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EKF: Convert GPS yaw observation method to use SymPy generated code (#880)
* EKF: add test comparison program for GPS yaw fusion equations * EKF: convert GPS yaw fusion method to use SymPy generated equations * Replace if/else with simple if * EKF: fix formatting of GPS yaw fusion auto-code comparison test * EKF: Use SparseVector type for GPS yaw fusion Jacobians * EKF: Fix bug in GPS yaw derivation comparison check * Add gps_yaw auto generated code file Co-authored-by: kamilritz <kritz@ethz.ch>
This commit is contained in:
Paul Riseborough
+81
-122
@@ -34,6 +34,7 @@
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/**
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* @file gps_yaw_fusion.cpp
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* Definition of functions required to use yaw obtained from GPS dual antenna measurements.
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* Equations generated using EKF/python/ekf_derivation/main.py
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*
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* @author Paul Riseborough <p_riseborough@live.com.au>
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*
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@@ -48,10 +49,10 @@
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void Ekf::fuseGpsYaw()
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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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// calculate the observed yaw angle of antenna array, converting a from body to antenna yaw measurement
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const float measured_hdg = wrap_pi(_gps_sample_delayed.yaw + _gps_yaw_offset);
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@@ -68,91 +69,61 @@ void Ekf::fuseGpsYaw()
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// calculate predicted antenna yaw angle
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const float predicted_hdg = atan2f(ant_vec_ef(1),ant_vec_ef(0));
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// calculate observation jacobian
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float t2 = sinf(_gps_yaw_offset);
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float t3 = cosf(_gps_yaw_offset);
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float t4 = q0*q3*2.0f;
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float t5 = q0*q0;
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float t6 = q1*q1;
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float t7 = q2*q2;
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float t8 = q3*q3;
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float t9 = q1*q2*2.0f;
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float t10 = t5+t6-t7-t8;
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float t11 = t3*t10;
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float t12 = t4+t9;
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float t13 = t3*t12;
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float t14 = t5-t6+t7-t8;
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float t15 = t2*t14;
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float t16 = t13+t15;
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float t17 = t4-t9;
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float t19 = t2*t17;
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float t20 = t11-t19;
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float t18 = (t20*t20);
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if (t18 < 1e-6f) {
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return;
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}
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t18 = 1.0f / t18;
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float t21 = t16*t16;
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float t22 = sq(t11-t19);
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if (t22 < 1e-6f) {
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return;
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}
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t22 = 1.0f/t22;
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float t23 = q1*t3*2.0f;
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float t24 = q2*t2*2.0f;
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float t25 = t23+t24;
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float t26 = 1.0f/t20;
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float t27 = q1*t2*2.0f;
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float t28 = t21*t22;
