*PS62 - P(13,21)*PS44 + P(14,21)*PS140 - P(15,21)*PS139 + P(2,21)*PS60 - P(3,21)*PS74 + P(4,21);
|
||||
nextP(5,21) = P(0,21)*PS74 - P(1,21)*PS60 - P(13,21)*PS162 - P(14,21)*PS65 + P(15,21)*PS160 + P(2,21)*PS62 + P(3,21)*PS72 + P(5,21);
|
||||
nextP(6,21) = P(0,21)*PS60 + P(1,21)*PS74 + P(13,21)*PS166 - P(14,21)*PS165 - P(15,21)*PS70 - P(2,21)*PS72 + P(3,21)*PS62 + P(6,21);
|
||||
nextP(7,21) = P(4,21)*dt + P(7,21);
|
||||
nextP(8,21) = P(5,21)*dt + P(8,21);
|
||||
nextP(9,21) = P(6,21)*dt + P(9,21);
|
||||
nextP(10,21) = P(10,21);
|
||||
nextP(11,21) = P(11,21);
|
||||
nextP(12,21) = P(12,21);
|
||||
nextP(13,21) = P(13,21);
|
||||
nextP(14,21) = P(14,21);
|
||||
nextP(15,21) = P(15,21);
|
||||
nextP(16,21) = P(16,21);
|
||||
nextP(17,21) = P(17,21);
|
||||
nextP(18,21) = P(18,21);
|
||||
nextP(19,21) = P(19,21);
|
||||
nextP(20,21) = P(20,21);
|
||||
nextP(21,21) = P(21,21);
|
||||
nextP(0,22) = P(0,22) - P(1,22)*PS11 + P(10,22)*PS6 + P(11,22)*PS7 + P(12,22)*PS9 - P(2,22)*PS12 - P(3,22)*PS13;
|
||||
nextP(1,22) = P(0,22)*PS11 + P(1,22) - P(10,22)*PS34 + P(11,22)*PS9 - P(12,22)*PS7 + P(2,22)*PS13 - P(3,22)*PS12;
|
||||
nextP(2,22) = P(0,22)*PS12 - P(1,22)*PS13 - P(10,22)*PS9 - P(11,22)*PS34 + P(12,22)*PS6 + P(2,22) + P(3,22)*PS11;
|
||||
nextP(3,22) = P(0,22)*PS13 + P(1,22)*PS12 + P(10,22)*PS7 - P(11,22)*PS6 - P(12,22)*PS34 - P(2,22)*PS11 + P(3,22);
|
||||
nextP(4,22) = P(0,22)*PS72 + P(1,22)*PS62 - P(13,22)*PS44 + P(14,22)*PS140 - P(15,22)*PS139 + P(2,22)*PS60 - P(3,22)*PS74 + P(4,22);
|
||||
nextP(5,22) = P(0,22)*PS74 - P(1,22)*PS60 - P(13,22)*PS162 - P(14,22)*PS65 + P(15,22)*PS160 + P(2,22)*PS62 + P(3,22)*PS72 + P(5,22);
|
||||
nextP(6,22) = P(0,22)*PS60 + P(1,22)*PS74 + P(13,22)*PS166 - P(14,22)*PS165 - P(15,22)*PS70 - P(2,22)*PS72 + P(3,22)*PS62 + P(6,22);
|
||||
nextP(7,22) = P(4,22)*dt + P(7,22);
|
||||
nextP(8,22) = P(5,22)*dt + P(8,22);
|
||||
nextP(9,22) = P(6,22)*dt + P(9,22);
|
||||
nextP(10,22) = P(10,22);
|
||||
nextP(11,22) = P(11,22);
|
||||
nextP(12,22) = P(12,22);
|
||||
nextP(13,22) = P(13,22);
|
||||
nextP(14,22) = P(14,22);
|
||||
nextP(15,22) = P(15,22);
|
||||
nextP(16,22) = P(16,22);
|
||||
nextP(17,22) = P(17,22);
|
||||
nextP(18,22) = P(18,22);
|
||||
nextP(19,22) = P(19,22);
|
||||
nextP(20,22) = P(20,22);
|
||||
nextP(21,22) = P(21,22);
|
||||
nextP(22,22) = P(22,22);
|
||||
nextP(0,23) = P(0,23) - P(1,23)*PS11 + P(10,23)*PS6 + P(11,23)*PS7 + P(12,23)*PS9 - P(2,23)*PS12 - P(3,23)*PS13;
|
||||
nextP(1,23) = P(0,23)*PS11 + P(1,23) - P(10,23)*PS34 + P(11,23)*PS9 - P(12,23)*PS7 + P(2,23)*PS13 - P(3,23)*PS12;
|
||||
nextP(2,23) = P(0,23)*PS12 - P(1,23)*PS13 - P(10,23)*PS9 - P(11,23)*PS34 + P(12,23)*PS6 + P(2,23) + P(3,23)*PS11;
|
||||
nextP(3,23) = P(0,23)*PS13 + P(1,23)*PS12 + P(10,23)*PS7 - P(11,23)*PS6 - P(12,23)*PS34 - P(2,23)*PS11 + P(3,23);
|
||||
nextP(4,23) = P(0,23)*PS72 + P(1,23)*PS62 - P(13,23)*PS44 + P(14,23)*PS140 - P(15,23)*PS139 + P(2,23)*PS60 - P(3,23)*PS74 + P(4,23);
|
||||
nextP(5,23) = P(0,23)*PS74 - P(1,23)*PS60 - P(13,23)*PS162 - P(14,23)*PS65 + P(15,23)*PS160 + P(2,23)*PS62 + P(3,23)*PS72 + P(5,23);
|
||||
nextP(6,23) = P(0,23)*PS60 + P(1,23)*PS74 + P(13,23)*PS166 - P(14,23)*PS165 - P(15,23)*PS70 - P(2,23)*PS72 + P(3,23)*PS62 + P(6,23);
|
||||
nextP(7,23) = P(4,23)*dt + P(7,23);
|
||||
nextP(8,23) = P(5,23)*dt + P(8,23);
|
||||
nextP(9,23) = P(6,23)*dt + P(9,23);
|
||||
nextP(10,23) = P(10,23);
|
||||
nextP(11,23) = P(11,23);
|
||||
nextP(12,23) = P(12,23);
|
||||
nextP(13,23) = P(13,23);
|
||||
nextP(14,23) = P(14,23);
|
||||
nextP(15,23) = P(15,23);
|
||||
nextP(16,23) = P(16,23);
|
||||
nextP(17,23) = P(17,23);
|
||||
nextP(18,23) = P(18,23);
|
||||
nextP(19,23) = P(19,23);
|
||||
nextP(20,23) = P(20,23);
|
||||
nextP(21,23) = P(21,23);
|
||||
nextP(22,23) = P(22,23);
|
||||
nextP(23,23) = P(23,23);
|
||||
|
||||
// save output and repeat calculation using legacy matlab generated code
|
||||
SquareMatrix24f nextP_sympy;
|
||||
for (int col=0; col<=23; col++) {
|
||||
for (int row=0; row<=col; row++) {
|
||||
nextP_sympy(row,col) = nextP(row,col);
|
||||
}
|
||||
}
|
||||
|
||||
// intermediate calculations
|
||||
float SF[21];
|
||||
SF[0] = dvz - dvz_b;
|
||||
SF[1] = dvy - dvy_b;
|
||||
SF[2] = dvx - dvx_b;
|
||||
SF[3] = 2*q1*SF[2] + 2*q2*SF[1] + 2*q3*SF[0];
|
||||
SF[4] = 2*q0*SF[1] - 2*q1*SF[0] + 2*q3*SF[2];
|
||||
SF[5] = 2*q0*SF[2] + 2*q2*SF[0] - 2*q3*SF[1];
|
||||
SF[6] = day*0.5f - day_b*0.5f;
|
||||
SF[7] = daz*0.5f - daz_b*0.5f;
|
||||
SF[8] = dax*0.5f - dax_b*0.5f;
|
||||
SF[9] = dax_b*0.5f - dax*0.5f;
|
||||
SF[10] = daz_b*0.5f - daz*0.5f;
|
||||
SF[11] = day_b*0.5f - day*0.5f;
|
||||
SF[12] = 2*q1*SF[1];
|
||||
SF[13] = 2*q0*SF[0];
|
||||
SF[14] = q1*0.5f;
|
||||
SF[15] = q2*0.5f;
|
||||
SF[16] = q3*0.5f;
|
||||
SF[17] = sq(q3);
|
||||
SF[18] = sq(q2);
|
||||
SF[19] = sq(q1);
|
||||
SF[20] = sq(q0);
|
||||
|
||||
float SG[8];
|
||||
SG[0] = q0*0.5f;
|
||||
SG[1] = sq(q3);
|
||||
SG[2] = sq(q2);
|
||||
SG[3] = sq(q1);
|
||||
SG[4] = sq(q0);
|
||||
SG[5] = 2*q2*q3;
|
||||
SG[6] = 2*q1*q3;
|
||||
SG[7] = 2*q1*q2;
|
||||
|
||||
float SQ[11];
|
||||
SQ[0] = dvzVar*(SG[5] - 2*q0*q1)*(SG[1] - SG[2] - SG[3] + SG[4]) - dvyVar*(SG[5] + 2*q0*q1)*(SG[1] - SG[2] + SG[3] - SG[4]) + dvxVar*(SG[6] - 2*q0*q2)*(SG[7] + 2*q0*q3);
|
||||
SQ[1] = dvzVar*(SG[6] + 2*q0*q2)*(SG[1] - SG[2] - SG[3] + SG[4]) - dvxVar*(SG[6] - 2*q0*q2)*(SG[1] + SG[2] - SG[3] - SG[4]) + dvyVar*(SG[5] + 2*q0*q1)*(SG[7] - 2*q0*q3);
|
||||
SQ[2] = dvzVar*(SG[5] - 2*q0*q1)*(SG[6] + 2*q0*q2) - dvyVar*(SG[7] - 2*q0*q3)*(SG[1] - SG[2] + SG[3] - SG[4]) - dvxVar*(SG[7] + 2*q0*q3)*(SG[1] + SG[2] - SG[3] - SG[4]);
|
||||
SQ[3] = (dayVar*q1*SG[0])*0.5f - (dazVar*q1*SG[0])*0.5f - (daxVar*q2*q3)*0.25f;
|
||||
SQ[4] = (dazVar*q2*SG[0])*0.5f - (daxVar*q2*SG[0])*0.5f - (dayVar*q1*q3)*0.25f;
|
||||
SQ[5] = (daxVar*q3*SG[0])*0.5f - (dayVar*q3*SG[0])*0.5f - (dazVar*q1*q2)*0.25f;
|
||||
SQ[6] = (daxVar*q1*q2)*0.25f - (dazVar*q3*SG[0])*0.5f - (dayVar*q1*q2)*0.25f;
|
||||
SQ[7] = (dazVar*q1*q3)*0.25f - (daxVar*q1*q3)*0.25f - (dayVar*q2*SG[0])*0.5f;
|
||||
SQ[8] = (dayVar*q2*q3)*0.25f - (daxVar*q1*SG[0])*0.5f - (dazVar*q2*q3)*0.25f;
|
||||
SQ[9] = sq(SG[0]);
|
||||
SQ[10] = sq(q1);
|
||||
|
||||
float SPP[11];
|
||||
SPP[0] = SF[12] + SF[13] - 2*q2*SF[2];
|
||||
SPP[1] = SF[17] - SF[18] - SF[19] + SF[20];
|
||||
SPP[2] = SF[17] - SF[18] + SF[19] - SF[20];
|
||||
SPP[3] = SF[17] + SF[18] - SF[19] - SF[20];
|
||||
SPP[4] = 2*q0*q2 - 2*q1*q3;
|
||||
SPP[5] = 2*q0*q1 - 2*q2*q3;
|
||||
SPP[6] = 2*q0*q3 - 2*q1*q2;
|
||||
SPP[7] = 2*q0*q1 + 2*q2*q3;
|
||||
SPP[8] = 2*q0*q3 + 2*q1*q2;
|
||||
SPP[9] = 2*q0*q2 + 2*q1*q3;
|
||||
SPP[10] = SF[16];
|
||||
|
||||
// calculate variances and upper diagonal covariances for quaternion, velocity, position and gyro bias states
|
||||
nextP(0,0) = P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10] + (daxVar*SQ[10])*0.25f + SF[9]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) + SF[11]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[10]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) + SF[14]*(P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10]) + SF[15]*(P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10]) + SPP[10]*(P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10]) + (dayVar*sq(q2))*0.25f + (dazVar*sq(q3))*0.25f;
|
||||
nextP(0,1) = P(0,1) + SQ[8] + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10] + SF[8]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[7]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[11]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) - SF[15]*(P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10]) + SPP[10]*(P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10]) - (q0*(P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10]))*0.5f;
|
||||
nextP(1,1) = P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] + daxVar*SQ[9] - (P(10,1)*q0)*0.5f + SF[8]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[7]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SF[11]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) - SF[15]*(P(1,12) + P(0,12)*SF[8] + P(2,12)*SF[7] + P(3,12)*SF[11] - P(12,12)*SF[15] + P(11,12)*SPP[10] - (P(10,12)*q0)*0.5f) + SPP[10]*(P(1,11) + P(0,11)*SF[8] + P(2,11)*SF[7] + P(3,11)*SF[11] - P(12,11)*SF[15] + P(11,11)*SPP[10] - (P(10,11)*q0)*0.5f) + (dayVar*sq(q3))*0.25f + (dazVar*sq(q2))*0.25f - (q0*(P(1,10) + P(0,10)*SF[8] + P(2,10)*SF[7] + P(3,10)*SF[11] - P(12,10)*SF[15] + P(11,10)*SPP[10] - (P(10,10)*q0)*0.5f))*0.5f;
|
||||
nextP(0,2) = P(0,2) + SQ[7] + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10] + SF[6]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[10]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) + SF[8]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) + SF[14]*(P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10]) - SPP[10]*(P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10]) - (q0*(P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10]))*0.5f;
|
||||
nextP(1,2) = P(1,2) + SQ[5] + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f + SF[6]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[10]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) + SF[8]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) + SF[14]*(P(1,12) + P(0,12)*SF[8] + P(2,12)*SF[7] + P(3,12)*SF[11] - P(12,12)*SF[15] + P(11,12)*SPP[10] - (P(10,12)*q0)*0.5f) - SPP[10]*(P(1,10) + P(0,10)*SF[8] + P(2,10)*SF[7] + P(3,10)*SF[11] - P(12,10)*SF[15] + P(11,10)*SPP[10] - (P(10,10)*q0)*0.5f) - (q0*(P(1,11) + P(0,11)*SF[8] + P(2,11)*SF[7] + P(3,11)*SF[11] - P(12,11)*SF[15] + P(11,11)*SPP[10] - (P(10,11)*q0)*0.5f))*0.5f;
|
||||
nextP(2,2) = P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] + dayVar*SQ[9] + (dazVar*SQ[10])*0.25f - (P(11,2)*q0)*0.5f + SF[6]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SF[10]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) + SF[8]*(P(2,3) + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f) + SF[14]*(P(2,12) + P(0,12)*SF[6] + P(1,12)*SF[10] + P(3,12)*SF[8] + P(12,12)*SF[14] - P(10,12)*SPP[10] - (P(11,12)*q0)*0.5f) - SPP[10]*(P(2,10) + P(0,10)*SF[6] + P(1,10)*SF[10] + P(3,10)*SF[8] + P(12,10)*SF[14] - P(10,10)*SPP[10] - (P(11,10)*q0)*0.5f) + (daxVar*sq(q3))*0.25f - (q0*(P(2,11) + P(0,11)*SF[6] + P(1,11)*SF[10] + P(3,11)*SF[8] + P(12,11)*SF[14] - P(10,11)*SPP[10] - (P(11,11)*q0)*0.5f))*0.5f;
|
||||
nextP(0,3) = P(0,3) + SQ[6] + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10] + SF[7]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[6]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) + SF[9]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[15]*(P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10]) - SF[14]*(P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10]) - (q0*(P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10]))*0.5f;