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float t29 = t28+1.0f;
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if (fabsf(t29) < 1e-6f) {
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return;
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}
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float t30 = 1.0f/t29;
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float t31 = q0*t3*2.0f;
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float t32 = t31-q3*t2*2.0f;
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float t33 = q3*t3*2.0f;
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float t34 = q0*t2*2.0f;
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float t35 = t33+t34;
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float H_YAW[4];
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H_YAW[0] = (t35/(t11-t2*(t4-q1*q2*2.0f))-t16*t18*t32)/(t18*t21+1.0f);
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H_YAW[1] = -t30*(t26*(t27-q2*t3*2.0f)+t16*t22*t25);
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H_YAW[2] = t30*(t25*t26-t16*t22*(t27-q2*t3*2.0f));
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H_YAW[3] = t30*(t26*t32+t16*t22*t35);
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// using magnetic heading tuning parameter
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// using magnetic heading process noise
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// TODO extend interface to use yaw uncertainty provided by GPS if available
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const float R_YAW = sq(fmaxf(_params.mag_heading_noise, 1.0e-2f));
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// calculate the innovation and define the innovation gate
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const float innov_gate = math::max(_params.heading_innov_gate, 1.0f);
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_heading_innov = predicted_hdg - measured_hdg;
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// wrap the innovation to the interval between +-pi
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_heading_innov = wrap_pi(_heading_innov);
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// Calculate innovation variance and Kalman gains, taking advantage of the fact that only the first 3 elements in H are non zero
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// calculate the innovation variance
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float PH[4];
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_heading_innov_var = R_YAW;
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for (unsigned row = 0; row <= 3; row++) {
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PH[row] = 0.0f;
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for (uint8_t col = 0; col <= 3; col++) {
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PH[row] += P(row,col) * H_YAW[col];
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}
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_heading_innov_var += H_YAW[row] * PH[row];
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// calculate intermediate variables
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const float HK0 = sinf(_gps_yaw_offset);
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const float HK1 = q0*q3;
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const float HK2 = q1*q2;
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const float HK3 = 2*HK0*(HK1 - HK2);
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const float HK4 = cosf(_gps_yaw_offset);
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const float HK5 = powf(q1, 2);
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const float HK6 = powf(q2, 2);
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const float HK7 = powf(q0, 2) - powf(q3, 2);
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const float HK8 = HK4*(HK5 - HK6 + HK7);
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const float HK9 = HK3 - HK8;
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if (fabsf(HK9) < 1e-3f) {
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return;
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}
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const float HK10 = 1.0F/HK9;
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const float HK11 = HK4*q0;
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const float HK12 = HK0*q3;
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const float HK13 = HK0*(-HK5 + HK6 + HK7) + 2*HK4*(HK1 + HK2);
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const float HK14 = HK10*HK13;
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const float HK15 = HK0*q0 + HK4*q3;
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const float HK16 = HK10*(HK14*(HK11 - HK12) + HK15);
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const float HK17 = powf(HK13, 2)/powf(HK9, 2) + 1;
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if (fabsf(HK17) < 1e-3f) {
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return;
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}
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const float HK18 = 2/HK17;
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// const float HK19 = 1.0F/(-HK3 + HK8);
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const float HK19_inverse = -HK3 + HK8;
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if (fabsf(HK19_inverse) < 1e-6f) {
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return;
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}
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const float HK19 = 1.0F/HK19_inverse;
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const float HK20 = HK4*q1;
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const float HK21 = HK0*q2;
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const float HK22 = HK13*HK19;
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const float HK23 = HK0*q1 - HK4*q2;
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const float HK24 = HK19*(HK22*(HK20 + HK21) + HK23);
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const float HK25 = HK19*(-HK20 - HK21 + HK22*HK23);
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const float HK26 = HK10*(-HK11 + HK12 + HK14*HK15);
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const float HK27 = -HK16*P(0,0) - HK24*P(0,1) - HK25*P(0,2) + HK26*P(0,3);
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const float HK28 = -HK16*P(0,1) - HK24*P(1,1) - HK25*P(1,2) + HK26*P(1,3);
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const float HK29 = 4/powf(HK17, 2);
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const float HK30 = -HK16*P(0,2) - HK24*P(1,2) - HK25*P(2,2) + HK26*P(2,3);
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const float HK31 = -HK16*P(0,3) - HK24*P(1,3) - HK25*P(2,3) + HK26*P(3,3);
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// const float HK32 = HK18/(-HK16*HK27*HK29 - HK24*HK28*HK29 - HK25*HK29*HK30 + HK26*HK29*HK31 + R_YAW);
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// check if the innovation variance calculation is badly conditioned
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if (_heading_innov_var >= R_YAW) {
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// the innovation variance contribution from the state covariances is not negative, no fault
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_fault_status.flags.bad_hdg = false;
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_heading_innov_var = (-HK16*HK27*HK29 - HK24*HK28*HK29 - HK25*HK29*HK30 + HK26*HK29*HK31 + R_YAW);
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} else {
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// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
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if (_heading_innov_var < R_YAW) {
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// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
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_fault_status.flags.bad_hdg = true;
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// we reinitialise the covariance matrix and abort this fusion step
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@@ -161,29 +132,15 @@ void Ekf::fuseGpsYaw()
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return;
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}
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const float heading_innov_var_inv = 1.f / _heading_innov_var;
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_fault_status.flags.bad_hdg = false;
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const float HK32 = HK18/_heading_innov_var;
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// calculate the Kalman gains
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// only calculate gains for states we are using
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Vector24f Kfusion;
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// calculate the innovation and define the innovation gate
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const float innov_gate = math::max(_params.heading_innov_gate, 1.0f);
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_heading_innov = predicted_hdg - measured_hdg;
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for (uint8_t row = 0; row <= 15; row++) {