|
||||
nextP(1,3) = P(1,3) + SQ[4] + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f + SF[7]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[6]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) + SF[9]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SF[15]*(P(1,10) + P(0,10)*SF[8] + P(2,10)*SF[7] + P(3,10)*SF[11] - P(12,10)*SF[15] + P(11,10)*SPP[10] - (P(10,10)*q0)*0.5f) - SF[14]*(P(1,11) + P(0,11)*SF[8] + P(2,11)*SF[7] + P(3,11)*SF[11] - P(12,11)*SF[15] + P(11,11)*SPP[10] - (P(10,11)*q0)*0.5f) - (q0*(P(1,12) + P(0,12)*SF[8] + P(2,12)*SF[7] + P(3,12)*SF[11] - P(12,12)*SF[15] + P(11,12)*SPP[10] - (P(10,12)*q0)*0.5f))*0.5f;
|
||||
nextP(2,3) = P(2,3) + SQ[3] + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f + SF[7]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SF[6]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) + SF[9]*(P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] - (P(11,2)*q0)*0.5f) + SF[15]*(P(2,10) + P(0,10)*SF[6] + P(1,10)*SF[10] + P(3,10)*SF[8] + P(12,10)*SF[14] - P(10,10)*SPP[10] - (P(11,10)*q0)*0.5f) - SF[14]*(P(2,11) + P(0,11)*SF[6] + P(1,11)*SF[10] + P(3,11)*SF[8] + P(12,11)*SF[14] - P(10,11)*SPP[10] - (P(11,11)*q0)*0.5f) - (q0*(P(2,12) + P(0,12)*SF[6] + P(1,12)*SF[10] + P(3,12)*SF[8] + P(12,12)*SF[14] - P(10,12)*SPP[10] - (P(11,12)*q0)*0.5f))*0.5f;
|
||||
nextP(3,3) = P(3,3) + P(0,3)*SF[7] + P(1,3)*SF[6] + P(2,3)*SF[9] + P(10,3)*SF[15] - P(11,3)*SF[14] + (dayVar*SQ[10])*0.25f + dazVar*SQ[9] - (P(12,3)*q0)*0.5f + SF[7]*(P(3,0) + P(0,0)*SF[7] + P(1,0)*SF[6] + P(2,0)*SF[9] + P(10,0)*SF[15] - P(11,0)*SF[14] - (P(12,0)*q0)*0.5f) + SF[6]*(P(3,1) + P(0,1)*SF[7] + P(1,1)*SF[6] + P(2,1)*SF[9] + P(10,1)*SF[15] - P(11,1)*SF[14] - (P(12,1)*q0)*0.5f) + SF[9]*(P(3,2) + P(0,2)*SF[7] + P(1,2)*SF[6] + P(2,2)*SF[9] + P(10,2)*SF[15] - P(11,2)*SF[14] - (P(12,2)*q0)*0.5f) + SF[15]*(P(3,10) + P(0,10)*SF[7] + P(1,10)*SF[6] + P(2,10)*SF[9] + P(10,10)*SF[15] - P(11,10)*SF[14] - (P(12,10)*q0)*0.5f) - SF[14]*(P(3,11) + P(0,11)*SF[7] + P(1,11)*SF[6] + P(2,11)*SF[9] + P(10,11)*SF[15] - P(11,11)*SF[14] - (P(12,11)*q0)*0.5f) + (daxVar*sq(q2))*0.25f - (q0*(P(3,12) + P(0,12)*SF[7] + P(1,12)*SF[6] + P(2,12)*SF[9] + P(10,12)*SF[15] - P(11,12)*SF[14] - (P(12,12)*q0)*0.5f))*0.5f;
|
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nextP(0,4) = P(0,4) + P(1,4)*SF[9] + P(2,4)*SF[11] + P(3,4)*SF[10] + P(10,4)*SF[14] + P(11,4)*SF[15] + P(12,4)*SPP[10] + SF[5]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[3]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) - SF[4]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) + SPP[0]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SPP[3]*(P(0,13) + P(1,13)*SF[9] + P(2,13)*SF[11] + P(3,13)*SF[10] + P(10,13)*SF[14] + P(11,13)*SF[15] + P(12,13)*SPP[10]) + SPP[6]*(P(0,14) + P(1,14)*SF[9] + P(2,14)*SF[11] + P(3,14)*SF[10] + P(10,14)*SF[14] + P(11,14)*SF[15] + P(12,14)*SPP[10]) - SPP[9]*(P(0,15) + P(1,15)*SF[9] + P(2,15)*SF[11] + P(3,15)*SF[10] + P(10,15)*SF[14] + P(11,15)*SF[15] + P(12,15)*SPP[10]);
|
||||
nextP(1,4) = P(1,4) + P(0,4)*SF[8] + P(2,4)*SF[7] + P(3,4)*SF[11] - P(12,4)*SF[15] + P(11,4)*SPP[10] - (P(10,4)*q0)*0.5f + SF[5]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[3]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) - SF[4]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) + SPP[0]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SPP[3]*(P(1,13) + P(0,13)*SF[8] + P(2,13)*SF[7] + P(3,13)*SF[11] - P(12,13)*SF[15] + P(11,13)*SPP[10] - (P(10,13)*q0)*0.5f) + SPP[6]*(P(1,14) + P(0,14)*SF[8] + P(2,14)*SF[7] + P(3,14)*SF[11] - P(12,14)*SF[15] + P(11,14)*SPP[10] - (P(10,14)*q0)*0.5f) - SPP[9]*(P(1,15) + P(0,15)*SF[8] + P(2,15)*SF[7] + P(3,15)*SF[11] - P(12,15)*SF[15] + P(11,15)*SPP[10] - (P(10,15)*q0)*0.5f);
|
||||
nextP(2,4) = P(2,4) + P(0,4)*SF[6] + P(1,4)*SF[10] + P(3,4)*SF[8] + P(12,4)*SF[14] - P(10,4)*SPP[10] - (P(11,4)*q0)*0.5f + SF[5]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SF[3]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) - SF[4]*(P(2,3) + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f) + SPP[0]*(P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] - (P(11,2)*q0)*0.5f) + SPP[3]*(P(2,13) + P(0,13)*SF[6] + P(1,13)*SF[10] + P(3,13)*SF[8] + P(12,13)*SF[14] - P(10,13)*SPP[10] - (P(11,13)*q0)*0.5f) + SPP[6]*(P(2,14) + P(0,14)*SF[6] + P(1,14)*SF[10] + P(3,14)*SF[8] + P(12,14)*SF[14] - P(10,14)*SPP[10] - (P(11,14)*q0)*0.5f) - SPP[9]*(P(2,15) + P(0,15)*SF[6] + P(1,15)*SF[10] + P(3,15)*SF[8] + P(12,15)*SF[14] - P(10,15)*SPP[10] - (P(11,15)*q0)*0.5f);
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nextP(3,4) = P(3,4) + P(0,4)*SF[7] + P(1,4)*SF[6] + P(2,4)*SF[9] + P(10,4)*SF[15] - P(11,4)*SF[14] - (P(12,4)*q0)*0.5f + SF[5]*(P(3,0) + P(0,0)*SF[7] + P(1,0)*SF[6] + P(2,0)*SF[9] + P(10,0)*SF[15] - P(11,0)*SF[14] - (P(12,0)*q0)*0.5f) + SF[3]*(P(3,1) + P(0,1)*SF[7] + P(1,1)*SF[6] + P(2,1)*SF[9] + P(10,1)*SF[15] - P(11,1)*SF[14] - (P(12,1)*q0)*0.5f) - SF[4]*(P(3,3) + P(0,3)*SF[7] + P(1,3)*SF[6] + P(2,3)*SF[9] + P(10,3)*SF[15] - P(11,3)*SF[14] - (P(12,3)*q0)*0.5f) + SPP[0]*(P(3,2) + P(0,2)*SF[7] + P(1,2)*SF[6] + P(2,2)*SF[9] + P(10,2)*SF[15] - P(11,2)*SF[14] - (P(12,2)*q0)*0.5f) + SPP[3]*(P(3,13) + P(0,13)*SF[7] + P(1,13)*SF[6] + P(2,13)*SF[9] + P(10,13)*SF[15] - P(11,13)*SF[14] - (P(12,13)*q0)*0.5f) + SPP[6]*(P(3,14) + P(0,14)*SF[7] + P(1,14)*SF[6] + P(2,14)*SF[9] + P(10,14)*SF[15] - P(11,14)*SF[14] - (P(12,14)*q0)*0.5f) - SPP[9]*(P(3,15) + P(0,15)*SF[7] + P(1,15)*SF[6] + P(2,15)*SF[9] + P(10,15)*SF[15] - P(11,15)*SF[14] - (P(12,15)*q0)*0.5f);
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nextP(4,4) = P(4,4) + P(0,4)*SF[5] + P(1,4)*SF[3] - P(3,4)*SF[4] + P(2,4)*SPP[0] + P(13,4)*SPP[3] + P(14,4)*SPP[6] - P(15,4)*SPP[9] + dvyVar*sq(SG[7] - 2*q0*q3) + dvzVar*sq(SG[6] + 2*q0*q2) + SF[5]*(P(4,0) + P(0,0)*SF[5] + P(1,0)*SF[3] - P(3,0)*SF[4] + P(2,0)*SPP[0] + P(13,0)*SPP[3] + P(14,0)*SPP[6] - P(15,0)*SPP[9]) + SF[3]*(P(4,1) + P(0,1)*SF[5] + P(1,1)*SF[3] - P(3,1)*SF[4] + P(2,1)*SPP[0] + P(13,1)*SPP[3] + P(14,1)*SPP[6] - P(15,1)*SPP[9]) - SF[4]*(P(4,3) + P(0,3)*SF[5] + P(1,3)*SF[3] - P(3,3)*SF[4] + P(2,3)*SPP[0] + P(13,3)*SPP[3] + P(14,3)*SPP[6] - P(15,3)*SPP[9]) + SPP[0]*(P(4,2) + P(0,2)*SF[5] + P(1,2)*SF[3] - P(3,2)*SF[4] + P(2,2)*SPP[0] + P(13,2)*SPP[3] + P(14,2)*SPP[6] - P(15,2)*SPP[9]) + SPP[3]*(P(4,13) + P(0,13)*SF[5] + P(1,13)*SF[3] - P(3,13)*SF[4] + P(2,13)*SPP[0] + P(13,13)*SPP[3] + P(14,13)*SPP[6] - P(15,13)*SPP[9]) + SPP[6]*(P(4,14) + P(0,14)*SF[5] + P(1,14)*SF[3] - P(3,14)*SF[4] + P(2,14)*SPP[0] + P(13,14)*SPP[3] + P(14,14)*SPP[6] - P(15,14)*SPP[9]) - SPP[9]*(P(4,15) + P(0,15)*SF[5] + P(1,15)*SF[3] - P(3,15)*SF[4] + P(2,15)*SPP[0] + P(13,15)*SPP[3] + P(14,15)*SPP[6] - P(15,15)*SPP[9]) + dvxVar*sq(SG[1] + SG[2] - SG[3] - SG[4]);
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nextP(0,5) = P(0,5) + P(1,5)*SF[9] + P(2,5)*SF[11] + P(3,5)*SF[10] + P(10,5)*SF[14] + P(11,5)*SF[15] + P(12,5)*SPP[10] + SF[4]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SF[3]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[5]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) - SPP[0]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) - SPP[8]*(P(0,13) + P(1,13)*SF[9] + P(2,13)*SF[11] + P(3,13)*SF[10] + P(10,13)*SF[14] + P(11,13)*SF[15] + P(12,13)*SPP[10]) + SPP[2]*(P(0,14) + P(1,14)*SF[9] + P(2,14)*SF[11] + P(3,14)*SF[10] + P(10,14)*SF[14] + P(11,14)*SF[15] + P(12,14)*SPP[10]) + SPP[5]*(P(0,15) + P(1,15)*SF[9] + P(2,15)*SF[11] + P(3,15)*SF[10] + P(10,15)*SF[14] + P(11,15)*SF[15] + P(12,15)*SPP[10]);
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||||
nextP(1,5) = P(1,5) + P(0,5)*SF[8] + P(2,5)*SF[7] + P(3,5)*SF[11] - P(12,5)*SF[15] + P(11,5)*SPP[10] - (P(10,5)*q0)*0.5f + SF[4]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SF[3]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SF[5]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) - SPP[0]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) - SPP[8]*(P(1,13) + P(0,13)*SF[8] + P(2,13)*SF[7] + P(3,13)*SF[11] - P(12,13)*SF[15] + P(11,13)*SPP[10] - (P(10,13)*q0)*0.5f) + SPP[2]*(P(1,14) + P(0,14)*SF[8] + P(2,14)*SF[7] + P(3,14)*SF[11] - P(12,14)*SF[15] + P(11,14)*SPP[10] - (P(10,14)*q0)*0.5f) + SPP[5]*(P(1,15) + P(0,15)*SF[8] + P(2,15)*SF[7] + P(3,15)*SF[11] - P(12,15)*SF[15] + P(11,15)*SPP[10] - (P(10,15)*q0)*0.5f);
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||||
nextP(2,5) = P(2,5) + P(0,5)*SF[6] + P(1,5)*SF[10] + P(3,5)*SF[8] + P(12,5)*SF[14] - P(10,5)*SPP[10] - (P(11,5)*q0)*0.5f + SF[4]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SF[3]*(P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] - (P(11,2)*q0)*0.5f) + SF[5]*(P(2,3) + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f) - SPP[0]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) - SPP[8]*(P(2,13) + P(0,13)*SF[6] + P(1,13)*SF[10] + P(3,13)*SF[8] + P(12,13)*SF[14] - P(10,13)*SPP[10] - (P(11,13)*q0)*0.5f) + SPP[2]*(P(2,14) + P(0,14)*SF[6] + P(1,14)*SF[10] + P(3,14)*SF[8] + P(12,14)*SF[14] - P(10,14)*SPP[10] - (P(11,14)*q0)*0.5f) + SPP[5]*(P(2,15) + P(0,15)*SF[6] + P(1,15)*SF[10] + P(3,15)*SF[8] + P(12,15)*SF[14] - P(10,15)*SPP[10] - (P(11,15)*q0)*0.5f);
|
||||
nextP(3,5) = P(3,5) + P(0,5)*SF[7] + P(1,5)*SF[6] + P(2,5)*SF[9] + P(10,5)*SF[15] - P(11,5)*SF[14] - (P(12,5)*q0)*0.5f + SF[4]*(P(3,0) + P(0,0)*SF[7] + P(1,0)*SF[6] + P(2,0)*SF[9] + P(10,0)*SF[15] - P(11,0)*SF[14] - (P(12,0)*q0)*0.5f) + SF[3]*(P(3,2) + P(0,2)*SF[7] + P(1,2)*SF[6] + P(2,2)*SF[9] + P(10,2)*SF[15] - P(11,2)*SF[14] - (P(12,2)*q0)*0.5f) + SF[5]*(P(3,3) + P(0,3)*SF[7] + P(1,3)*SF[6] + P(2,3)*SF[9] + P(10,3)*SF[15] - P(11,3)*SF[14] - (P(12,3)*q0)*0.5f) - SPP[0]*(P(3,1) + P(0,1)*SF[7] + P(1,1)*SF[6] + P(2,1)*SF[9] + P(10,1)*SF[15] - P(11,1)*SF[14] - (P(12,1)*q0)*0.5f) - SPP[8]*(P(3,13) + P(0,13)*SF[7] + P(1,13)*SF[6] + P(2,13)*SF[9] + P(10,13)*SF[15] - P(11,13)*SF[14] - (P(12,13)*q0)*0.5f) + SPP[2]*(P(3,14) + P(0,14)*SF[7] + P(1,14)*SF[6] + P(2,14)*SF[9] + P(10,14)*SF[15] - P(11,14)*SF[14] - (P(12,14)*q0)*0.5f) + SPP[5]*(P(3,15) + P(0,15)*SF[7] + P(1,15)*SF[6] + P(2,15)*SF[9] + P(10,15)*SF[15] - P(11,15)*SF[14] - (P(12,15)*q0)*0.5f);
|
||||
nextP(4,5) = P(4,5) + SQ[2] + P(0,5)*SF[5] + P(1,5)*SF[3] - P(3,5)*SF[4] + P(2,5)*SPP[0] + P(13,5)*SPP[3] + P(14,5)*SPP[6] - P(15,5)*SPP[9] + SF[4]*(P(4,0) + P(0,0)*SF[5] + P(1,0)*SF[3] - P(3,0)*SF[4] + P(2,0)*SPP[0] + P(13,0)*SPP[3] + P(14,0)*SPP[6] - P(15,0)*SPP[9]) + SF[3]*(P(4,2) + P(0,2)*SF[5] + P(1,2)*SF[3] - P(3,2)*SF[4] + P(2,2)*SPP[0] + P(13,2)*SPP[3] + P(14,2)*SPP[6] - P(15,2)*SPP[9]) + SF[5]*(P(4,3) + P(0,3)*SF[5] + P(1,3)*SF[3] - P(3,3)*SF[4] + P(2,3)*SPP[0] + P(13,3)*SPP[3] + P(14,3)*SPP[6] - P(15,3)*SPP[9]) - SPP[0]*(P(4,1) + P(0,1)*SF[5] + P(1,1)*SF[3] - P(3,1)*SF[4] + P(2,1)*SPP[0] + P(13,1)*SPP[3] + P(14,1)*SPP[6] - P(15,1)*SPP[9]) - SPP[8]*(P(4,13) + P(0,13)*SF[5] + P(1,13)*SF[3] - P(3,13)*SF[4] + P(2,13)*SPP[0] + P(13,13)*SPP[3] + P(14,13)*SPP[6] - P(15,13)*SPP[9]) + SPP[2]*(P(4,14) + P(0,14)*SF[5] + P(1,14)*SF[3] - P(3,14)*SF[4] + P(2,14)*SPP[0] + P(13,14)*SPP[3] + P(14,14)*SPP[6] - P(15,14)*SPP[9]) + SPP[5]*(P(4,15) + P(0,15)*SF[5] + P(1,15)*SF[3] - P(3,15)*SF[4] + P(2,15)*SPP[0] + P(13,15)*SPP[3] + P(14,15)*SPP[6] - P(15,15)*SPP[9]);
|
||||
nextP(5,5) = P(5,5) + P(0,5)*SF[4] + P(2,5)*SF[3] + P(3,5)*SF[5] - P(1,5)*SPP[0] - P(13,5)*SPP[8] + P(14,5)*SPP[2] + P(15,5)*SPP[5] + dvxVar*sq(SG[7] + 2*q0*q3) + dvzVar*sq(SG[5] - 2*q0*q1) + SF[4]*(P(5,0) + P(0,0)*SF[4] + P(2,0)*SF[3] + P(3,0)*SF[5] - P(1,0)*SPP[0] - P(13,0)*SPP[8] + P(14,0)*SPP[2] + P(15,0)*SPP[5]) + SF[3]*(P(5,2) + P(0,2)*SF[4] + P(2,2)*SF[3] + P(3,2)*SF[5] - P(1,2)*SPP[0] - P(13,2)*SPP[8] + P(14,2)*SPP[2] + P(15,2)*SPP[5]) + SF[5]*(P(5,3) + P(0,3)*SF[4] + P(2,3)*SF[3] + P(3,3)*SF[5] - P(1,3)*SPP[0] - P(13,3)*SPP[8] + P(14,3)*SPP[2] + P(15,3)*SPP[5]) - SPP[0]*(P(5,1) + P(0,1)*SF[4] + P(2,1)*SF[3] + P(3,1)*SF[5] - P(1,1)*SPP[0] - P(13,1)*SPP[8] + P(14,1)*SPP[2] + P(15,1)*SPP[5]) - SPP[8]*(P(5,13) + P(0,13)*SF[4] + P(2,13)*SF[3] + P(3,13)*SF[5] - P(1,13)*SPP[0] - P(13,13)*SPP[8] + P(14,13)*SPP[2] + P(15,13)*SPP[5]) + SPP[2]*(P(5,14) + P(0,14)*SF[4] + P(2,14)*SF[3] + P(3,14)*SF[5] - P(1,14)*SPP[0] - P(13,14)*SPP[8] + P(14,14)*SPP[2] + P(15,14)*SPP[5]) + SPP[5]*(P(5,15) + P(0,15)*SF[4] + P(2,15)*SF[3] + P(3,15)*SF[5] - P(1,15)*SPP[0] - P(13,15)*SPP[8] + P(14,15)*SPP[2] + P(15,15)*SPP[5]) + dvyVar*sq(SG[1] - SG[2] + SG[3] - SG[4]);
|
||||
nextP(0,6) = P(0,6) + P(1,6)*SF[9] + P(2,6)*SF[11] + P(3,6)*SF[10] + P(10,6)*SF[14] + P(11,6)*SF[15] + P(12,6)*SPP[10] + SF[4]*(P(0,1) + P(1,1)*SF[9] + P(2,1)*SF[11] + P(3,1)*SF[10] + P(10,1)*SF[14] + P(11,1)*SF[15] + P(12,1)*SPP[10]) - SF[5]*(P(0,2) + P(1,2)*SF[9] + P(2,2)*SF[11] + P(3,2)*SF[10] + P(10,2)*SF[14] + P(11,2)*SF[15] + P(12,2)*SPP[10]) + SF[3]*(P(0,3) + P(1,3)*SF[9] + P(2,3)*SF[11] + P(3,3)*SF[10] + P(10,3)*SF[14] + P(11,3)*SF[15] + P(12,3)*SPP[10]) + SPP[0]*(P(0,0) + P(1,0)*SF[9] + P(2,0)*SF[11] + P(3,0)*SF[10] + P(10,0)*SF[14] + P(11,0)*SF[15] + P(12,0)*SPP[10]) + SPP[4]*(P(0,13) + P(1,13)*SF[9] + P(2,13)*SF[11] + P(3,13)*SF[10] + P(10,13)*SF[14] + P(11,13)*SF[15] + P(12,13)*SPP[10]) - SPP[7]*(P(0,14) + P(1,14)*SF[9] + P(2,14)*SF[11] + P(3,14)*SF[10] + P(10,14)*SF[14] + P(11,14)*SF[15] + P(12,14)*SPP[10]) - SPP[1]*(P(0,15) + P(1,15)*SF[9] + P(2,15)*SF[11] + P(3,15)*SF[10] + P(10,15)*SF[14] + P(11,15)*SF[15] + P(12,15)*SPP[10]);
|
||||
nextP(1,6) = P(1,6) + P(0,6)*SF[8] + P(2,6)*SF[7] + P(3,6)*SF[11] - P(12,6)*SF[15] + P(11,6)*SPP[10] - (P(10,6)*q0)*0.5f + SF[4]*(P(1,1) + P(0,1)*SF[8] + P(2,1)*SF[7] + P(3,1)*SF[11] - P(12,1)*SF[15] + P(11,1)*SPP[10] - (P(10,1)*q0)*0.5f) - SF[5]*(P(1,2) + P(0,2)*SF[8] + P(2,2)*SF[7] + P(3,2)*SF[11] - P(12,2)*SF[15] + P(11,2)*SPP[10] - (P(10,2)*q0)*0.5f) + SF[3]*(P(1,3) + P(0,3)*SF[8] + P(2,3)*SF[7] + P(3,3)*SF[11] - P(12,3)*SF[15] + P(11,3)*SPP[10] - (P(10,3)*q0)*0.5f) + SPP[0]*(P(1,0) + P(0,0)*SF[8] + P(2,0)*SF[7] + P(3,0)*SF[11] - P(12,0)*SF[15] + P(11,0)*SPP[10] - (P(10,0)*q0)*0.5f) + SPP[4]*(P(1,13) + P(0,13)*SF[8] + P(2,13)*SF[7] + P(3,13)*SF[11] - P(12,13)*SF[15] + P(11,13)*SPP[10] - (P(10,13)*q0)*0.5f) - SPP[7]*(P(1,14) + P(0,14)*SF[8] + P(2,14)*SF[7] + P(3,14)*SF[11] - P(12,14)*SF[15] + P(11,14)*SPP[10] - (P(10,14)*q0)*0.5f) - SPP[1]*(P(1,15) + P(0,15)*SF[8] + P(2,15)*SF[7] + P(3,15)*SF[11] - P(12,15)*SF[15] + P(11,15)*SPP[10] - (P(10,15)*q0)*0.5f);
|
||||
nextP(2,6) = P(2,6) + P(0,6)*SF[6] + P(1,6)*SF[10] + P(3,6)*SF[8] + P(12,6)*SF[14] - P(10,6)*SPP[10] - (P(11,6)*q0)*0.5f + SF[4]*(P(2,1) + P(0,1)*SF[6] + P(1,1)*SF[10] + P(3,1)*SF[8] + P(12,1)*SF[14] - P(10,1)*SPP[10] - (P(11,1)*q0)*0.5f) - SF[5]*(P(2,2) + P(0,2)*SF[6] + P(1,2)*SF[10] + P(3,2)*SF[8] + P(12,2)*SF[14] - P(10,2)*SPP[10] - (P(11,2)*q0)*0.5f) + SF[3]*(P(2,3) + P(0,3)*SF[6] + P(1,3)*SF[10] + P(3,3)*SF[8] + P(12,3)*SF[14] - P(10,3)*SPP[10] - (P(11,3)*q0)*0.5f) + SPP[0]*(P(2,0) + P(0,0)*SF[6] + P(1,0)*SF[10] + P(3,0)*SF[8] + P(12,0)*SF[14] - P(10,0)*SPP[10] - (P(11,0)*q0)*0.5f) + SPP[4]*(P(2,13) + P(0,13)*SF[6] + P(1,13)*SF[10] + P(3,13)*SF[8] + P(12,13)*SF[14] - P(10,13)*SPP[10] - (P(11,13)*q0)*0.5f) - SPP[7]*(P(2,14) + P(0,14)*SF[6] + P(1,14)*SF[10] + P(3,14)*SF[8] + P(12,14)*SF[14] - P(10,14)*SPP[10] - (P(11,14)*q0)*0.5f) - SPP[1]*(P(2,15) + P(0,15)*SF[6] + P(1,15)*SF[10] + P(3,15)*SF[8] + P(12,15)*SF[14] - P(10,15)*SPP[10] - (P(11,15)*q0)*0.5f);
|
||||
nextP(3,6) = P(3,6) + P(0,6)*SF[7] + P(1,6)*SF[6] + P(2,6)*SF[9] + P(10,6)*SF[15] - P(11,6)*SF[14] - (P(12,6)*q0)*0.5f + SF[4]*(P(3,1) + P(0,1)*SF[7] + P(1,1)*SF[6] + P(2,1)*SF[9] + P(10,1)*SF[15] - P(11,1)*SF[14] - (P(12,1)*q0)*0.5f) - SF[5]*(P(3,2) + P(0,2)*SF[7] + P(1,2)*SF[6] + P(2,2)*SF[9] + P(10,2)*SF[15] - P(11,2)*SF[14] - (P(12,2)*q0)*0.5f) + SF[3]*(P(3,3) + P(0,3)*SF[7] + P(1,3)*SF[6] + P(2,3)*SF[9] + P(10,3)*SF[15] - P(11,3)*SF[14] - (P(12,3)*q0)*0.5f) + SPP[0]*(P(3,0) + P(0,0)*SF[7] + P(1,0)*SF[6] + P(2,0)*SF[9] + P(10,0)*SF[15] - P(11,0)*SF[14] - (P(12,0)*q0)*0.5f) + SPP[4]*(P(3,13) + P(0,13)*SF[7] + P(1,13)*SF[6] + P(2,13)*SF[9] + P(10,13)*SF[15] - P(11,13)*SF[14] - (P(12,13)*q0)*0.5f) - SPP[7]*(P(3,14) + P(0,14)*SF[7] + P(1,14)*SF[6] + P(2,14)*SF[9] + P(10,14)*SF[15] - P(11,14)*SF[14] - (P(12,14)*q0)*0.5f) - SPP[1]*(P(3,15) + P(0,15)*SF[7] + P(1,15)*SF[6] + P(2,15)*SF[9] + P(10,15)*SF[15] - P(11,15)*SF[14] - (P(12,15)*q0)*0.5f);
|
||||
nextP(4,6) = P(4,6) + SQ[1] + P(0,6)*SF[5] + P(1,6)*SF[3] - P(3,6)*SF[4] + P(2,6)*SPP[0] + P(13,6)*SPP[3] + P(14,6)*SPP[6] - P(15,6)*SPP[9] + SF[4]*(P(4,1) + P(0,1)*SF[5] + P(1,1)*SF[3] - P(3,1)*SF[4] + P(2,1)*SPP[0] + P(13,1)*SPP[3] + P(14,1)*SPP[6] - P(15,1)*SPP[9]) - SF[5]*(P(4,2) + P(0,2)*SF[5] + P(1,2)*SF[3] - P(3,2)*SF[4] + P(2,2)*SPP[0] + P(13,2)*SPP[3] + P(14,2)*SPP[6] - P(15,2)*SPP[9]) + SF[3]*(P(4,3) + P(0,3)*SF[5] + P(1,3)*SF[3] - P(3,3)*SF[4] + P(2,3)*SPP[0] + P(13,3)*SPP[3] + P(14,3)*SPP[6] - P(15,3)*SPP[9]) + SPP[0]*(P(4,0) + P(0,0)*SF[5] + P(1,0)*SF[3] - P(3,0)*SF[4] + P(2,0)*SPP[0] + P(13,0)*SPP[3] + P(14,0)*SPP[6] - P(15,0)*SPP[9]) + SPP[4]*(P(4,13) + P(0,13)*SF[5] + P(1,13)*SF[3] - P(3,13)*SF[4] + P(2,13)*SPP[0] + P(13,13)*SPP[3] + P(14,13)*SPP[6] - P(15,13)*SPP[9]) - SPP[7]*(P(4,14) + P(0,14)*SF[5] + P(1,14)*SF[3] - P(3,14)*SF[4] + P(2,14)*SPP[0] + P(13,14)*SPP[3] + P(14,14)*SPP[6] - P(15,14)*SPP[9]) - SPP[1]*(P(4,15) + P(0,15)*SF[5] + P(1,15)*SF[3] - P(3,15)*SF[4] + P(2,15)*SPP[0] + P(13,15)*SPP[3] + P(14,15)*SPP[6] - P(15,15)*SPP[9]);
|
||||
nextP(5,6) = P(5,6) + SQ[0] + P(0,6)*SF[4] + P(2,6)*SF[3] + P(3,6)*SF[5] - P(1,6)*SPP[0] - P(13,6)*SPP[8] + P(14,6)*SPP[2] + P(15,6)*SPP[5] + SF[4]*(P(5,1) + P(0,1)*SF[4] + P(2,1)*SF[3] + P(3,1)*SF[5] - P(1,1)*SPP[0] - P(13,1)*SPP[8] + P(14,1)*SPP[2] + P(15,1)*SPP[5]) - SF[5]*(P(5,2) + P(0,2)*SF[4] + P(2,2)*SF[3] + P(3,2)*SF[5] - P(1,2)*SPP[0] - P(13,2)*SPP[8] + P(14,2)*SPP[2] + P(15,2)*SPP[5]) + SF[3]*(P(5,3) + P(0,3)*SF[4] + P(2,3)*SF[3] + P(3,3)*SF[5] - P(1,3)*SPP[0] - P(13,3)*SPP[8] + P(14,3)*SPP[2] + P(15,3)*SPP[5]) + SPP[0]*(P(5,0) + P(0,0)*SF[4] + P(2,0)*SF[3] + P(3,0)*SF[5] - P(1,0)*SPP[0] - P(13,0)*SPP[8] + P(14,0)*SPP[2] + P(15,0)*SPP[5]) + SPP[4]*(P(5,13) + P(0,13)*SF[4] + P(2,13)*SF[3] + P(3,13)*SF[5] - P(1,13)*SPP[0] - P(13,13)*SPP[8] + P(14,13)*SPP[2] + P(15,13)*SPP[5]) - SPP[7]*(P(5,14) + P(0,14)*SF[4] + P(2,14)*SF[3] + P(3,14)*SF[5] - P(1,14)*SPP[0] - P(13,14)*SPP[8] + P(14,14)*SPP[2] + P(15,14)*SPP[5]) - SPP[1]*(P(5,15) + P(0,15)*SF[4] + P(2,15)*SF[3] + P(3,15)*SF[5] - P(1,15)*SPP[0] - P(13,15)*SPP[8] + P(14,15)*SPP[2] + P(15,15)*SPP[5]);
|
||||
nextP(6,6) = P(6,6) + P(1,6)*SF[4] - P(2,6)*SF[5] + P(3,6)*SF[3] + P(0,6)*SPP[0] + P(13,6)*SPP[4] - P(14,6)*SPP[7] - P(15,6)*SPP[1] + dvxVar*sq(SG[6] - 2*q0*q2) + dvyVar*sq(SG[5] + 2*q0*q1) + SF[4]*(P(6,1) + P(1,1)*SF[4] - P(2,1)*SF[5] + P(3,1)*SF[3] + P(0,1)*SPP[0] + P(13,1)*SPP[4] - P(14,1)*SPP[7] - P(15,1)*SPP[1]) - SF[5]*(P(6,2) + P(1,2)*SF[4] - P(2,2)*SF[5] + P(3,2)*SF[3] + P(0,2)*SPP[0] + P(13,2)*SPP[4] - P(14,2)*SPP[7] - P(15,2)*SPP[1]) + SF[3]*(P(6,3) + P(1,3)*SF[4] - P(2,3)*SF[5] + P(3,3)*SF[3] + P(0,3)*SPP[0] + P(13,3)*SPP[4] - P(14,3)*SPP[7] - P(15,3)*SPP[1]) + SPP[0]*(P(6,0) + P(1,0)*SF[4] - P(2,0)*SF[5] + P(3,0)*SF[3] + P(0,0)*SPP[0] + P(13,0)*SPP[4] - P(14,0)*SPP[7] - P(15,0)*SPP[1]) + SPP[4]*(P(6,13) + P(1,13)*SF[4] - P(2,13)*SF[5] + P(3,13)*SF[3] + P(0,13)*SPP[0] + P(13,13)*SPP[4] - P(14,13)*SPP[7] - P(15,13)*SPP[1]) - SPP[7]*(P(6,14) + P(1,14)*SF[4] - P(2,14)*SF[5] + P(3,14)*SF[3] + P(0,14)*SPP[0] + P(13,14)*SPP[4] - P(14,14)*SPP[7] - P(15,14)*SPP[1]) - SPP[1]*(P(6,15) + P(1,15)*SF[4] - P(2,15)*SF[5] + P(3,15)*SF[3] + P(0,15)*SPP[0] + P(13,15)*SPP[4] - P(14,15)*SPP[7] - P(15,15)*SPP[1]) + dvzVar*sq(SG[1] - SG[2] - SG[3] + SG[4]);
|
||||
nextP(0,7) = P(0,7) + P(1,7)*SF[9] + P(2,7)*SF[11] + P(3,7)*SF[10] + P(10,7)*SF[14] + P(11,7)*SF[15] + P(12,7)*SPP[10] + dt*(P(0,4) + P(1,4)*SF[9] + P(2,4)*SF[11] + P(3,4)*SF[10] + P(10,4)*SF[14] + P(11,4)*SF[15] + P(12,4)*SPP[10]);
|
||||
nextP(1,7) = P(1,7) + P(0,7)*SF[8] + P(2,7)*SF[7] + P(3,7)*SF[11] - P(12,7)*SF[15] + P(11,7)*SPP[10] - (P(10,7)*q0)*0.5f + dt*(P(1,4) + P(0,4)*SF[8] + P(2,4)*SF[7] + P(3,4)*SF[11] - P(12,4)*SF[15] + P(11,4)*SPP[10] - (P(10,4)*q0)*0.5f);
|
||||
nextP(2,7) = P(2,7) + P(0,7)*SF[6] + P(1,7)*SF[10] + P(3,7)*SF[8] + P(12,7)*SF[14] - P(10,7)*SPP[10] - (P(11,7)*q0)*0.5f + dt*(P(2,4) + P(0,4)*SF[6] + P(1,4)*SF[10] + P(3,4)*SF[8] + P(12,4)*SF[14] - P(10,4)*SPP[10] - (P(11,4)*q0)*0.5f);
|
||||
nextP(3,7) = P(3,7) + P(0,7)*SF[7] + P(1,7)*SF[6] + P(2,7)*SF[9] + P(10,7)*SF[15] - P(11,7)*SF[14] - (P(12,7)*q0)*0.5f + dt*(P(3,4) + P(0,4)*SF[7] + P(1,4)*SF[6] + P(2,4)*SF[9] + P(10,4)*SF[15] - P(11,4)*SF[14] - (P(12,4)*q0)*0.5f);
|
||||
nextP(4,7) = P(4,7) + P(0,7)*SF[5] + P(1,7)*SF[3] - P(3,7)*SF[4] + P(2,7)*SPP[0] + P(13,7)*SPP[3] + P(14,7)*SPP[6] - P(15,7)*SPP[9] + dt*(P(4,4) + P(0,4)*SF[5] + P(1,4)*SF[3] - P(3,4)*SF[4] + P(2,4)*SPP[0] + P(13,4)*SPP[3] + P(14,4)*SPP[6] - P(15,4)*SPP[9]);
|
||||
nextP(5,7) = P(5,7) + P(0,7)*SF[4] + P(2,7)*SF[3] + P(3,7)*SF[5] - P(1,7)*SPP[0] - P(13,7)*SPP[8] + P(14,7)*SPP[2] + P(15,7)*SPP[5] + dt*(P(5,4) + P(0,4)*SF[4] + P(2,4)*SF[3] + P(3,4)*SF[5] - P(1,4)*SPP[0] - P(13,4)*SPP[8] + P(14,4)*SPP[2] + P(15,4)*SPP[5]);
|
||||
nextP(6,7) = P(6,7) + P(1,7)*SF[4] - P(2,7)*SF[5] + P(3,7)*SF[3] + P(0,7)*SPP[0] + P(13,7)*SPP[4] - P(14,7)*SPP[7] - P(15,7)*SPP[1] + dt*(P(6,4) + P(1,4)*SF[4] - P(2,4)*SF[5] + P(3,4)*SF[3] + P(0,4)*SPP[0] + P(13,4)*SPP[4] - P(14,4)*SPP[7] - P(15,4)*SPP[1]);
|
||||