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for (uint8_t col = 0; col <= 3; col++) {
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Kfusion(row) += P(row,col) * H_YAW[col];
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}
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Kfusion(row) *= heading_innov_var_inv;
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}
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if (_control_status.flags.wind) {
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for (uint8_t row = 22; row <= 23; row++) {
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for (uint8_t col = 0; col <= 3; col++) {
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Kfusion(row) += P(row,col) * H_YAW[col];
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}
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Kfusion(row) *= heading_innov_var_inv;
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}
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}
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// wrap the innovation to the interval between +-pi
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_heading_innov = wrap_pi(_heading_innov);
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// innovation test ratio
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_yaw_test_ratio = sq(_heading_innov) / (sq(innov_gate) * _heading_innov_var);
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@@ -210,27 +167,29 @@ void Ekf::fuseGpsYaw()
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_innov_check_fail_status.flags.reject_yaw = false;
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}
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// calculate observation jacobian
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// Observation jacobian and Kalman gain vectors
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SparseVector24f<0,1,2,3> Hfusion;
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Hfusion.at<0>() = -HK16*HK18;
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Hfusion.at<1>() = -HK18*HK24;
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Hfusion.at<2>() = -HK18*HK25;
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Hfusion.at<3>() = HK18*HK26;
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// calculate the Kalman gains
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// only calculate gains for states we are using
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Vector24f Kfusion;
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Kfusion(0) = HK27*HK32;
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Kfusion(1) = HK28*HK32;
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Kfusion(2) = HK30*HK32;
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Kfusion(3) = HK31*HK32;
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for (unsigned row = 4; row <= 23; row++) {
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Kfusion(row) = HK32*(-HK16*P(0,row) - HK24*P(1,row) - HK25*P(2,row) + HK26*P(3,row));
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}
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// apply covariance correction via P_new = (I -K*H)*P
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// first calculate expression for KHP
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// then calculate P - KHP
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SquareMatrix24f KHP;
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float KH[4];
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for (unsigned row = 0; row < _k_num_states; row++) {
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KH[0] = Kfusion(row) * H_YAW[0];
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KH[1] = Kfusion(row) * H_YAW[1];
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KH[2] = Kfusion(row) * H_YAW[2];
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KH[3] = Kfusion(row) * H_YAW[3];
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for (unsigned column = 0; column < _k_num_states; column++) {
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float tmp = KH[0] * P(0,column);
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tmp += KH[1] * P(1,column);
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tmp += KH[2] * P(2,column);
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tmp += KH[3] * P(3,column);
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KHP(row,column) = tmp;
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}
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}
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const SquareMatrix24f KHP = computeKHP(Kfusion, Hfusion);