nextP(7,7) = P(7,7) + P(4,7)*dt + dt*(P(7,4) + P(4,4)*dt);
|
||||
nextP(0,8) = P(0,8) + P(1,8)*SF[9] + P(2,8)*SF[11] + P(3,8)*SF[10] + P(10,8)*SF[14] + P(11,8)*SF[15] + P(12,8)*SPP[10] + dt*(P(0,5) + P(1,5)*SF[9] + P(2,5)*SF[11] + P(3,5)*SF[10] + P(10,5)*SF[14] + P(11,5)*SF[15] + P(12,5)*SPP[10]);
|
||||
nextP(1,8) = P(1,8) + P(0,8)*SF[8] + P(2,8)*SF[7] + P(3,8)*SF[11] - P(12,8)*SF[15] + P(11,8)*SPP[10] - (P(10,8)*q0)*0.5f + dt*(P(1,5) + P(0,5)*SF[8] + P(2,5)*SF[7] + P(3,5)*SF[11] - P(12,5)*SF[15] + P(11,5)*SPP[10] - (P(10,5)*q0)*0.5f);
|
||||
nextP(2,8) = P(2,8) + P(0,8)*SF[6] + P(1,8)*SF[10] + P(3,8)*SF[8] + P(12,8)*SF[14] - P(10,8)*SPP[10] - (P(11,8)*q0)*0.5f + dt*(P(2,5) + P(0,5)*SF[6] + P(1,5)*SF[10] + P(3,5)*SF[8] + P(12,5)*SF[14] - P(10,5)*SPP[10] - (P(11,5)*q0)*0.5f);
|
||||
nextP(3,8) = P(3,8) + P(0,8)*SF[7] + P(1,8)*SF[6] + P(2,8)*SF[9] + P(10,8)*SF[15] - P(11,8)*SF[14] - (P(12,8)*q0)*0.5f + dt*(P(3,5) + P(0,5)*SF[7] + P(1,5)*SF[6] + P(2,5)*SF[9] + P(10,5)*SF[15] - P(11,5)*SF[14] - (P(12,5)*q0)*0.5f);
|
||||
nextP(4,8) = P(4,8) + P(0,8)*SF[5] + P(1,8)*SF[3] - P(3,8)*SF[4] + P(2,8)*SPP[0] + P(13,8)*SPP[3] + P(14,8)*SPP[6] - P(15,8)*SPP[9] + dt*(P(4,5) + P(0,5)*SF[5] + P(1,5)*SF[3] - P(3,5)*SF[4] + P(2,5)*SPP[0] + P(13,5)*SPP[3] + P(14,5)*SPP[6] - P(15,5)*SPP[9]);
|
||||
nextP(5,8) = P(5,8) + P(0,8)*SF[4] + P(2,8)*SF[3] + P(3,8)*SF[5] - P(1,8)*SPP[0] - P(13,8)*SPP[8] + P(14,8)*SPP[2] + P(15,8)*SPP[5] + dt*(P(5,5) + P(0,5)*SF[4] + P(2,5)*SF[3] + P(3,5)*SF[5] - P(1,5)*SPP[0] - P(13,5)*SPP[8] + P(14,5)*SPP[2] + P(15,5)*SPP[5]);
|
||||
nextP(6,8) = P(6,8) + P(1,8)*SF[4] - P(2,8)*SF[5] + P(3,8)*SF[3] + P(0,8)*SPP[0] + P(13,8)*SPP[4] - P(14,8)*SPP[7] - P(15,8)*SPP[1] + dt*(P(6,5) + P(1,5)*SF[4] - P(2,5)*SF[5] + P(3,5)*SF[3] + P(0,5)*SPP[0] + P(13,5)*SPP[4] - P(14,5)*SPP[7] - P(15,5)*SPP[1]);
|
||||
nextP(7,8) = P(7,8) + P(4,8)*dt + dt*(P(7,5) + P(4,5)*dt);
|
||||
nextP(8,8) = P(8,8) + P(5,8)*dt + dt*(P(8,5) + P(5,5)*dt);
|
||||
nextP(0,9) = P(0,9) + P(1,9)*SF[9] + P(2,9)*SF[11] + P(3,9)*SF[10] + P(10,9)*SF[14] + P(11,9)*SF[15] + P(12,9)*SPP[10] + dt*(P(0,6) + P(1,6)*SF[9] + P(2,6)*SF[11] + P(3,6)*SF[10] + P(10,6)*SF[14] + P(11,6)*SF[15] + P(12,6)*SPP[10]);
|
||||
nextP(1,9) = P(1,9) + P(0,9)*SF[8] + P(2,9)*SF[7] + P(3,9)*SF[11] - P(12,9)*SF[15] + P(11,9)*SPP[10] - (P(10,9)*q0)*0.5f + dt*(P(1,6) + P(0,6)*SF[8] + P(2,6)*SF[7] + P(3,6)*SF[11] - P(12,6)*SF[15] + P(11,6)*SPP[10] - (P(10,6)*q0)*0.5f);
|
||||
nextP(2,9) = P(2,9) + P(0,9)*SF[6] + P(1,9)*SF[10] + P(3,9)*SF[8] + P(12,9)*SF[14] - P(10,9)*SPP[10] - (P(11,9)*q0)*0.5f + dt*(P(2,6) + P(0,6)*SF[6] + P(1,6)*SF[10] + P(3,6)*SF[8] + P(12,6)*SF[14] - P(10,6)*SPP[10] - (P(11,6)*q0)*0.5f);
|
||||
nextP(3,9) = P(3,9) + P(0,9)*SF[7] + P(1,9)*SF[6] + P(2,9)*SF[9] + P(10,9)*SF[15] - P(11,9)*SF[14] - (P(12,9)*q0)*0.5f + dt*(P(3,6) + P(0,6)*SF[7] + P(1,6)*SF[6] + P(2,6)*SF[9] + P(10,6)*SF[15] - P(11,6)*SF[14] - (P(12,6)*q0)*0.5f);
|
||||
nextP(4,9) = P(4,9) + P(0,9)*SF[5] + P(1,9)*SF[3] - P(3,9)*SF[4] + P(2,9)*SPP[0] + P(13,9)*SPP[3] + P(14,9)*SPP[6] - P(15,9)*SPP[9] + dt*(P(4,6) + P(0,6)*SF[5] + P(1,6)*SF[3] - P(3,6)*SF[4] + P(2,6)*SPP[0] + P(13,6)*SPP[3] + P(14,6)*SPP[6] - P(15,6)*SPP[9]);
|
||||
nextP(5,9) = P(5,9) + P(0,9)*SF[4] + P(2,9)*SF[3] + P(3,9)*SF[5] - P(1,9)*SPP[0] - P(13,9)*SPP[8] + P(14,9)*SPP[2] + P(15,9)*SPP[5] + dt*(P(5,6) + P(0,6)*SF[4] + P(2,6)*SF[3] + P(3,6)*SF[5] - P(1,6)*SPP[0] - P(13,6)*SPP[8] + P(14,6)*SPP[2] + P(15,6)*SPP[5]);
|
||||
nextP(6,9) = P(6,9) + P(1,9)*SF[4] - P(2,9)*SF[5] + P(3,9)*SF[3] + P(0,9)*SPP[0] + P(13,9)*SPP[4] - P(14,9)*SPP[7] - P(15,9)*SPP[1] + dt*(P(6,6) + P(1,6)*SF[4] - P(2,6)*SF[5] + P(3,6)*SF[3] + P(0,6)*SPP[0] + P(13,6)*SPP[4] - P(14,6)*SPP[7] - P(15,6)*SPP[1]);
|
||||
nextP(7,9) = P(7,9) + P(4,9)*dt + dt*(P(7,6) + P(4,6)*dt);
|
||||
nextP(8,9) = P(8,9) + P(5,9)*dt + dt*(P(8,6) + P(5,6)*dt);
|
||||
nextP(9,9) = P(9,9) + P(6,9)*dt + dt*(P(9,6) + P(6,6)*dt);
|
||||
nextP(0,10) = P(0,10) + P(1,10)*SF[9] + P(2,10)*SF[11] + P(3,10)*SF[10] + P(10,10)*SF[14] + P(11,10)*SF[15] + P(12,10)*SPP[10];
|
||||
nextP(1,10) = P(1,10) + P(0,10)*SF[8] + P(2,10)*SF[7] + P(3,10)*SF[11] - P(12,10)*SF[15] + P(11,10)*SPP[10] - (P(10,10)*q0)*0.5f;
|
||||
nextP(2,10) = P(2,10) + P(0,10)*SF[6] + P(1,10)*SF[10] + P(3,10)*SF[8] + P(12,10)*SF[14] - P(10,10)*SPP[10] - (P(11,10)*q0)*0.5f;
|
||||
nextP(3,10) = P(3,10) + P(0,10)*SF[7] + P(1,10)*SF[6] + P(2,10)*SF[9] + P(10,10)*SF[15] - P(11,10)*SF[14] - (P(12,10)*q0)*0.5f;
|
||||
nextP(4,10) = P(4,10) + P(0,10)*SF[5] + P(1,10)*SF[3] - P(3,10)*SF[4] + P(2,10)*SPP[0] + P(13,10)*SPP[3] + P(14,10)*SPP[6] - P(15,10)*SPP[9];
|
||||
nextP(5,10) = P(5,10) + P(0,10)*SF[4] + P(2,10)*SF[3] + P(3,10)*SF[5] - P(1,10)*SPP[0] - P(13,10)*SPP[8] + P(14,10)*SPP[2] + P(15,10)*SPP[5];
|
||||
nextP(6,10) = P(6,10) + P(1,10)*SF[4] - P(2,10)*SF[5] + P(3,10)*SF[3] + P(0,10)*SPP[0] + P(13,10)*SPP[4] - P(14,10)*SPP[7] - P(15,10)*SPP[1];
|
||||
nextP(7,10) = P(7,10) + P(4,10)*dt;
|
||||
nextP(8,10) = P(8,10) + P(5,10)*dt;
|
||||
nextP(9,10) = P(9,10) + P(6,10)*dt;
|
||||
nextP(10,10) = P(10,10);
|
||||
nextP(0,11) = P(0,11) + P(1,11)*SF[9] + P(2,11)*SF[11] + P(3,11)*SF[10] + P(10,11)*SF[14] + P(11,11)*SF[15] + P(12,11)*SPP[10];
|
||||
nextP(1,11) = P(1,11) + P(0,11)*SF[8] + P(2,11)*SF[7] + P(3,11)*SF[11] - P(12,11)*SF[15] + P(11,11)*SPP[10] - (P(10,11)*q0)*0.5f;
|
||||
nextP(2,11) = P(2,11) + P(0,11)*SF[6] + P(1,11)*SF[10] + P(3,11)*SF[8] + P(12,11)*SF[14] - P(10,11)*SPP[10] - (P(11,11)*q0)*0.5f;
|
||||
nextP(3,11) = P(3,11) + P(0,11)*SF[7] + P(1,11)*SF[6] + P(2,11)*SF[9] + P(10,11)*SF[15] - P(11,11)*SF[14] - (P(12,11)*q0)*0.5f;
|
||||
nextP(4,11) = P(4,11) + P(0,11)*SF[5] + P(1,11)*SF[3] - P(3,11)*SF[4] + P(2,11)*SPP[0] + P(13,11)*SPP[3] + P(14,11)*SPP[6] - P(15,11)*SPP[9];
|
||||
nextP(5,11) = P(5,11) + P(0,11)*SF[4] + P(2,11)*SF[3] + P(3,11)*SF[5] - P(1,11)*SPP[0] - P(13,11)*SPP[8] + P(14,11)*SPP[2] + P(15,11)*SPP[5];
|
||||
nextP(6,11) = P(6,11) + P(1,11)*SF[4] - P(2,11)*SF[5] + P(3,11)*SF[3] + P(0,11)*SPP[0] + P(13,11)*SPP[4] - P(14,11)*SPP[7] - P(15,11)*SPP[1];
|
||||
nextP(7,11) = P(7,11) + P(4,11)*dt;
|
||||
nextP(8,11) = P(8,11) + P(5,11)*dt;
|
||||
nextP(9,11) = P(9,11) + P(6,11)*dt;
|
||||
nextP(10,11) = P(10,11);
|
||||
nextP(11,11) = P(11,11);
|
||||
nextP(0,12) = P(0,12) + P(1,12)*SF[9] + P(2,12)*SF[11] + P(3,12)*SF[10] + P(10,12)*SF[14] + P(11,12)*SF[15] + P(12,12)*SPP[10];
|
||||
nextP(1,12) = P(1,12) + P(0,12)*SF[8] + P(2,12)*SF[7] + P(3,12)*SF[11] - P(12,12)*SF[15] + P(11,12)*SPP[10] - (P(10,12)*q0)*0.5f;
|
||||
nextP(2,12) = P(2,12) + P(0,12)*SF[6] + P(1,12)*SF[10] + P(3,12)*SF[8] + P(12,12)*SF[14] - P(10,12)*SPP[10] - (P(11,12)*q0)*0.5f;
|
||||
nextP(3,12) = P(3,12) + P(0,12)*SF[7] + P(1,12)*SF[6] + P(2,12)*SF[9] + P(10,12)*SF[15] - P(11,12)*SF[14] - (P(12,12)*q0)*0.5f;
|
||||
nextP(4,12) = P(4,12) + P(0,12)*SF[5] + P(1,12)*SF[3] - P(3,12)*SF[4] + P(2,12)*SPP[0] + P(13,12)*SPP[3] + P(14,12)*SPP[6] - P(15,12)*SPP[9];
|
||||
nextP(5,12) = P(5,12) + P(0,12)*SF[4] + P(2,12)*SF[3] + P(3,12)*SF[5] - P(1,12)*SPP[0] - P(13,12)*SPP[8] + P(14,12)*SPP[2] + P(15,12)*SPP[5];
|
||||
nextP(6,12) = P(6,12) + P(1,12)*SF[4] - P(2,12)*SF[5] + P(3,12)*SF[3] + P(0,12)*SPP[0] + P(13,12)*SPP[4] - P(14,12)*SPP[7] - P(15,12)*SPP[1];
|
||||
nextP(7,12) = P(7,12) + P(4,12)*dt;
|
||||
nextP(8,12) = P(8,12) + P(5,12)*dt;
|
||||
nextP(9,12) = P(9,12) + P(6,12)*dt;
|
||||
nextP(10,12) = P(10,12);
|
||||
nextP(11,12) = P(11,12);
|
||||
nextP(12,12) = P(12,12);
|
||||
|
||||
for (unsigned i = 13; i <= 15; i++) {
|
||||
nextP(0,i) = P(0,i) + P(1,i)*SF[9] + P(2,i)*SF[11] + P(3,i)*SF[10] + P(10,i)*SF[14] + P(11,i)*SF[15] + P(12,i)*SPP[10];
|
||||
nextP(1,i) = P(1,i) + P(0,i)*SF[8] + P(2,i)*SF[7] + P(3,i)*SF[11] - P(12,i)*SF[15] + P(11,i)*SPP[10] - (P(10,i)*q0)*0.5f;
|
||||
nextP(2,i) = P(2,i) + P(0,i)*SF[6] + P(1,i)*SF[10] + P(3,i)*SF[8] + P(12,i)*SF[14] - P(10,i)*SPP[10] - (P(11,i)*q0)*0.5f;
|
||||
nextP(3,i) = P(3,i) + P(0,i)*SF[7] + P(1,i)*SF[6] + P(2,i)*SF[9] + P(10,i)*SF[15] - P(11,i)*SF[14] - (P(12,i)*q0)*0.5f;
|
||||
nextP(4,i) = P(4,i) + P(0,i)*SF[5] + P(1,i)*SF[3] - P(3,i)*SF[4] + P(2,i)*SPP[0] + P(13,i)*SPP[3] + P(14,i)*SPP[6] - P(15,i)*SPP[9];
|
||||
nextP(5,i) = P(5,i) + P(0,i)*SF[4] + P(2,i)*SF[3] + P(3,i)*SF[5] - P(1,i)*SPP[0] - P(13,i)*SPP[8] + P(14,i)*SPP[2] + P(15,i)*SPP[5];
|
||||
nextP(6,i) = P(6,i) + P(1,i)*SF[4] - P(2,i)*SF[5] + P(3,i)*SF[3] + P(0,i)*SPP[0] + P(13,i)*SPP[4] - P(14,i)*SPP[7] - P(15,i)*SPP[1];
|
||||
nextP(7,i) = P(7,i) + P(4,i)*dt;
|
||||
nextP(8,i) = P(8,i) + P(5,i)*dt;
|
||||
nextP(9,i) = P(9,i) + P(6,i)*dt;
|
||||
nextP(10,i) = P(10,i);
|
||||
nextP(11,i) = P(11,i);
|
||||
nextP(12,i) = P(12,i);
|
||||
nextP(13,i) = P(13,i);
|
||||
|
||||
if (i > 13) {
|
||||
nextP(14,i) = P(14,i);
|
||||
}
|
||||
|
||||
if (i > 14) {
|
||||
nextP(15,i) = P(15,i);
|
||||
}
|
||||
}
|
||||
|
||||
nextP(0,16) = P(0,16) + P(1,16)*SF[9] + P(2,16)*SF[11] + P(3,16)*SF[10] + P(10,16)*SF[14] + P(11,16)*SF[15] + P(12,16)*SPP[10];
|
||||
nextP(1,16) = P(1,16) + P(0,16)*SF[8] + P(2,16)*SF[7] + P(3,16)*SF[11] - P(12,16)*SF[15] + P(11,16)*SPP[10] - (P(10,16)*q0)*0.5f;
|
||||
nextP(2,16) = P(2,16) + P(0,16)*SF[6] + P(1,16)*SF[10] + P(3,16)*SF[8] + P(12,16)*SF[14] - P(10,16)*SPP[10] - (P(11,16)*q0)*0.5f;
|
||||
nextP(3,16) = P(3,16) + P(0,16)*SF[7] + P(1,16)*SF[6] + P(2,16)*SF[9] + P(10,16)*SF[15] - P(11,16)*SF[14] - (P(12,16)*q0)*0.5f;
|
||||
nextP(4,16) = P(4,16) + P(0,16)*SF[5] + P(1,16)*SF[3] - P(3,16)*SF[4] + P(2,16)*SPP[0] + P(13,16)*SPP[3] + P(14,16)*SPP[6] - P(15,16)*SPP[9];
|
||||
nextP(5,16) = P(5,16) + P(0,16)*SF[4] + P(2,16)*SF[3] + P(3,16)*SF[5] - P(1,16)*SPP[0] - P(13,16)*SPP[8] + P(14,16)*SPP[2] + P(15,16)*SPP[5];
|
||||
nextP(6,16) = P(6,16) + P(1,16)*SF[4] - P(2,16)*SF[5] + P(3,16)*SF[3] + P(0,16)*SPP[0] + P(13,16)*SPP[4] - P(14,16)*SPP[7] - P(15,16)*SPP[1];
|
||||
nextP(7,16) = P(7,16) + P(4,16)*dt;
|
||||
nextP(8,16) = P(8,16) + P(5,16)*dt;
|
||||
nextP(9,16) = P(9,16) + P(6,16)*dt;
|
||||
nextP(10,16) = P(10,16);
|
||||
nextP(11,16) = P(11,16);
|
||||
nextP(12,16) = P(12,16);
|
||||
nextP(13,16) = P(13,16);
|
||||
nextP(14,16) = P(14,16);
|
||||
nextP(15,16) = P(15,16);
|
||||
nextP(16,16) = P(16,16);
|
||||
nextP(0,17) = P(0,17) + P(1,17)*SF[9] + P(2,17)*SF[11] + P(3,17)*SF[10] + P(10,17)*SF[14] + P(11,17)*SF[15] + P(12,17)*SPP[10];
|
||||
nextP(1,17) = P(1,17) + P(0,17)*SF[8] + P(2,17)*SF[7] + P(3,17)*SF[11] - P(12,17)*SF[15] + P(11,17)*SPP[10] - (P(10,17)*q0)*0.5f;
|
||||
nextP(2,17) = P(2,17) + P(0,17)*SF[6] + P(1,17)*SF[10] + P(3,17)*SF[8] + P(12,17)*SF[14] - P(10,17)*SPP[10] - (P(11,17)*q0)*0.5f;
|
||||
nextP(3,17) = P(3,17) + P(0,17)*SF[7] + P(1,17)*SF[6] + P(2,17)*SF[9] + P(10,17)*SF[15] - P(11,17)*SF[14] - (P(12,17)*q0)*0.5f;
|
||||
nextP(4,17) = P(4,17) + P(0,17)*SF[5] + P(1,17)*SF[3] - P(3,17)*SF[4] + P(2,17)*SPP[0] + P(13,17)*SPP[3] + P(14,17)*SPP[6] - P(15,17)*SPP[9];
|
||||
nextP(5,17) = P(5,17) + P(0,17)*SF[4] + P(2,17)*SF[3] + P(3,17)*SF[5] - P(1,17)*SPP[0] - P(13,17)*SPP[8] + P(14,17)*SPP[2] + P(15,17)*SPP[5];
|
||||
nextP(6,17) = P(6,17) + P(1,17)*SF[4] - P(2,17)*SF[5] + P(3,17)*SF[3] + P(0,17)*SPP[0] + P(13,17)*SPP[4] - P(14,17)*SPP[7] - P(15,17)*SPP[1];
|
||||
nextP(7,17) = P(7,17) + P(4,17)*dt;
|
||||
nextP(8,17) = P(8,17) + P(5,17)*dt;
|
||||
nextP(9,17) = P(9,17) + P(6,17)*dt;
|
||||
nextP(10,17) = P(10,17);
|
||||
nextP(11,17) = P(11,17);
|
||||
nextP(12,17) = P(12,17);
|
||||
nextP(13,17) = P(13,17);
|
||||
nextP(14,17) = P(14,17);
|
||||
nextP(15,17) = P(15,17);
|
||||
nextP(16,17) = P(16,17);
|
||||
nextP(17,17) = P(17,17);
|
||||
nextP(0,18) = P(0,18) + P(1,18)*SF[9] + P(2,18)*SF[11] + P(3,18)*SF[10] + P(10,18)*SF[14] + P(11,18)*SF[15] + P(12,18)*SPP[10];
|
||||
nextP(1,18) = P(1,18) + P(0,18)*SF[8] + P(2,18)*SF[7] + P(3,18)*SF[11] - P(12,18)*SF[15] + P(11,18)*SPP[10] - (P(10,18)*q0)*0.5f;
|
||||
nextP(2,18) = P(2,18) + P(0,18)*SF[6] + P(1,18)*SF[10] + P(3,18)*SF[8] + P(12,18)*SF[14] - P(10,18)*SPP[10] - (P(11,18)*q0)*0.5f;
|
||||
nextP(3,18) = P(3,18) + P(0,18)*SF[7] + P(1,18)*SF[6] + P(2,18)*SF[9] + P(10,18)*SF[15] - P(11,18)*SF[14] - (P(12,18)*q0)*0.5f;
|
||||
nextP(4,18) = P(4,18) + P(0,18)*SF[5] + P(1,18)*SF[3] - P(3,18)*SF[4] + P(2,18)*SPP[0] + P(13,18)*SPP[3] + P(14,18)*SPP[6] - P(15,18)*SPP[9];
|
||||
nextP(5,18) = P(5,18) + P(0,18)*SF[4] + P(2,18)*SF[3] + P(3,18)*SF[5] - P(1,18)*SPP[0] - P(13,18)*SPP[8] + P(14,18)*SPP[2] + P(15,18)*SPP[5];
|
||||
nextP(6,18) = P(6,18) + P(1,18)*SF[4] - P(2,18)*SF[5] + P(3,18)*SF[3] + P(0,18)*SPP[0] + P(13,18)*SPP[4] - P(14,18)*SPP[7] - P(15,18)*SPP[1];
|
||||
nextP(7,18) = P(7,18) + P(4,18)*dt;
|
||||
nextP(8,18) = P(8,18) + P(5,18)*dt;
|
||||
nextP(9,18) = P(9,18) + P(6,18)*dt;
|
||||
nextP(10,18) = P(10,18);
|
||||
nextP(11,18) = P(11,18);
|
||||
nextP(12,18) = P(12,18);
|
||||
nextP(13,18) = P(13,18);
|
||||
nextP(14,18) = P(14,18);
|
||||
nextP(15,18) = P(15,18);
|
||||
nextP(16,18) = P(16,18);
|
||||
nextP(17,18) = P(17,18);
|
||||
nextP(18,18) = P(18,18);
|
||||
nextP(0,19) = P(0,19) + P(1,19)*SF[9] + P(2,19)*SF[11] + P(3,19)*SF[10] + P(10,19)*SF[14] + P(11,19)*SF[15] + P(12,19)*SPP[10];
|
||||
nextP(1,19) = P(1,19) + P(0,19)*SF[8] + P(2,19)*SF[7] + P(3,19)*SF[11] - P(12,19)*SF[15] + P(11,19)*SPP[10] - (P(10,19)*q0)*0.5f;
|
||||
nextP(2,19) = P(2,19) + P(0,19)*SF[6] + P(1,19)*SF[10] + P(3,19)*SF[8] + P(12,19)*SF[14] - P(10,19)*SPP[10] - (P(11,19)*q0)*0.5f;
|
||||
nextP(3,19) = P(3,19) + P(0,19)*SF[7] + P(1,19)*SF[6] + P(2,19)*SF[9] + P(10,19)*SF[15] - P(11,19)*SF[14] - (P(12,19)*q0)*0.5f;
|
||||
nextP(4,19) = P(4,19) + P(0,19)*SF[5] + P(1,19)*SF[3] - P(3,19)*SF[4] + P(2,19)*SPP[0] + P(13,19)*SPP[3] + P(14,19)*SPP[6] - P(15,19)*SPP[9];
|
||||
nextP(5,19) = P(5,19) + P(0,19)*SF[4] + P(2,19)*SF[3] + P(3,19)*SF[5] - P(1,19)*SPP[0] - P(13,19)*SPP[8] + P(14,19)*SPP[2] + P(15,19)*SPP[5];
|
||||
nextP(6,19) = P(6,19) + P(1,19)*SF[4] - P(2,19)*SF[5] + P(3,19)*SF[3] + P(0,19)*SPP[0] + P(13,19)*SPP[4] - P(14,19)*SPP[7] - P(15,19)*SPP[1];
|
||||
nextP(7,19) = P(7,19) + P(4,19)*dt;
|
||||
nextP(8,19) = P(8,19) + P(5,19)*dt;
|
||||
nextP(9,19) = P(9,19) + P(6,19)*dt;
|
||||
nextP(10,19) = P(10,19);
|
||||
nextP(11,19) = P(11,19);
|
||||
nextP(12,19) = P(12,19);
|
||||
nextP(13,19) = P(13,19);
|
||||
nextP(14,19) = P(14,19);
|
||||
nextP(15,19) = P(15,19);
|
||||
nextP(16,19) = P(16,19);
|
||||
nextP(17,19) = P(17,19);
|
||||
nextP(18,19) = P(18,19);
|
||||
nextP(19,19) = P(19,19);
|
||||
nextP(0,20) = P(0,20) + P(1,20)*SF[9] + P(2,20)*SF[11] + P(3,20)*SF[10] + P(10,20)*SF[14] + P(11,20)*SF[15] + P(12,20)*SPP[10];
|
||||
nextP(1,20) = P(1,20) + P(0,20)*SF[8] + P(2,20)*SF[7] + P(3,20)*SF[11] - P(12,20)*SF[15] + P(11,20)*SPP[10] - (P(10,20)*q0)*0.5f;
|
||||
nextP(2,20) = P(2,20) + P(0,20)*SF[6] + P(1,20)*SF[10] + P(3,20)*SF[8] + P(12,20)*SF[14] - P(10,20)*SPP[10] - (P(11,20)*q0)*0.5f;
|
||||
nextP(3,20) = P(3,20) + P(0,20)*SF[7] + P(1,20)*SF[6] + P(2,20)*SF[9] + P(10,20)*SF[15] - P(11,20)*SF[14] - (P(12,20)*q0)*0.5f;
|
||||
nextP(4,20) = P(4,20) + P(0,20)*SF[5] + P(1,20)*SF[3] - P(3,20)*SF[4] + P(2,20)*SPP[0] + P(13,20)*SPP[3] + P(14,20)*SPP[6] - P(15,20)*SPP[9];
|
||||
nextP(5,20) = P(5,20) + P(0,20)*SF[4] + P(2,20)*SF[3] + P(3,20)*SF[5] - P(1,20)*SPP[0] - P(13,20)*SPP[8] + P(14,20)*SPP[2] + P(15,20)*SPP[5];
|
||||
nextP(6,20) = P(6,20) + P(1,20)*SF[4] - P(2,20)*SF[5] + P(3,20)*SF[3] + P(0,20)*SPP[0] + P(13,20)*SPP[4] - P(14,20)*SPP[7] - P(15,20)*SPP[1];
|
||||
nextP(7,20) = P(7,20) + P(4,20)*dt;
|
||||
nextP(8,20) = P(8,20) + P(5,20)*dt;
|
||||
nextP(9,20) = P(9,20) + P(6,20)*dt;
|
||||
nextP(10,20) = P(10,20);
|
||||
nextP(11,20) = P(11,20);
|
||||
nextP(12,20) = P(12,20);
|
||||
nextP(13,20) = P(13,20);
|
||||
nextP(14,20) = P(14,20);
|
||||
nextP(15,20) = P(15,20);
|
||||
nextP(16,20) = P(16,20);
|
||||
nextP(17,20) = P(17,20);
|
||||
nextP(18,20) = P(18,20);
|
||||
nextP(19,20) = P(19,20);
|
||||
nextP(20,20) = P(20,20);
|
||||
nextP(0,21) = P(0,21) + P(1,21)*SF[9] + P(2,21)*SF[11] + P(3,21)*SF[10] + P(10,21)*SF[14] + P(11,21)*SF[15] + P(12,21)*SPP[10];
|
||||
nextP(1,21) = P(1,21) + P(0,21)*SF[8] + P(2,21)*SF[7] + P(3,21)*SF[11] - P(12,21)*SF[15] + P(11,21)*SPP[10] - (P(10,21)*q0)*0.5f;
|
||||
nextP(2,21) = P(2,21) + P(0,21)*SF[6] + P(1,21)*SF[10] + P(3,21)*SF[8] + P(12,21)*SF[14] - P(10,21)*SPP[10] - (P(11,21)*q0)*0.5f;
|
||||
nextP(3,21) = P(3,21) + P(0,21)*SF[7] + P(1,21)*SF[6] + P(2,21)*SF[9] + P(10,21)*SF[15] - P(11,21)*SF[14] - (P(12,21)*q0)*0.5f;
|
||||
nextP(4,21) = P(4,21) + P(0,21)*SF[5] + P(1,21)*SF[3] - P(3,21)*SF[4] + P(2,21)*SPP[0] + P(13,21)*SPP[3] + P(14,21)*SPP[6] - P(15,21)*SPP[9];
|
||||
nextP(5,21) = P(5,21) + P(0,21)*SF[4] + P(2,21)*SF[3] + P(3,21)*SF[5] - P(1,21)*SPP[0] - P(13,21)*SPP[8] + P(14,21)*SPP[2] + P(15,21)*SPP[5];
|
||||
nextP(6,21) = P(6,21) + P(1,21)*SF[4] - P(2,21)*SF[5] + P(3,21)*SF[3] + P(0,21)*SPP[0] + P(13,21)*SPP[4] - P(14,21)*SPP[7] - P(15,21)*SPP[1];
|
||||
nextP(7,21) = P(7,21) + P(4,21)*dt;
|
||||
nextP(8,21) = P(8,21) + P(5,21)*dt;
|
||||
nextP(9,21) = P(9,21) + P(6,21)*dt;
|
||||
nextP(10,21) = P(10,21);
|
||||
nextP(11,21) = P(11,21);
|
||||
nextP(12,21) = P(12,21);
|
||||
nextP(13,21) = P(13,21);
|
||||
nextP(14,21) = P(14,21);
|
||||
nextP(15,21) = P(15,21);
|
||||
nextP(16,21) = P(16,21);
|
||||
nextP(17,21) = P(17,21);
|
||||
nextP(18,21) = P(18,21);
|
||||
nextP(19,21) = P(19,21);
|
||||
nextP(20,21) = P(20,21);
|
||||
nextP(21,21) = P(21,21);
|
||||
nextP(0,22) = P(0,22) + P(1,22)*SF[9] + P(2,22)*SF[11] + P(3,22)*SF[10] + P(10,22)*SF[14] + P(11,22)*SF[15] + P(12,22)*SPP[10];
|
||||
nextP(1,22) = P(1,22) + P(0,22)*SF[8] + P(2,22)*SF[7] + P(3,22)*SF[11] - P(12,22)*SF[15] + P(11,22)*SPP[10] - (P(10,22)*q0)*0.5f;
|
||||
nextP(2,22) = P(2,22) + P(0,22)*SF[6] + P(1,22)*SF[10] + P(3,22)*SF[8] + P(12,22)*SF[14] - P(10,22)*SPP[10] - (P(11,22)*q0)*0.5f;
|
||||
nextP(3,22) = P(3,22) + P(0,22)*SF[7] + P(1,22)*SF[6] + P(2,22)*SF[9] + P(10,22)*SF[15] - P(11,22)*SF[14] - (P(12,22)*q0)*0.5f;
|
||||
nextP(4,22) = P(4,22) + P(0,22)*SF[5] + P(1,22)*SF[3] - P(3,22)*SF[4] + P(2,22)*SPP[0] + P(13,22)*SPP[3] + P(14,22)*SPP[6] - P(15,22)*SPP[9];
|
||||
nextP(5,22) = P(5,22) + P(0,22)*SF[4] + P(2,22)*SF[3] + P(3,22)*SF[5] - P(1,22)*SPP[0] - P(13,22)*SPP[8] + P(14,22)*SPP[2] + P(15,22)*SPP[5];
|
||||
nextP(6,22) = P(6,22) + P(1,22)*SF[4] - P(2,22)*SF[5] + P(3,22)*SF[3] + P(0,22)*SPP[0] + P(13,22)*SPP[4] - P(14,22)*SPP[7] - P(15,22)*SPP[1];
|
||||
nextP(7,22) = P(7,22) + P(4,22)*dt;
|
||||
nextP(8,22) = P(8,22) + P(5,22)*dt;
|
||||
nextP(9,22) = P(9,22) + P(6,22)*dt;
|
||||
nextP(10,22) = P(10,22);
|
||||
nextP(11,22) = P(11,22);
|
||||
nextP(12,22) = P(12,22);
|
||||
nextP(13,22) = P(13,22);
|
||||
nextP(14,22) = P(14,22);
|
||||
nextP(15,22) = P(15,22);
|
||||
nextP(16,22) = P(16,22);
|
||||
nextP(17,22) = P(17,22);
|
||||
nextP(18,22) = P(18,22);
|
||||
nextP(19,22) = P(19,22);
|
||||
nextP(20,22) = P(20,22);
|
||||
nextP(21,22) = P(21,22);
|
||||
nextP(22,22) = P(22,22);
|
||||
nextP(0,23) = P(0,23) + P(1,23)*SF[9] + P(2,23)*SF[11] + P(3,23)*SF[10] + P(10,23)*SF[14] + P(11,23)*SF[15] + P(12,23)*SPP[10];
|
||||
nextP(1,23) = P(1,23) + P(0,23)*SF[8] + P(2,23)*SF[7] + P(3,23)*SF[11] - P(12,23)*SF[15] + P(11,23)*SPP[10] - (P(10,23)*q0)*0.5f;
|
||||
nextP(2,23) = P(2,23) + P(0,23)*SF[6] + P(1,23)*SF[10] + P(3,23)*SF[8] + P(12,23)*SF[14] - P(10,23)*SPP[10] - (P(11,23)*q0)*0.5f;
|
||||
nextP(3,23) = P(3,23) + P(0,23)*SF[7] + P(1,23)*SF[6] + P(2,23)*SF[9] + P(10,23)*SF[15] - P(11,23)*SF[14] - (P(12,23)*q0)*0.5f;
|
||||
nextP(4,23) = P(4,23) + P(0,23)*SF[5] + P(1,23)*SF[3] - P(3,23)*SF[4] + P(2,23)*SPP[0] + P(13,23)*SPP[3] + P(14,23)*SPP[6] - P(15,23)*SPP[9];
|
||||
nextP(5,23) = P(5,23) + P(0,23)*SF[4] + P(2,23)*SF[3] + P(3,23)*SF[5] - P(1,23)*SPP[0] - P(13,23)*SPP[8] + P(14,23)*SPP[2] + P(15,23)*SPP[5];
|
||||
nextP(6,23) = P(6,23) + P(1,23)*SF[4] - P(2,23)*SF[5] + P(3,23)*SF[3] + P(0,23)*SPP[0] + P(13,23)*SPP[4] - P(14,23)*SPP[7] - P(15,23)*SPP[1];
|
||||
nextP(7,23) = P(7,23) + P(4,23)*dt;
|
||||
nextP(8,23) = P(8,23) + P(5,23)*dt;
|
||||
nextP(9,23) = P(9,23) + P(6,23)*dt;
|
||||
nextP(10,23) = P(10,23);
|
||||
nextP(11,23) = P(11,23);
|
||||
nextP(12,23) = P(12,23);
|
||||
nextP(13,23) = P(13,23);
|
||||
nextP(14,23) = P(14,23);
|
||||
nextP(15,23) = P(15,23);
|
||||
nextP(16,23) = P(16,23);
|
||||
nextP(17,23) = P(17,23);
|
||||
nextP(18,23) = P(18,23);
|
||||
nextP(19,23) = P(19,23);
|
||||
nextP(20,23) = P(20,23);
|
||||
nextP(21,23) = P(21,23);
|
||||
nextP(22,23) = P(22,23);
|
||||
nextP(23,23) = P(23,23);
|
||||
|
||||
// capture largest difference
|
||||
float max_diff_fraction = 0.0f;
|
||||
int max_row, max_col;
|
||||
float max_old, max_new;
|
||||
|
||||
for (int col=0; col<=23; col++) {
|
||||
for (int row=0; row<=col; row++) {
|
||||
float diff_fraction = fabsf(nextP_sympy(row,col)-nextP(row,col)) / fabsf(nextP(row,col));
|
||||
if (diff_fraction > max_diff_fraction) {
|
||||
max_diff_fraction = diff_fraction;
|
||||
max_row = row;
|
||||
max_col = col;
|
||||
max_old = nextP(row,col);
|
||||
max_new = nextP_sympy(row,col);
|
||||
}
|
||||
}
|
||||
}
|
||||
if (max_diff_fraction > 5E-5f) {
|
||||
printf("Fail: Covariance Prediction max diff fraction = %e , old = %e , new = %e , location index = %i,%i\n",max_diff_fraction, max_old, max_new, max_row, max_col);
|
||||
} else {
|
||||
printf("Pass: Covariance Prediction max diff fraction = %e , old = %e , new = %e , location index = %i,%i\n",max_diff_fraction, max_old, max_new, max_row, max_col);
|
||||
}
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
@@ -0,0 +1,489 @@