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const bool healthy = checkAndFixCovarianceUpdate(KHP);
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@@ -0,0 +1,266 @@
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#include <math.h>
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#include <stdio.h>
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#include <cstdlib>
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#include "../../../../../matrix/matrix/math.hpp"
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typedef matrix::Vector<float, 24> Vector24f;
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typedef matrix::SquareMatrix<float, 24> SquareMatrix24f;
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template<int ... Idxs>
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using SparseVector24f = matrix::SparseVectorf<24, Idxs...>;
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float sq(float in) {
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return in * in;
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}
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int main()
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{
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// Compare calculation of observation Jacobians and Kalman gains for sympy and matlab generated equations
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float H_YAW[24];
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Vector24f Kfusion;
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float _heading_innov_var;
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const float R_YAW = sq(0.3f);
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const float _gps_yaw_offset = 1.5f;
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// quaternion inputs must be normalised
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float q0 = 2.0f * ((float)rand() - 0.5f);
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float q1 = 2.0f * ((float)rand() - 0.5f);
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float q2 = 2.0f * ((float)rand() - 0.5f);
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float q3 = 2.0f * ((float)rand() - 0.5f);
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const float length = sqrtf(sq(q0) + sq(q1) + sq(q2) + sq(q3));
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q0 /= length;
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q1 /= length;
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q2 /= length;
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q3 /= length;
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// create a symmetrical positive dfinite matrix with off diagonals between -1 and 1 and diagonals between 0 and 1
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SquareMatrix24f P;
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for (int col=0; col<=23; col++) {
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for (int row=0; row<=col; row++) {
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if (row == col) {
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P(row,col) = (float)rand();
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} else {
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P(col,row) = P(row,col) = 2.0f * ((float)rand() - 0.5f);
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}
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}
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}
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// First calculate observationjacobians and Kalman gains using sympy generated equations
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// calculate intermediate variables
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const float HK0 = sinf(_gps_yaw_offset);
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const float HK1 = q0*q3;
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const float HK2 = q1*q2;
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const float HK3 = 2*HK0*(HK1 - HK2);
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const float HK4 = cosf(_gps_yaw_offset);
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const float HK5 = powf(q1, 2);
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const float HK6 = powf(q2, 2);
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const float HK7 = powf(q0, 2) - powf(q3, 2);
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const float HK8 = HK4*(HK5 - HK6 + HK7);
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const float HK9 = HK3 - HK8;
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if (fabsf(HK9) < 1e-3f) {
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return 0;