|
||||
from sympy import *
|
||||
from code_gen import *
|
||||
|
||||
# q: quaternion describing rotation from frame 1 to frame 2
|
||||
# returns a rotation matrix derived form q which describes the same
|
||||
# rotation
|
||||
def quat2Rot(q):
|
||||
q0 = q[0]
|
||||
q1 = q[1]
|
||||
q2 = q[2]
|
||||
q3 = q[3]
|
||||
|
||||
Rot = Matrix([[q0**2 + q1**2 - q2**2 - q3**2, 2*(q1*q2 - q0*q3), 2*(q1*q3 + q0*q2)],
|
||||
[2*(q1*q2 + q0*q3), q0**2 - q1**2 + q2**2 - q3**2, 2*(q2*q3 - q0*q1)],
|
||||
[2*(q1*q3-q0*q2), 2*(q2*q3 + q0*q1), q0**2 - q1**2 - q2**2 + q3**2]])
|
||||
|
||||
return Rot
|
||||
|
||||
def create_cov_matrix(i, j):
|
||||
if j >= i:
|
||||
return Symbol("P(" + str(i) + "," + str(j) + ")", real=True)
|
||||
# legacy array format
|
||||
# return Symbol("P[" + str(i) + "][" + str(j) + "]", real=True)
|
||||
else:
|
||||
return 0
|
||||
|
||||
def create_Tbs_matrix(i, j):
|
||||
return Symbol("Tbs(" + str(i) + "," + str(j) + ")", real=True)
|
||||
# legacy array format
|
||||
# return Symbol("Tbs[" + str(i) + "][" + str(j) + "]", real=True)
|
||||
|
||||
def quat_mult(p,q):
|
||||
r = Matrix([p[0] * q[0] - p[1] * q[1] - p[2] * q[2] - p[3] * q[3],
|
||||
p[0] * q[1] + p[1] * q[0] + p[2] * q[3] - p[3] * q[2],
|
||||
p[0] * q[2] - p[1] * q[3] + p[2] * q[0] + p[3] * q[1],
|
||||
p[0] * q[3] + p[1] * q[2] - p[2] * q[1] + p[3] * q[0]])
|
||||
|
||||
return r
|
||||
|
||||
def create_symmetric_cov_matrix():
|
||||
# define a symbolic covariance matrix
|
||||
P = Matrix(24,24,create_cov_matrix)
|
||||
|
||||
for index in range(24):
|
||||
for j in range(24):
|
||||
if index > j:
|
||||
P[index,j] = P[j,index]
|
||||
|
||||
return P
|
||||
|
||||
# generate equations for observation Jacobian and Kalman gain
|
||||
def generate_observation_equations(P,state,observation,variance):
|
||||
H = Matrix([observation]).jacobian(state)
|
||||
innov_var = H * P * H.T + Matrix([variance])
|
||||
assert(innov_var.shape[0] == 1)
|
||||
assert(innov_var.shape[1] == 1)
|
||||
K = P * H.T / innov_var[0,0]
|
||||
HK_simple = cse(Matrix([H.transpose(), K]), symbols("HK0:1000"), optimizations='basic')
|
||||
|
||||
return HK_simple
|
||||
|
||||
# generate equations for observation vector Jacobian and Kalman gain
|
||||
# n_obs is the vector dimension and must be >= 2
|
||||
def generate_observation_vector_equations(P,state,observation,variance,n_obs):
|
||||
K = zeros(24,n_obs)
|
||||
H = observation.jacobian(state)
|
||||
HK = zeros(n_obs*48,1)
|
||||
for index in range(n_obs):
|
||||
H[index,:] = Matrix([observation[index]]).jacobian(state)
|
||||
innov_var = H[index,:] * P * H[index,:].T + Matrix([variance])
|
||||
assert(innov_var.shape[0] == 1)
|
||||
assert(innov_var.shape[1] == 1)
|
||||
K[:,index] = P * H[index,:].T / innov_var[0,0]
|
||||
HK[index*48:(index+1)*48,0] = Matrix([H[index,:].transpose(), K[:,index]])
|
||||
|
||||
HK_simple = cse(HK, symbols("HK0:1000"), optimizations='basic')
|
||||
|
||||
return HK_simple
|
||||
|
||||
# write single observation equations to file
|
||||
def write_equations_to_file(equations,code_generator_id,n_obs):
|
||||
if (n_obs < 1):
|
||||
return
|
||||
|
||||
if (n_obs == 1):
|
||||
code_generator_id.print_string("Sub Expressions")
|
||||
code_generator_id.write_subexpressions(equations[0])
|
||||
code_generator_id.print_string("Observation Jacobians")
|
||||
code_generator_id.write_matrix(Matrix(equations[1][0][0:24]), "Hfusion")
|
||||
code_generator_id.print_string("Kalman gains")
|
||||
code_generator_id.write_matrix(Matrix(equations[1][0][24:]), "Kfusion")
|
||||
else:
|
||||
code_generator_id.print_string("Sub Expressions")
|
||||
code_generator_id.write_subexpressions(equations[0])
|
||||
for axis_index in range(n_obs):
|
||||
start_index = axis_index*48
|
||||
code_generator_id.print_string("Observation Jacobians - axis %i" % axis_index)
|
||||
code_generator_id.write_matrix(Matrix(equations[1][0][start_index:start_index+24]), "Hfusion")
|
||||
code_generator_id.print_string("Kalman gains - axis %i" % axis_index)
|
||||
code_generator_id.write_matrix(Matrix(equations[1][0][start_index+24:start_index+48]), "Kfusion")
|
||||
|
||||
return
|
||||
|
||||
# derive equations for sequential fusion of optical flow measurements
|
||||
def optical_flow_observation(P,state,R_to_body,vx,vy,vz):
|
||||
flow_code_generator = CodeGenerator("./generated/flow_generated.cpp")
|
||||
range = symbols("range", real=True) # range from camera focal point to ground along sensor Z axis
|
||||
obs_var = symbols("R_LOS", real=True) # optical flow line of sight rate measurement noise variance
|
||||
|
||||
# Define rotation matrix from body to sensor frame
|
||||
Tbs = Matrix(3,3,create_Tbs_matrix)
|
||||
|
||||
# Calculate earth relative velocity in a non-rotating sensor frame
|
||||
relVelSensor = Tbs * R_to_body * Matrix([vx,vy,vz])
|
||||
|
||||
# Divide by range to get predicted angular LOS rates relative to X and Y
|
||||
# axes. Note these are rates in a non-rotating sensor frame
|
||||
losRateSensorX = +relVelSensor[1]/range
|
||||
losRateSensorY = -relVelSensor[0]/range
|
||||
|
||||
# calculate the observation Jacobian and Kalman gains for the X axis
|
||||
equations = generate_observation_equations(P,state,losRateSensorX,obs_var)
|
||||
|
||||
flow_code_generator.print_string("X Axis Equations")
|
||||
write_equations_to_file(equations,flow_code_generator,1)
|
||||
|
||||
# calculate the observation Jacobian and Kalman gains for the Y axis
|
||||
equations = generate_observation_equations(P,state,losRateSensorY,obs_var)
|
||||
|
||||
flow_code_generator.print_string("Y Axis Equations")
|
||||
write_equations_to_file(equations,flow_code_generator,1)
|
||||
|
||||
flow_code_generator.close()
|
||||
|
||||
# calculate a combined result for a possible reduction in operations, but will use more stack
|
||||
observation = Matrix([relVelSensor[1]/range,-relVelSensor[0]/range])
|
||||
equations = generate_observation_vector_equations(P,state,observation,obs_var,2)
|
||||
flow_code_generator_alt = CodeGenerator("./generated/flow_generated_alt.cpp")
|
||||
write_equations_to_file(equations,flow_code_generator_alt,2)
|
||||
flow_code_generator_alt.close()
|
||||
|
||||
return
|
||||
|
||||
# Derive equations for sequential fusion of body frame velocity measurements
|
||||
def body_frame_velocity_observation(P,state,R_to_body,vx,vy,vz):
|
||||
obs_var = symbols("R_VEL", real=True) # measurement noise variance
|
||||
|
||||
# Calculate earth relative velocity in a non-rotating sensor frame
|
||||
vel_bf = R_to_body * Matrix([vx,vy,vz])
|
||||
|
||||
vel_bf_code_generator = CodeGenerator("./generated/vel_bf_generated.cpp")
|
||||
axes = [0,1,2]
|
||||
H_obs = vel_bf.jacobian(state) # observation Jacobians
|
||||
K_gain = zeros(24,3)
|
||||
for index in axes:
|
||||
equations = generate_observation_equations(P,state,vel_bf[index],obs_var)
|
||||
|
||||
vel_bf_code_generator.print_string("axis %i" % index)
|
||||
vel_bf_code_generator.write_subexpressions(equations[0])
|
||||
vel_bf_code_generator.write_matrix(Matrix(equations[1][0][0:24]), "H_VEL")
|
||||
vel_bf_code_generator.write_matrix(Matrix(equations[1][0][24:]), "Kfusion")
|
||||
|
||||
vel_bf_code_generator.close()
|
||||
|
||||
# calculate a combined result for a possible reduction in operations, but will use more stack
|
||||
equations = generate_observation_vector_equations(P,state,vel_bf,obs_var,3)
|
||||
|
||||
vel_bf_code_generator_alt = CodeGenerator("./generated/vel_bf_generated_alt.cpp")
|
||||
write_equations_to_file(equations,vel_bf_code_generator_alt,3)
|
||||
vel_bf_code_generator_alt.close()
|
||||
|
||||
# derive equations for fusion of dual antenna yaw measurement
|
||||
def gps_yaw_observation(P,state,R_to_body):
|
||||
obs_var = symbols("R_YAW", real=True) # measurement noise variance
|
||||
ant_yaw = symbols("ant_yaw", real=True) # yaw angle of antenna array axis wrt X body axis
|
||||
|
||||
# define antenna vector in body frame
|
||||
ant_vec_bf = Matrix([cos(ant_yaw),sin(ant_yaw),0])
|
||||
|
||||
# rotate into earth frame
|
||||
ant_vec_ef = R_to_body.T * ant_vec_bf
|
||||
|
||||
# Calculate the yaw angle from the projection
|
||||
observation = atan(ant_vec_ef[1]/ant_vec_ef[0])
|
||||
|
||||
equations = generate_observation_equations(P,state,observation,obs_var)
|
||||
|
||||
gps_yaw_code_generator = CodeGenerator("./generated/gps_yaw_generated.cpp")
|
||||
write_equations_to_file(equations,gps_yaw_code_generator,1)
|
||||
gps_yaw_code_generator.close()
|
||||
|
||||
return
|
||||
|
||||
# derive equations for fusion of declination
|
||||
def declination_observation(P,state,ix,iy):
|
||||
obs_var = symbols("R_DECL", real=True) # measurement noise variance
|
||||
|
||||
# the predicted measurement is the angle wrt magnetic north of the horizontal
|
||||
# component of the measured field
|
||||
observation = atan(iy/ix)
|
||||
|
||||
equations = generate_observation_equations(P,state,observation,obs_var)
|
||||
|
||||
mag_decl_code_generator = CodeGenerator("./generated/mag_decl_generated.cpp")
|
||||
write_equations_to_file(equations,mag_decl_code_generator,1)
|
||||
mag_decl_code_generator.close()
|
||||
|
||||
return
|
||||
|
||||
# derive equations for fusion of lateral body acceleration (multirotors only)
|
||||
def body_frame_accel_observation(P,state,R_to_body,vx,vy,vz,wx,wy):
|
||||
obs_var = symbols("R_ACC", real=True) # measurement noise variance
|
||||
Kaccx = symbols("Kaccx", real=True) # measurement noise variance
|
||||
Kaccy = symbols("Kaccy", real=True) # measurement noise variance
|
||||
|
||||
# use relationship between airspeed along the X and Y body axis and the
|
||||
# drag to predict the lateral acceleration for a multirotor vehicle type
|
||||
# where propulsion forces are generated primarily along the Z body axis
|
||||
|
||||
vrel = R_to_body*Matrix([vx-wx,vy-wy,vz]) # predicted wind relative velocity
|
||||
|
||||
# Use this nonlinear model for the prediction in the implementation only
|
||||
# It uses a ballistic coefficient for each axis
|
||||
# accXpred = -0.5*rho*vrel[0]*vrel[0]*BCXinv # predicted acceleration measured along X body axis
|
||||
# accYpred = -0.5*rho*vrel[1]*vrel[1]*BCYinv # predicted acceleration measured along Y body axis
|
||||
|
||||
# Use a simple viscous drag model for the linear estimator equations
|
||||
# Use the the derivative from speed to acceleration averaged across the
|
||||
# speed range. This avoids the generation of a dirac function in the derivation
|
||||
# The nonlinear equation will be used to calculate the predicted measurement in implementation
|
||||
observation = Matrix([-Kaccx*vrel[0],-Kaccy*vrel[1]])
|
||||
|
||||
acc_bf_code_generator = CodeGenerator("./generated/acc_bf_generated.cpp")
|
||||
H = observation.jacobian(state)
|
||||
K = zeros(24,2)
|
||||
axes = [0,1]
|
||||
for index in axes:
|
||||
equations = generate_observation_equations(P,state,observation[index],obs_var)
|
||||
acc_bf_code_generator.print_string("Axis %i equations" % index)
|
||||
write_equations_to_file(equations,acc_bf_code_generator,1)
|
||||
|
||||
acc_bf_code_generator.close()
|
||||
|
||||
# calculate a combined result for a possible reduction in operations, but will use more stack
|
||||
equations = generate_observation_vector_equations(P,state,observation,obs_var,2)
|
||||
|
||||
acc_bf_code_generator_alt = CodeGenerator("./generated/acc_bf_generated_alt.cpp")
|
||||
write_equations_to_file(equations,acc_bf_code_generator_alt,3)
|
||||
acc_bf_code_generator_alt.close()
|
||||
|
||||
return
|
||||
|
||||
# yaw fusion
|
||||
def yaw_observation(P,state,R_to_earth):
|
||||
yaw_code_generator = CodeGenerator("./generated/yaw_generated.cpp")
|
||||
|
||||
# Derive observation Jacobian for fusion of 321 sequence yaw measurement
|
||||
# Calculate the yaw (first rotation) angle from the 321 rotation sequence
|
||||
# Provide alternative angle that avoids singularity at +-pi/2 yaw
|
||||
angMeasA = atan(R_to_earth[1,0]/R_to_earth[0,0])
|
||||
H_YAW321_A = Matrix([angMeasA]).jacobian(state)
|
||||
H_YAW321_A_simple = cse(H_YAW321_A, symbols('SA0:200'))
|
||||
|
||||
angMeasB = pi/2 - atan(R_to_earth[0,0]/R_to_earth[1,0])
|
||||
H_YAW321_B = Matrix([angMeasB]).jacobian(state)
|
||||
H_YAW321_B_simple = cse(H_YAW321_B, symbols('SB0:200'))
|
||||
|
||||
yaw_code_generator.print_string("calculate 321 yaw observation matrix - option A")
|
||||
yaw_code_generator.write_subexpressions(H_YAW321_A_simple[0])
|
||||
yaw_code_generator.write_matrix(Matrix(H_YAW321_A_simple[1]).T, "H_YAW")
|
||||
|
||||
yaw_code_generator.print_string("calculate 321 yaw observation matrix - option B")
|
||||
yaw_code_generator.write_subexpressions(H_YAW321_B_simple[0])
|
||||
yaw_code_generator.write_matrix(Matrix(H_YAW321_B_simple[1]).T, "H_YAW")
|
||||
|
||||
# Derive observation Jacobian for fusion of 312 sequence yaw measurement
|
||||
# Calculate the yaw (first rotation) angle from an Euler 312 sequence
|
||||
# Provide alternative angle that avoids singularity at +-pi/2 yaw
|
||||
angMeasA = atan(-R_to_earth[0,1]/R_to_earth[1,1])
|
||||
H_YAW312_A = Matrix([angMeasA]).jacobian(state)
|
||||
H_YAW312_A_simple = cse(H_YAW312_A, symbols('SA0:200'))
|
||||
|
||||
angMeasB = pi/2 - atan(-R_to_earth[1,1]/R_to_earth[0,1])
|
||||
H_YAW312_B = Matrix([angMeasB]).jacobian(state)
|
||||
H_YAW312_B_simple = cse(H_YAW312_B, symbols('SB0:200'))
|
||||
|
||||
yaw_code_generator.print_string("calculate 312 yaw observation matrix - option A")
|
||||
yaw_code_generator.write_subexpressions(H_YAW312_A_simple[0])
|
||||
yaw_code_generator.write_matrix(Matrix(H_YAW312_A_simple[1]).T, "H_YAW")
|
||||
|
||||
yaw_code_generator.print_string("calculate 312 yaw observation matrix - option B")
|
||||
yaw_code_generator.write_subexpressions(H_YAW312_B_simple[0])
|
||||
yaw_code_generator.write_matrix(Matrix(H_YAW312_B_simple[1]).T, "H_YAW")
|
||||
|
||||
yaw_code_generator.close()
|
||||
|
||||
return
|
||||
|
||||
# 3D magnetometer fusion
|
||||
def mag_observation(P,state,R_to_body,i,ib):
|
||||
obs_var = symbols("R_MAG", real=True) # magnetometer measurement noise variance
|
||||
|
||||
m_mag = R_to_body * i + ib
|
||||
|
||||
# calculate a separate set of equations for each axis
|
||||
mag_code_generator = CodeGenerator("./generated/3Dmag_generated.cpp")
|
||||
|
||||
axes = [0,1,2]
|
||||
for index in axes:
|
||||
equations = generate_observation_equations(P,state,m_mag[index],obs_var)
|
||||
mag_code_generator.print_string("Axis %i equations" % index)
|
||||
write_equations_to_file(equations,mag_code_generator,1)
|
||||
|
||||
mag_code_generator.close()
|
||||
|
||||
# calculate a combined set of equations for a possible reduction in operations, but will use slighlty more stack
|
||||
equations = generate_observation_vector_equations(P,state,m_mag,obs_var,3)
|
||||
|
||||
mag_code_generator_alt = CodeGenerator("./generated/3Dmag_generated_alt.cpp")
|
||||
write_equations_to_file(equations,mag_code_generator_alt,3)
|
||||
mag_code_generator_alt.close()
|
||||
|
||||
return
|
||||
|
||||
# airspeed fusion
|
||||
def tas_observation(P,state,vx,vy,vz,wx,wy):
|
||||
obs_var = symbols("R_TAS", real=True) # true airspeed measurement noise variance
|
||||
|
||||
observation = sqrt((vx-wx)*(vx-wx)+(vy-wy)*(vy-wy)+vz*vz)
|
||||
|
||||
equations = generate_observation_equations(P,state,observation,obs_var)
|
||||
|
||||
tas_code_generator = CodeGenerator("./generated/tas_generated.cpp")
|
||||
write_equations_to_file(equations,tas_code_generator,1)
|
||||
tas_code_generator.close()
|
||||
|
||||
return
|
||||
|
||||
# sideslip fusion
|
||||
def beta_observation(P,state,R_to_body,vx,vy,vz,wx,wy):
|
||||
obs_var = symbols("R_BETA", real=True) # sideslip measurement noise variance
|
||||
|
||||
v_rel_ef = Matrix([vx-wx,vy-wy,vz])
|
||||
v_rel_bf = R_to_body * v_rel_ef
|
||||
observation = v_rel_bf[1]/v_rel_bf[0]
|
||||
|
||||
equations = generate_observation_equations(P,state,observation,obs_var)
|
||||
|
||||
beta_code_generator = CodeGenerator("./generated/beta_generated.cpp")
|
||||
write_equations_to_file(equations,beta_code_generator,1)
|
||||
beta_code_generator.close()
|
||||
|
||||
return
|
||||
|
||||
def generate_code():
|
||||
print('Starting code generation:')
|
||||
print('Creating symbolic variables ...')
|
||||
|
||||
dt = symbols("dt", real=True) # dt
|
||||
g = symbols("g", real=True) # gravity constant
|
||||
|
||||
r_hor_vel = symbols("R_hor_vel", real=True) # horizontal velocity noise variance
|
||||
r_ver_vel = symbols("R_vert_vel", real=True) # vertical velocity noise variance
|
||||
r_hor_pos = symbols("R_hor_pos", real=True) # horizontal position noise variance
|
||||
|
||||
# inputs, integrated gyro measurements
|
||||
# delta angle x y z
|
||||
d_ang_x, d_ang_y, d_ang_z = symbols("dax day daz", real=True) # delta angle x
|
||||
d_ang = Matrix([d_ang_x, d_ang_y, d_ang_z])
|
||||
|
||||
# inputs, integrated accelerometer measurements
|
||||
# delta velocity x y z
|
||||
d_v_x, d_v_y, d_v_z = symbols("dvx dvy dvz", real=True)
|
||||
d_v = Matrix([d_v_x, d_v_y,d_v_z])
|
||||
|
||||
u = Matrix([d_ang, d_v])
|
||||
|
||||
# input noise
|
||||
d_ang_x_var, d_ang_y_var, d_ang_z_var = symbols("daxVar dayVar dazVar", real=True)
|
||||
|
||||
d_v_x_var, d_v_y_var, d_v_z_var = symbols("dvxVar dvyVar dvzVar", real=True)
|
||||
|
||||
var_u = Matrix.diag(d_ang_x_var, d_ang_y_var, d_ang_z_var, d_v_x_var, d_v_y_var, d_v_z_var)
|
||||
|
||||
# define state vector
|
||||
|
||||
# attitude quaternion
|
||||
qw, qx, qy, qz = symbols("q0 q1 q2 q3", real=True)
|
||||
q = Matrix([qw,qx,qy,qz])
|
||||
R_to_earth = quat2Rot(q)
|
||||
R_to_body = R_to_earth.T
|
||||
|
||||
# velocity in NED local frame (north, east, down)
|
||||
vx, vy, vz = symbols("vn ve vd", real=True)
|
||||
v = Matrix([vx,vy,vz])
|
||||
|
||||
# position in NED local frame (north, east, down)
|
||||
px, py, pz = symbols("pn pe pd", real=True)
|
||||
p = Matrix([px,py,pz])
|
||||
|
||||
# delta angle bias x y z
|
||||
d_ang_bx, d_ang_by, d_ang_bz = symbols("dax_b day_b daz_b", real=True)
|
||||
d_ang_b = Matrix([d_ang_bx, d_ang_by, d_ang_bz])
|
||||
d_ang_true = d_ang - d_ang_b
|
||||
|
||||
# delta velocity bias x y z
|
||||
d_vel_bx, d_vel_by, d_vel_bz = symbols("dvx_b dvy_b dvz_b", real=True)
|
||||
d_vel_b = Matrix([d_vel_bx, d_vel_by, d_vel_bz])
|
||||
d_vel_true = d_v - d_vel_b
|
||||
|
||||
# earth magnetic field vector x y z
|
||||
ix, iy, iz = symbols("magN magE magD", real=True)
|
||||
i = Matrix([ix,iy,iz])
|
||||
|
||||
# earth magnetic field bias in body frame
|
||||
ibx, iby, ibz = symbols("ibx iby ibz", real=True)
|
||||
|
||||
ib = Matrix([ibx,iby,ibz])
|
||||
|
||||
# wind in local NE frame (north, east)
|
||||
wx, wy = symbols("vwn, vwe", real=True)
|
||||
w = Matrix([wx,wy])
|
||||
|
||||
# state vector at arbitrary time t
|
||||
state = Matrix([q,v,p,d_ang_b,d_vel_b,i,ib,w])
|
||||
|
||||
print('Defining state propagation ...')
|
||||
q_new = quat_mult(q, Matrix([1, 0.5 * d_ang_true[0], 0.5 * d_ang_true[1], 0.5 * d_ang_true[2]]))
|
||||
v_new = v + R_to_earth * d_vel_true + Matrix([0,0,g]) * dt
|
||||
p_new = p + v * dt
|
||||
|
||||
d_ang_b_new = d_ang_b
|
||||
d_vel_b_new = d_vel_b
|
||||
i_new = i
|
||||
ib_new = ib
|
||||
w_new = w
|
||||
|
||||
# predicted state vector at time t + dt
|
||||
state_new = Matrix([q_new, v_new, p_new, d_ang_b_new, d_vel_b_new, i_new, ib_new, w_new])
|
||||
|
||||
print('Computing state propagation jacobian ...')
|
||||
A = state_new.jacobian(state)
|
||||
G = state_new.jacobian(u)
|
||||
|
||||
P = create_symmetric_cov_matrix()
|
||||
|
||||
print('Computing covariance propagation ...')
|
||||
P_new = A * P * A.T + G * var_u * G.T
|
||||
|
||||
for index in range(24):
|
||||
for j in range(24):
|
||||
if index > j:
|
||||
P_new[index,j] = 0
|
||||
|
||||
print('Simplifying covariance propagation ...')
|
||||
P_new_simple = cse(P_new, symbols("PS0:400"), optimizations='basic')
|
||||
|
||||
print('Writing covariance propagation to file ...')
|
||||
cov_code_generator = CodeGenerator("./generated/covariance_generated.cpp")
|
||||
cov_code_generator.print_string("Equations for covariance matrix prediction, without process noise!")
|
||||
cov_code_generator.write_subexpressions(P_new_simple[0])
|
||||
cov_code_generator.write_matrix(Matrix(P_new_simple[1]), "nextP", True)
|
||||
|
||||
cov_code_generator.close()
|
||||
|
||||
# derive autocode for observation methods
|
||||
print('Generating heading observation code ...')
|
||||
yaw_observation(P,state,R_to_earth)
|
||||
print('Generating gps heading observation code ...')
|
||||
gps_yaw_observation(P,state,R_to_body)
|
||||
print('Generating mag observation code ...')
|
||||
mag_observation(P,state,R_to_body,i,ib)
|
||||
print('Generating declination observation code ...')
|
||||
declination_observation(P,state,ix,iy)
|
||||
print('Generating airspeed observation code ...')
|
||||
tas_observation(P,state,vx,vy,vz,wx,wy)
|
||||
print('Generating sideslip observation code ...')
|
||||
beta_observation(P,state,R_to_body,vx,vy,vz,wx,wy)
|
||||
print('Generating optical flow observation code ...')
|
||||
optical_flow_observation(P,state,R_to_body,vx,vy,vz)
|
||||
print('Generating body frame velocity observation code ...')
|
||||
body_frame_velocity_observation(P,state,R_to_body,vx,vy,vz)
|
||||
print('Generating body frame acceleration observation code ...')
|
||||
body_frame_accel_observation(P,state,R_to_body,vx,vy,vz,wx,wy)
|
||||
print('Code generation finished!')