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}
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const float HK10 = 1.0F/HK9;
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const float HK11 = HK4*q0;
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const float HK12 = HK0*q3;
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const float HK13 = HK0*(-HK5 + HK6 + HK7) + 2*HK4*(HK1 + HK2);
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const float HK14 = HK10*HK13;
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const float HK15 = HK0*q0 + HK4*q3;
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const float HK16 = HK10*(HK14*(HK11 - HK12) + HK15);
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const float HK17 = powf(HK13, 2)/powf(HK9, 2) + 1;
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if (fabsf(HK17) < 1e-3f) {
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return 0;
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}
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const float HK18 = 2/HK17;
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// const float HK19 = 1.0F/(-HK3 + HK8);
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const float HK19_inverse = -HK3 + HK8;
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if (fabsf(HK19_inverse) < 1e-6f) {
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return 0;
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}
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const float HK19 = 1.0F/HK19_inverse;
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const float HK20 = HK4*q1;
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const float HK21 = HK0*q2;
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const float HK22 = HK13*HK19;
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const float HK23 = HK0*q1 - HK4*q2;
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const float HK24 = HK19*(HK22*(HK20 + HK21) + HK23);
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const float HK25 = HK19*(-HK20 - HK21 + HK22*HK23);
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const float HK26 = HK10*(-HK11 + HK12 + HK14*HK15);
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const float HK27 = -HK16*P(0,0) - HK24*P(0,1) - HK25*P(0,2) + HK26*P(0,3);
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const float HK28 = -HK16*P(0,1) - HK24*P(1,1) - HK25*P(1,2) + HK26*P(1,3);
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const float HK29 = 4/powf(HK17, 2);
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const float HK30 = -HK16*P(0,2) - HK24*P(1,2) - HK25*P(2,2) + HK26*P(2,3);
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const float HK31 = -HK16*P(0,3) - HK24*P(1,3) - HK25*P(2,3) + HK26*P(3,3);
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const float HK32 = HK18/(-HK16*HK27*HK29 - HK24*HK28*HK29 - HK25*HK29*HK30 + HK26*HK29*HK31 + R_YAW);
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// calculate observation jacobian
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// Observation jacobian and Kalman gain vectors
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SparseVector24f<0,1,2,3> Hfusion;
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Hfusion.at<0>() = -HK16*HK18;
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Hfusion.at<1>() = -HK18*HK24;
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Hfusion.at<2>() = -HK18*HK25;
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Hfusion.at<3>() = HK18*HK26;
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// calculate the Kalman gains
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// only calculate gains for states we are using
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Kfusion(0) = HK27*HK32;
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Kfusion(1) = HK28*HK32;
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Kfusion(2) = HK30*HK32;
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Kfusion(3) = HK31*HK32;
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for (unsigned row = 4; row <= 23; row++) {
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Kfusion(row) = HK32*(-HK16*P(0,row) - HK24*P(1,row) - HK25*P(2,row) + HK26*P(3,row));
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}
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// save output and repeat calculation using legacy matlab generated code
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float Hfusion_sympy[24] = {};
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Vector24f Kfusion_sympy;
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Hfusion_sympy[0] = Hfusion.at<0>();