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
generate_code()
|
||||
@@ -1,5 +1,6 @@
|
||||
#include <matrix/math.hpp>
|
||||
|
||||
#pragma once
|
||||
|
||||
// converts Tait-Bryan 312 sequence of rotations from frame 1 to frame 2
|
||||
// to the corresponding rotation matrix that rotates from frame 2 to frame 1
|
||||
@@ -18,3 +19,20 @@ float kahanSummation(float sum_previous, float input, float &accumulator);
|
||||
// calculate the inverse rotation matrix from a quaternion rotation
|
||||
// this produces the inverse rotation to that produced by the math library quaternion to Dcmf operator
|
||||
matrix::Dcmf quatToInverseRotMat(const matrix::Quatf &quat);
|
||||
|
||||
namespace ecl{
|
||||
inline float powf(float x, int exp)
|
||||
{
|
||||
float ret;
|
||||
if (exp > 0) {
|
||||
ret = x;
|
||||
for (int count = 1; count < exp; count++) {
|
||||
ret *= x;
|
||||
}
|
||||
return ret;
|
||||
} else if (exp < 0) {
|
||||
return 1.0f / ecl::powf(x, -exp);
|
||||
}
|
||||
return 1.0f;
|
||||
}
|
||||
}
|
||||
|
||||
@@ -55,6 +55,7 @@ set(SRCS
|
||||
test_SensorRangeFinder.cpp
|
||||
test_geo.cpp
|
||||
test_geo_lookup.cpp
|
||||
test_EKF_utils.cpp
|
||||
)
|
||||
add_executable(ECL_GTESTS ${SRCS})
|
||||
|
||||
|
||||
+346
-346
@@ -3,349 +3,349 @@ Timestamp,state[0],state[1],state[2],state[3],state[4],state[5],state[6],state[7
|
||||
85000,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
|
||||
185000,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
|
||||
285000,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
|
||||
385000,0.982906,-0.00775222,-0.0134292,0.183453,0.000445835,0.000257906,-0.00515775,3.74516e-06,5.43776e-06,-7.479e-05,0,0,0,0,0,0,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,0.000168954,0.00247418,0.00247368,0.00483311,25.0004,25.0004,0.562573,0.259374,0.259374,4.00051,1e-06,1e-06,1e-06,0,0,4e-06,0,0,0,0,0,0,0,0
|
||||
485000,0.983207,-0.00779267,-0.0137988,0.181806,0.00149516,0.000487556,-0.0226199,0.000128857,3.88731e-05,0.012004,3.89716e-08,1.38181e-10,1.63937e-06,0,0,5.50648e-08,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,9.05599e-05,0.00251394,0.0025137,0.00257812,25.0144,25.0144,0.56266,0.609418,0.609418,0.802449,9.99999e-07,1e-06,9.98121e-07,0,0,4.00001e-06,0,0,0,0,0,0,0,0
|
||||
585000,0.983235,-0.00781283,-0.0140176,0.181633,0.000142817,0.000425494,-0.0407873,4.57242e-05,1.65576e-05,0.00559437,4.92314e-08,-1.10892e-10,2.06611e-06,0,0,1.69579e-07,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,6.31735e-05,0.00260317,0.00260303,0.00179033,7.81663,7.81663,0.56147,0.228172,0.228172,0.451638,9.99994e-07,9.99999e-07,9.91443e-07,0,0,4e-06,0,0,0,0,0,0,0,0
|
||||
685000,0.983166,-0.00784229,-0.0143846,0.181978,0.00273131,0.00149319,-0.0490413,0.00022836,0.000116917,0.0168581,1.00722e-08,-3.0771e-10,4.6197e-07,0,0,-3.88273e-07,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,4.99494e-05,0.00274313,0.00274301,0.00140913,7.85794,7.85794,0.557235,0.486139,0.486139,0.322026,9.99986e-07,9.99999e-07,9.77538e-07,0,0,3.99989e-06,0,0,0,0,0,0,0,0
|
||||
785000,0.983129,-0.00784217,-0.0146116,0.18216,0.00372337,0.00338268,-0.0598125,0.000120916,8.73528e-05,0.0131548,-2.03628e-08,-5.71333e-09,-8.26481e-07,0,0,-6.61608e-07,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,4.2747e-05,0.00292596,0.00292586,0.00120115,2.60141,2.60142,0.548781,0.195736,0.195736,0.259034,9.99886e-07,9.99914e-07,9.55188e-07,0,0,3.99951e-06,0,0,0,0,0,0,0,0
|
||||
885000,0.983035,-0.0078867,-0.0149611,0.182637,0.00537375,0.00623852,-0.0766231,0.000540952,0.000537906,-0.000216641,-1.6477e-07,-9.61094e-09,-6.50679e-06,0,0,9.87685e-08,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.8706e-05,0.00316567,0.00316556,0.00108283,2.66545,2.66547,0.534815,0.329581,0.329582,0.225286,9.99866e-07,9.99914e-07,9.23082e-07,0,0,3.99856e-06,0,0,0,0,0,0,0,0
|
||||
985000,0.982858,-0.00782901,-0.0152572,0.183566,0.00823652,0.00902617,-0.0901081,0.00123165,0.00123919,-0.00832501,-4.8827e-07,-1.48091e-08,-1.91202e-05,0,0,-1.56205e-07,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.82299e-05,0.00345539,0.00345524,0.00106637,2.75673,2.75676,0.521629,0.517615,0.517616,0.218362,9.99846e-07,9.99914e-07,8.92597e-07,0,0,3.99721e-06,0,0,0,0,0,0,0,0
|
||||
1085000,0.982942,-0.00793611,-0.0154438,0.183097,0.0140873,0.00748822,-0.109262,0.0013254,0.00114805,-0.0271139,-2.76351e-07,-7.16625e-08,-1.192e-05,0,0,2.02263e-06,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.6974e-05,0.00376377,0.00376359,0.00102686,1.29637,1.29641,0.497696,0.244345,0.244346,0.207776,9.98973e-07,9.99074e-07,8.44402e-07,0,0,3.99418e-06,0,0,0,0,0,0,0,0
|
||||
1185000,0.982986,-0.00789683,-0.0157172,0.182837,0.0200033,0.00774763,-0.10944,0.00300045,0.00190009,-0.0224507,-1.67147e-07,-5.74796e-08,-7.66274e-06,0,0,-3.17895e-06,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.64378e-05,0.00415181,0.00415156,0.00100717,1.42437,1.42444,0.469193,0.352138,0.352141,0.202802,9.98935e-07,9.99074e-07,7.89548e-07,0,0,3.98936e-06,0,0,0,0,0,0,0,0
|
||||
1285000,0.983228,-0.0078191,-0.0159541,0.181511,0.0248719,0.00741285,-0.118106,0.00314531,0.00131956,-0.0274478,4.83599e-07,-3.64063e-07,1.44699e-05,0,0,-5.99276e-06,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.61687e-05,0.00448529,0.00448496,0.000997098,0.899467,0.899538,0.437026,0.197243,0.197244,0.200584,9.94637e-07,9.94818e-07,7.29674e-07,0,0,3.98218e-06,0,0,0,0,0,0,0,0
|
||||
1385000,0.983298,-0.00779835,-0.0161705,0.181118,0.0336815,0.00815884,-0.117744,0.00609985,0.00212856,-0.0250338,6.08962e-07,-3.33023e-07,1.90582e-05,0,0,-1.3188e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.60413e-05,0.00496644,0.00496601,0.000990509,1.07437,1.07449,0.402816,0.274389,0.274394,0.199431,9.9459e-07,9.94818e-07,6.67293e-07,0,0,3.97225e-06,0,0,0,0,0,0,0,0
|
||||
1485000,0.983221,-0.00778091,-0.0161964,0.181532,0.0329266,0.0073408,-0.131168,0.0054041,0.00161758,-0.0377952,3.2572e-07,-1.54916e-06,1.05507e-05,0,0,-1.32214e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.58839e-05,0.00520925,0.00520879,0.000984313,0.83815,0.83827,0.368572,0.171805,0.171809,0.198527,9.80091e-07,9.80363e-07,6.05295e-07,0,0,3.95945e-06,0,0,0,0,0,0,0,0
|
||||
1585000,0.983218,-0.00787221,-0.0165617,0.181513,0.0407795,0.00829228,-0.142897,0.00908255,0.00236705,-0.0487389,3.18934e-07,-1.53709e-06,1.02505e-05,0,0,-1.50662e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.74386e-05,0.00576907,0.00576849,0.00102231,1.06615,1.06633,0.345438,0.239486,0.239496,0.207551,9.80056e-07,9.80363e-07,5.60027e-07,0,0,3.94785e-06,0,0,0,0,0,0,0,0
|
||||
1685000,0.983244,-0.00798178,-0.0164415,0.181374,0.0397497,0.00800314,-0.149395,0.00739773,0.0017971,-0.0545586,4.61745e-08,-4.39663e-06,1.25191e-05,0,0,-2.08158e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.70136e-05,0.00572877,0.00572826,0.00100996,0.909048,0.909223,0.313729,0.160449,0.160456,0.205396,9.44133e-07,9.44473e-07,5.02322e-07,0,0,3.92954e-06,0,0,0,0,0,0,0,0
|
||||
1785000,0.983211,-0.00812528,-0.0167314,0.181525,0.0500155,0.00828673,-0.150961,0.0119333,0.00261026,-0.0574123,-6.28687e-08,-4.33172e-06,8.13446e-06,0,0,-2.95762e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.67506e-05,0.00633743,0.00633678,0.00099398,1.18508,1.18535,0.284486,0.229233,0.22925,0.202407,9.44093e-07,9.44472e-07,4.48613e-07,0,0,3.90791e-06,0,0,0,0,0,0,0,0
|
||||
1885000,0.983329,-0.008071,-0.0162732,0.180926,0.0439593,0.00901281,-0.152979,0.00905303,0.00190364,-0.0623796,-6.43542e-07,-9.51365e-06,1.69775e-05,0,0,-3.75597e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.58607e-05,0.00582732,0.00582685,0.000975149,0.997286,0.997509,0.258346,0.157537,0.157547,0.198874,8.7715e-07,8.7754e-07,3.99727e-07,0,0,3.88319e-06,0,0,0,0,0,0,0,0
|
||||
1985000,0.983356,-0.00817263,-0.0166403,0.18074,0.0524564,0.0100551,-0.151652,0.0138998,0.00281358,-0.0616902,-5.74976e-07,-9.39287e-06,1.86412e-05,0,0,-5.10333e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.54401e-05,0.00644038,0.00643974,0.000953698,1.3017,1.30203,0.235188,0.231153,0.231176,0.194764,8.77119e-07,8.77538e-07,3.55598e-07,0,0,3.85509e-06,0,0,0,0,0,0,0,0
|
||||
2085000,0.983278,-0.00824902,-0.0159796,0.181223,0.0423133,0.00766312,-0.150052,0.00962687,0.00189525,-0.0592164,-1.97347e-06,-1.64931e-05,1.03483e-05,0,0,-6.7451e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.41815e-05,0.00545387,0.00545355,0.000930439,1.032,1.03222,0.215118,0.157316,0.157327,0.190412,7.81977e-07,7.8238e-07,3.16277e-07,0,0,3.82386e-06,0,0,0,0,0,0,0,0
|
||||
2185000,0.983296,-0.00821787,-0.0163173,0.181093,0.0499701,0.00842154,-0.151875,0.014255,0.00276072,-0.0637417,-1.93576e-06,-1.63949e-05,1.09397e-05,0,0,-7.80004e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.36451e-05,0.00602725,0.00602675,0.000905951,1.33555,1.33586,0.19779,0.234207,0.234233,0.185808,7.81957e-07,7.82377e-07,2.81393e-07,0,0,3.78909e-06,0,0,0,0,0,0,0,0
|
||||
2285000,0.983449,-0.00829695,-0.0155482,0.180329,0.0363965,0.00624905,-0.149364,0.00912446,0.00173222,-0.0631072,-3.09465e-06,-2.41594e-05,2.03215e-05,0,0,-9.45512e-05,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.34003e-05,0.00478277,0.00478261,0.000917772,0.993006,0.993186,0.188684,0.15558,0.155591,0.189826,6.74557e-07,6.74939e-07,2.57849e-07,0,0,3.76059e-06,0,0,0,0,0,0,0,0
|
||||
2385000,0.983469,-0.00835843,-0.0157261,0.1802,0.0434517,0.00562693,-0.149239,0.0131525,0.00231492,-0.0614994,-3.04487e-06,-2.40114e-05,2.08998e-05,0,0,-0.000112629,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.26693e-05,0.00529045,0.00529019,0.000890197,1.27336,1.27361,0.175645,0.231693,0.231716,0.184795,6.74544e-07,6.74936e-07,2.2987e-07,0,0,3.71943e-06,0,0,0,0,0,0,0,0
|
||||
2485000,0.983603,-0.00828275,-0.0150001,0.17953,0.029255,0.0037607,-0.150956,0.00801574,0.00132731,-0.0648776,-4.27571e-06,-3.10751e-05,2.90678e-05,0,0,-0.00012596,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.1076e-05,0.00405365,0.00405362,0.000862728,0.907778,0.907908,0.164701,0.151099,0.151107,0.179986,5.7159e-07,5.71939e-07,2.05298e-07,0,0,3.67475e-06,0,0,0,0,0,0,0,0
|
||||
2585000,0.983643,-0.00840973,-0.0151349,0.179296,0.0323446,0.00229609,-0.153886,0.0110928,0.00167314,-0.0690116,-4.24891e-06,-3.09813e-05,2.90745e-05,0,0,-0.000139431,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.02732e-05,0.0044909,0.0044908,0.000835868,1.15351,1.15368,0.155524,0.223054,0.223072,0.175337,5.7158e-07,5.71936e-07,1.83745e-07,0,0,3.62596e-06,0,0,0,0,0,0,0,0
|
||||
2685000,0.98371,-0.00847264,-0.0145357,0.178976,0.0217589,0.00156795,-0.153275,0.00655819,0.000880254,-0.0681838,-5.45805e-06,-3.64499e-05,3.15734e-05,0,0,-0.000161173,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,2.87529e-05,0.00341288,0.00341295,0.000809219,0.808184,0.808272,0.147821,0.144645,0.144652,0.170893,4.81467e-07,4.81778e-07,1.64742e-07,0,0,3.57283e-06,0,0,0,0,0,0,0,0
|
||||
2785000,0.98369,-0.00842791,-0.0146958,0.17907,0.0271298,0.00123464,-0.150514,0.00913909,0.00102508,-0.0647036,-5.47649e-06,-3.62672e-05,2.79765e-05,0,0,-0.000187638,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,2.79807e-05,0.00378709,0.00378709,0.000783899,1.01998,1.02011,0.141514,0.210823,0.210836,0.166798,4.8146e-07,4.81775e-07,1.48141e-07,0,0,3.51578e-06,0,0,0,0,0,0,0,0
|
||||
2885000,0.983783,-0.00844618,-0.0142704,0.178596,0.0195799,-0.00138268,-0.152025,0.00545396,0.000471641,-0.0659934,-6.61286e-06,-4.04882e-05,3.07905e-05,0,0,-0.000207842,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,2.75279e-05,0.00290065,0.00290076,0.000786818,0.714774,0.714835,0.139977,0.137385,0.13739,0.169975,4.05328e-07,4.05602e-07,1.36973e-07,0,0,3.47017e-06,0,0,0,0,0,0,0,0
|
||||
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||||
34385000,0.983516,-0.00914415,-0.012633,0.180147,-0.00389612,-0.064632,-0.0849739,0.0818784,-0.0352132,-0.062808,-1.34381e-05,-5.49671e-05,6.64543e-06,0.000134706,-0.000335639,-0.00108603,0.204181,0.00196475,0.434409,0,0,0,0,0,3.85129e-06,1.22205e-05,1.22031e-05,0.000111729,0.0220675,0.0220751,0.00733349,0.041168,0.0411719,0.0552086,4.60529e-11,4.60313e-11,7.21639e-10,0,0,5.0001e-08,0,0,0,0,0,0,0,0
|
||||
34485000,0.983521,-0.00922737,-0.0125676,0.180121,-0.00671741,-0.0678918,-0.0834901,0.0813481,-0.0419077,-0.0663075,-1.34364e-05,-5.49687e-05,6.71912e-06,0.000134706,-0.000335639,-0.00108639,0.204181,0.00196475,0.434409,0,0,0,0,0,3.84625e-06,1.24214e-05,1.24043e-05,0.000111584,0.0239921,0.0240007,0.0073933,0.046006,0.046011,0.0550444,4.61493e-11,4.61281e-11,7.13363e-10,0,0,5e-08,0,0,0,0,0,0,0,0
|
||||
34585000,0.983525,-0.00903438,-0.0123775,0.180119,-0.00860069,-0.0573819,0.662421,0.0807244,-0.0350088,-0.0411829,-1.36259e-05,-5.48861e-05,6.67215e-06,0.000134706,-0.000335639,-0.00108775,0.204181,0.00196475,0.434409,0,0,0,0,0,3.83885e-06,1.13249e-05,1.13082e-05,0.000111436,0.0204658,0.0204724,0.00736626,0.041264,0.0412678,0.0545278,4.43934e-11,4.43689e-11,7.05144e-10,0,0,5e-08,0,0,0,0,0,0,0,0
|
||||
34685000,0.983531,-0.00901958,-0.0120954,0.18011,-0.0113346,-0.0545748,1.65309,0.079737,-0.0406042,0.0716704,-1.3627e-05,-5.4885e-05,6.62559e-06,0.000134706,-0.000335639,-0.00108748,0.204181,0.00196475,0.434409,0,0,0,0,0,3.83153e-06,1.15142e-05,1.14983e-05,0.000111285,0.0205706,0.0205773,0.00744265,0.0458986,0.0459034,0.0543843,4.44898e-11,4.44658e-11,6.96987e-10,0,0,5e-08,0,0,0,0,0,0,0,0
|
||||
34785000,0.983543,-0.00886932,-0.0118592,0.180065,-0.0130252,-0.0442325,2.61955,0.0795802,-0.0339024,0.233693,-1.37741e-05,-5.48068e-05,6.66661e-06,0.000134706,-0.000335639,-0.00106151,0.204181,0.00196475,0.434409,0,0,0,0,0,3.84327e-06,1.06234e-05,1.0608e-05,0.0001117,0.0173848,0.0173899,0.00748222,0.0411363,0.0411399,0.0546363,4.30832e-11,4.30569e-11,6.90927e-10,0,0,5.0002e-08,0,0,0,0,0,0,0,0
|
||||
34885000,0.983548,-0.00885328,-0.0115784,0.180057,-0.0156976,-0.0414105,3.60512,0.0781945,-0.0381592,0.523545,-1.37758e-05,-5.48053e-05,6.62188e-06,0.000134706,-0.000335639,-0.00105927,0.204181,0.00196475,0.434409,0,0,0,0,0,3.83563e-06,1.08044e-05,1.07897e-05,0.000111539,0.0174924,0.0174975,0.00757633,0.045452,0.0454566,0.0545154,4.31795e-11,4.31539e-11,6.82876e-10,0,0,5.0001e-08,0,0,0,0,0,0,0,0
|
||||
|
||||
|
@@ -0,0 +1,57 @@
|
||||
/****************************************************************************
|
||||
*
|
||||
* Copyright (c) 2019 ECL Development Team. All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
*
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in
|
||||
* the documentation and/or other materials provided with the
|
||||
* distribution.
|
||||
* 3. Neither the name PX4 nor the names of its contributors may be
|
||||
* used to endorse or promote products derived from this software
|
||||
* without specific prior written permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
||||
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
||||
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
||||
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
||||
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
|
||||
* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
|
||||
* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
||||
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
* POSSIBILITY OF SUCH DAMAGE.
|
||||
*
|
||||
****************************************************************************/
|
||||
|
||||
/**
|
||||
* @file test_EKF_utils.cpp
|
||||
*
|
||||
* @brief Unit tests for the miscellaneous EKF utilities
|
||||
*/
|
||||
|
||||
#include <gtest/gtest.h>
|
||||
#include <cmath>
|
||||
#include <vector>
|
||||
|
||||
#include "EKF/utils.hpp"
|
||||
|
||||
TEST(eclPowfTest, compareToStandardImplementation)
|
||||
{
|
||||
std::vector<int> exponents = {-3,-2,-1,-0,0,1,2,3};
|
||||
std::vector<float> bases = {-INFINITY, -11.1f,-0.5f, -0.f, 0.f, 0.5f, 11.1f, INFINITY};
|
||||
|
||||
for (auto const exponent : exponents) {
|
||||
for (auto const basis : bases) {
|
||||
EXPECT_EQ(ecl::powf(basis, exponent),
|
||||
std::pow(basis, static_cast<float>(exponent)));
|
||||
}
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user