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Hfusion_sympy[1] = Hfusion.at<1>();
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Hfusion_sympy[2] = Hfusion.at<2>();
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Hfusion_sympy[3] = Hfusion.at<3>();
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for (int row=0; row<24; row++) {
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Kfusion_sympy(row) = Kfusion(row);
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||||
}
|
||||
|
||||
// repeat calculation using matlab generated equations
|
||||
// calculate observation jacobian
|
||||
float t2 = sinf(_gps_yaw_offset);
|
||||
float t3 = cosf(_gps_yaw_offset);
|
||||
float t4 = q0*q3*2.0f;
|
||||
float t5 = q0*q0;
|
||||
float t6 = q1*q1;
|
||||
float t7 = q2*q2;
|
||||
float t8 = q3*q3;
|
||||
float t9 = q1*q2*2.0f;
|
||||
float t10 = t5+t6-t7-t8;
|
||||
float t11 = t3*t10;
|
||||
float t12 = t4+t9;
|
||||
float t13 = t3*t12;
|
||||
float t14 = t5-t6+t7-t8;
|
||||
float t15 = t2*t14;
|
||||
float t16 = t13+t15;
|
||||
float t17 = t4-t9;
|
||||
float t19 = t2*t17;
|
||||
float t20 = t11-t19;
|
||||
float t18 = (t20*t20);
|
||||
|
||||
t18 = 1.0f / t18;
|
||||
float t21 = t16*t16;
|
||||
float t22 = sq(t11-t19);
|
||||
|
||||
t22 = 1.0f/t22;
|
||||
float t23 = q1*t3*2.0f;
|
||||
float t24 = q2*t2*2.0f;
|
||||
float t25 = t23+t24;
|
||||
float t26 = 1.0f/t20;
|
||||
float t27 = q1*t2*2.0f;
|
||||
float t28 = t21*t22;
|
||||
float t29 = t28+1.0f;
|
||||
|
||||
float t30 = 1.0f/t29;
|
||||
float t31 = q0*t3*2.0f;
|
||||
float t32 = t31-q3*t2*2.0f;
|
||||
float t33 = q3*t3*2.0f;
|
||||
float t34 = q0*t2*2.0f;
|
||||
float t35 = t33+t34;
|
||||
|
||||
memset(&H_YAW, 0, sizeof(H_YAW));
|
||||
H_YAW[0] = (t35/(t11-t2*(t4-q1*q2*2.0f))-t16*t18*t32)/(t18*t21+1.0f);
|
||||
H_YAW[1] = -t30*(t26*(t27-q2*t3*2.0f)+t16*t22*t25);
|
||||
H_YAW[2] = t30*(t25*t26-t16*t22*(t27-q2*t3*2.0f));
|
||||
H_YAW[3] = t30*(t26*t32+t16*t22*t35);
|
||||
|
||||
// Calculate innovation variance and Kalman gains, taking advantage of the fact that only the first 3 elements in H are non zero
|
||||
// calculate the innovation variance
|
||||
float PH[4];
|
||||
_heading_innov_var = R_YAW;
|
||||
|
||||
for (unsigned row = 0; row <= 3; row++) {
|
||||
PH[row] = 0.0f;
|
||||
|
||||
for (uint8_t col = 0; col <= 3; col++) {
|
||||
PH[row] += P(row,col) * H_YAW[col];
|
||||
}
|
||||
|
||||
_heading_innov_var += H_YAW[row] * PH[row];
|
||||
}
|
||||
|
||||
const float heading_innov_var_inv = 1.f / _heading_innov_var;
|
||||
|
||||
// calculate the Kalman gains
|
||||
// only calculate gains for states we are using
|
||||
memset(&Kfusion, 0, sizeof(Kfusion));
|
||||
|
||||
for (uint8_t row = 0; row <= 15; row++) {
|
||||
for (uint8_t col = 0; col <= 3; col++) {
|
||||
Kfusion(row) += P(row,col) * H_YAW[col];
|
||||
}
|
||||
Kfusion(row) *= heading_innov_var_inv;
|
||||
}
|
||||
|
||||
if (true) {
|
||||
for (uint8_t row = 22; row <= 23; row++) {
|
||||
for (uint8_t col = 0; col <= 3; col++) {
|
||||
Kfusion(row) += P(row,col) * H_YAW[col];
|
||||
}
|
||||
Kfusion(row) *= heading_innov_var_inv;
|
||||
}
|
||||
}
|
||||
|
||||
// find largest observation variance difference as a fraction of the matlab value
|
||||
float max_diff_fraction = 0.0f;
|
||||
int max_row;
|
||||
float max_old, max_new;
|
||||
for (int row=0; row<24; row++) {
|
||||
float diff_fraction;
|
||||
if (H_YAW[row] != 0.0f) {
|
||||
diff_fraction = fabsf(Hfusion_sympy[row] - H_YAW[row]) / fabsf(H_YAW[row]);
|
||||
} else if (Hfusion_sympy[row] != 0.0f) {
|
||||
diff_fraction = fabsf(Hfusion_sympy[row] - H_YAW[row]) / fabsf(Hfusion_sympy[row]);
|
||||
} else {
|
||||
diff_fraction = 0.0f;
|
||||
}
|
||||
if (diff_fraction > max_diff_fraction) {
|
||||
max_diff_fraction = diff_fraction;
|
||||
max_row = row;
|
||||
max_old = H_YAW[row];
|
||||
max_new = Hfusion_sympy[row];
|
||||
}
|
||||
}
|
||||
|
||||
if (max_diff_fraction > 1E-5f) {
|
||||
printf("Fail: GPS yaw Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
|
||||
} else {
|
||||
printf("Pass: GPS yaw Hfusion max diff fraction = %e\n",max_diff_fraction);
|
||||
}
|
||||
|
||||
// find largest Kalman gain difference as a fraction of the matlab value
|
||||
max_diff_fraction = 0.0f;
|
||||
for (int row=0; row<4; row++) {
|
||||
float diff_fraction;
|
||||
if (Kfusion(row) != 0.0f) {
|
||||
diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion(row));
|
||||
} else if (Kfusion_sympy(row) != 0.0f) {
|
||||
diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion_sympy(row));
|
||||
} else {
|
||||
diff_fraction = 0.0f;
|
||||
}
|
||||
if (diff_fraction > max_diff_fraction) {
|
||||
max_diff_fraction = diff_fraction;
|
||||
max_row = row;
|
||||
max_old = Kfusion(row);
|
||||
max_new = Kfusion_sympy(row);
|
||||
}
|
||||
}
|
||||
|
||||
if (max_diff_fraction > 1E-5f) {
|
||||
printf("Fail: GPS yaw Kfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
|
||||
} else {
|
||||
printf("Pass: GPS yaw Kfusion max diff fraction = %e\n",max_diff_fraction);
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
@@ -0,0 +1,90 @@
|
||||
// Sub Expressions
|
||||
const float HK0 = sinf(ant_yaw);
|
||||
const float HK1 = q0*q3;
|
||||
const float HK2 = q1*q2;
|
||||
const float HK3 = 2*HK0*(HK1 - HK2);
|
||||
const float HK4 = cosf(ant_yaw);
|
||||
const float HK5 = powf(q1, 2);
|
||||
const float HK6 = powf(q2, 2);
|
||||
const float HK7 = powf(q0, 2) - powf(q3, 2);
|
||||
const float HK8 = HK4*(HK5 - HK6 + HK7);
|
||||
const float HK9 = HK3 - HK8;
|
||||
const float HK10 = 1.0F/HK9;
|
||||
const float HK11 = HK4*q0;
|
||||
const float HK12 = HK0*q3;
|
||||
const float HK13 = HK0*(-HK5 + HK6 + HK7) + 2*HK4*(HK1 + HK2);
|
||||
const float HK14 = HK10*HK13;
|
||||
const float HK15 = HK0*q0 + HK4*q3;
|
||||
const float HK16 = HK10*(HK14*(HK11 - HK12) + HK15);
|
||||
const float HK17 = powf(HK13, 2)/powf(HK9, 2) + 1;
|
||||
const float HK18 = 2/HK17;
|
||||
const float HK19 = 1.0F/(-HK3 + HK8);
|
||||
const float HK20 = HK4*q1;
|
||||
const float HK21 = HK0*q2;
|
||||
const float HK22 = HK13*HK19;
|
||||
const float HK23 = HK0*q1 - HK4*q2;
|
||||
const float HK24 = HK19*(HK22*(HK20 + HK21) + HK23);
|
||||
const float HK25 = HK19*(-HK20 - HK21 + HK22*HK23);
|
||||
const float HK26 = HK10*(-HK11 + HK12 + HK14*HK15);
|
||||
const float HK27 = -HK16*P(0,0) - HK24*P(0,1) - HK25*P(0,2) + HK26*P(0,3);
|
||||
const float HK28 = -HK16*P(0,1) - HK24*P(1,1) - HK25*P(1,2) + HK26*P(1,3);
|
||||
const float HK29 = 4/powf(HK17, 2);
|
||||
const float HK30 = -HK16*P(0,2) - HK24*P(1,2) - HK25*P(2,2) + HK26*P(2,3);
|
||||
const float HK31 = -HK16*P(0,3) - HK24*P(1,3) - HK25*P(2,3) + HK26*P(3,3);
|
||||
const float HK32 = HK18/(-HK16*HK27*HK29 - HK24*HK28*HK29 - HK25*HK29*HK30 + HK26*HK29*HK31 + R_YAW);
|
||||
|
||||
|
||||
// Observation Jacobians
|
||||
Hfusion.at<0>() = -HK16*HK18;
|
||||
Hfusion.at<1>() = -HK18*HK24;
|
||||
Hfusion.at<2>() = -HK18*HK25;
|
||||
Hfusion.at<3>() = HK18*HK26;
|
||||
Hfusion.at<4>() = 0;
|
||||
Hfusion.at<5>() = 0;
|
||||
Hfusion.at<6>() = 0;
|
||||
Hfusion.at<7>() = 0;
|
||||
Hfusion.at<8>() = 0;
|
||||
Hfusion.at<9>() = 0;
|
||||
Hfusion.at<10>() = 0;
|
||||
Hfusion.at<11>() = 0;
|
||||
Hfusion.at<12>() = 0;
|
||||
Hfusion.at<13>() = 0;
|
||||
Hfusion.at<14>() = 0;
|
||||
Hfusion.at<15>() = 0;
|
||||
Hfusion.at<16>() = 0;
|
||||
Hfusion.at<17>() = 0;
|
||||
Hfusion.at<18>() = 0;
|
||||
Hfusion.at<19>() = 0;
|
||||
Hfusion.at<20>() = 0;
|
||||
Hfusion.at<21>() = 0;
|
||||
Hfusion.at<22>() = 0;
|
||||
Hfusion.at<23>() = 0;
|
||||
|
||||
|
||||
// Kalman gains
|
||||
Kfusion(0) = HK27*HK32;
|
||||
Kfusion(1) = HK28*HK32;
|
||||
Kfusion(2) = HK30*HK32;
|
||||
Kfusion(3) = HK31*HK32;
|
||||
Kfusion(4) = HK32*(-HK16*P(0,4) - HK24*P(1,4) - HK25*P(2,4) + HK26*P(3,4));
|
||||
Kfusion(5) = HK32*(-HK16*P(0,5) - HK24*P(1,5) - HK25*P(2,5) + HK26*P(3,5));
|
||||
Kfusion(6) = HK32*(-HK16*P(0,6) - HK24*P(1,6) - HK25*P(2,6) + HK26*P(3,6));
|
||||
Kfusion(7) = HK32*(-HK16*P(0,7) - HK24*P(1,7) - HK25*P(2,7) + HK26*P(3,7));
|
||||
Kfusion(8) = HK32*(-HK16*P(0,8) - HK24*P(1,8) - HK25*P(2,8) + HK26*P(3,8));
|
||||
Kfusion(9) = HK32*(-HK16*P(0,9) - HK24*P(1,9) - HK25*P(2,9) + HK26*P(3,9));
|
||||
Kfusion(10) = HK32*(-HK16*P(0,10) - HK24*P(1,10) - HK25*P(2,10) + HK26*P(3,10));
|
||||
Kfusion(11) = HK32*(-HK16*P(0,11) - HK24*P(1,11) - HK25*P(2,11) + HK26*P(3,11));
|
||||
Kfusion(12) = HK32*(-HK16*P(0,12) - HK24*P(1,12) - HK25*P(2,12) + HK26*P(3,12));
|
||||
Kfusion(13) = HK32*(-HK16*P(0,13) - HK24*P(1,13) - HK25*P(2,13) + HK26*P(3,13));
|
||||
Kfusion(14) = HK32*(-HK16*P(0,14) - HK24*P(1,14) - HK25*P(2,14) + HK26*P(3,14));
|
||||
Kfusion(15) = HK32*(-HK16*P(0,15) - HK24*P(1,15) - HK25*P(2,15) + HK26*P(3,15));
|
||||
Kfusion(16) = HK32*(-HK16*P(0,16) - HK24*P(1,16) - HK25*P(2,16) + HK26*P(3,16));
|
||||
Kfusion(17) = HK32*(-HK16*P(0,17) - HK24*P(1,17) - HK25*P(2,17) + HK26*P(3,17));
|
||||
Kfusion(18) = HK32*(-HK16*P(0,18) - HK24*P(1,18) - HK25*P(2,18) + HK26*P(3,18));
|
||||
Kfusion(19) = HK32*(-HK16*P(0,19) - HK24*P(1,19) - HK25*P(2,19) + HK26*P(3,19));
|
||||
Kfusion(20) = HK32*(-HK16*P(0,20) - HK24*P(1,20) - HK25*P(2,20) + HK26*P(3,20));
|
||||
Kfusion(21) = HK32*(-HK16*P(0,21) - HK24*P(1,21) - HK25*P(2,21) + HK26*P(3,21));
|
||||
Kfusion(22) = HK32*(-HK16*P(0,22) - HK24*P(1,22) - HK25*P(2,22) + HK26*P(3,22));
|
||||
Kfusion(23) = HK32*(-HK16*P(0,23) - HK24*P(1,23) - HK25*P(2,23) + HK26*P(3,23));
|
||||
|
||||
|
||||
Reference in New Issue
Block a user