ekf2: generate yaw fusion jacobians using symforce

This commit is contained in:
bresch
2022-10-14 17:05:41 +02:00
committed by Mathieu Bresciani
parent ccd90ede7a
commit f11908a266
7 changed files with 475 additions and 0 deletions
@@ -253,6 +253,74 @@ def compute_mag_z_innov_var_and_h(
return (innov_var, H.T)
def compute_yaw_321_innov_var_and_h(
state: VState,
P: MState,
R: sf.Scalar,
epsilon: sf.Scalar
) -> (sf.Scalar, VState):
q_att = sf.V4(state[State.qw], state[State.qx], state[State.qy], state[State.qz])
R_to_earth = quat_to_rot(q_att)
# Fix the singularity at pi/2 by inserting epsilon
meas_pred = sf.atan2(R_to_earth[1,0], R_to_earth[0,0], epsilon=epsilon)
H = sf.V1(meas_pred).jacobian(state)
innov_var = (H * P * H.T + R)[0,0]
return (innov_var, H.T)
def compute_yaw_321_innov_var_and_h_alternate(
state: VState,
P: MState,
R: sf.Scalar,
epsilon: sf.Scalar
) -> (sf.Scalar, VState):
q_att = sf.V4(state[State.qw], state[State.qx], state[State.qy], state[State.qz])
R_to_earth = quat_to_rot(q_att)
# Alternate form that has a singularity at yaw 0 instead of pi/2
meas_pred = sf.pi/2 - sf.atan2(R_to_earth[0,0], R_to_earth[1,0], epsilon=epsilon)
H = sf.V1(meas_pred).jacobian(state)
innov_var = (H * P * H.T + R)[0,0]
return (innov_var, H.T)
def compute_yaw_312_innov_var_and_h(
state: VState,
P: MState,
R: sf.Scalar,
epsilon: sf.Scalar
) -> (sf.Scalar, VState):
q_att = sf.V4(state[State.qw], state[State.qx], state[State.qy], state[State.qz])
R_to_earth = quat_to_rot(q_att)
# Alternate form to be used when close to pitch +-pi/2
meas_pred = sf.atan2(-R_to_earth[0,1], R_to_earth[1,1], epsilon=epsilon)
H = sf.V1(meas_pred).jacobian(state)
innov_var = (H * P * H.T + R)[0,0]
return (innov_var, H.T)
def compute_yaw_312_innov_var_and_h_alternate(
state: VState,
P: MState,
R: sf.Scalar,
epsilon: sf.Scalar
) -> (sf.Scalar, VState):
q_att = sf.V4(state[State.qw], state[State.qx], state[State.qy], state[State.qz])
R_to_earth = quat_to_rot(q_att)
# Alternate form to be used when close to pitch +-pi/2
meas_pred = sf.pi/2 - sf.atan2(-R_to_earth[1,1], R_to_earth[0,1], epsilon=epsilon)
H = sf.V1(meas_pred).jacobian(state)
innov_var = (H * P * H.T + R)[0,0]
return (innov_var, H.T)
print("Derive EKF2 equations...")
generate_px4_function(compute_airspeed_innov_and_innov_var, output_names=["innov", "innov_var"])
generate_px4_function(compute_airspeed_h_and_k, output_names=["H", "K"])
@@ -263,3 +331,7 @@ generate_px4_function(predict_covariance, output_names=["P_new"])
generate_px4_function(compute_mag_innov_innov_var_and_hx, output_names=["innov", "innov_var", "Hx"])
generate_px4_function(compute_mag_y_innov_var_and_h, output_names=["innov_var", "H"])
generate_px4_function(compute_mag_z_innov_var_and_h, output_names=["innov_var", "H"])
generate_px4_function(compute_yaw_321_innov_var_and_h, output_names=["innov_var", "H"])
generate_px4_function(compute_yaw_321_innov_var_and_h_alternate, output_names=["innov_var", "H"])
generate_px4_function(compute_yaw_312_innov_var_and_h, output_names=["innov_var", "H"])
generate_px4_function(compute_yaw_312_innov_var_and_h_alternate, output_names=["innov_var", "H"])
@@ -0,0 +1,75 @@
// -----------------------------------------------------------------------------
// This file was autogenerated by symforce from template:
// backends/cpp/templates/function/FUNCTION.h.jinja
// Do NOT modify by hand.
// -----------------------------------------------------------------------------
#pragma once
#include <matrix/math.hpp>
namespace sym {
/**
* This function was autogenerated from a symbolic function. Do not modify by hand.
*
* Symbolic function: compute_yaw_312_innov_var_and_h
*
* Args:
* state: Matrix24_1
* P: Matrix24_24
* R: Scalar
* epsilon: Scalar
*
* Outputs:
* innov_var: Scalar
* H: Matrix24_1
*/
template <typename Scalar>
void ComputeYaw312InnovVarAndH(const matrix::Matrix<Scalar, 24, 1>& state,
const matrix::Matrix<Scalar, 24, 24>& P, const Scalar R,
const Scalar epsilon, Scalar* const innov_var = nullptr,
matrix::Matrix<Scalar, 24, 1>* const H = nullptr) {
// Total ops: 75
// Input arrays
// Intermediate terms (11)
const Scalar _tmp0 = -state(0, 0) * state(3, 0) + state(1, 0) * state(2, 0);
const Scalar _tmp1 = std::pow(state(0, 0), Scalar(2)) - std::pow(state(1, 0), Scalar(2)) +
std::pow(state(2, 0), Scalar(2)) - std::pow(state(3, 0), Scalar(2));
const Scalar _tmp2 = _tmp1 + epsilon * ((((_tmp1) > 0) - ((_tmp1) < 0)) + Scalar(0.5));
const Scalar _tmp3 = std::pow(_tmp2, Scalar(2));
const Scalar _tmp4 = 4 * _tmp0 / _tmp3;
const Scalar _tmp5 = 2 / _tmp2;
const Scalar _tmp6 = _tmp3 / (4 * std::pow(_tmp0, Scalar(2)) + _tmp3);
const Scalar _tmp7 = _tmp6 * (-_tmp4 * state(1, 0) - _tmp5 * state(2, 0));
const Scalar _tmp8 = _tmp6 * (_tmp4 * state(2, 0) - _tmp5 * state(1, 0));
const Scalar _tmp9 = _tmp6 * (-_tmp4 * state(3, 0) + _tmp5 * state(0, 0));
const Scalar _tmp10 = _tmp6 * (_tmp4 * state(0, 0) + _tmp5 * state(3, 0));
// Output terms (2)
if (innov_var != nullptr) {
Scalar& _innov_var = (*innov_var);
_innov_var = R +
_tmp10 * (P(0, 0) * _tmp10 + P(1, 0) * _tmp7 + P(2, 0) * _tmp8 + P(3, 0) * _tmp9) +
_tmp7 * (P(0, 1) * _tmp10 + P(1, 1) * _tmp7 + P(2, 1) * _tmp8 + P(3, 1) * _tmp9) +
_tmp8 * (P(0, 2) * _tmp10 + P(1, 2) * _tmp7 + P(2, 2) * _tmp8 + P(3, 2) * _tmp9) +
_tmp9 * (P(0, 3) * _tmp10 + P(1, 3) * _tmp7 + P(2, 3) * _tmp8 + P(3, 3) * _tmp9);
}
if (H != nullptr) {
matrix::Matrix<Scalar, 24, 1>& _H = (*H);
_H.setZero();
_H(0, 0) = _tmp10;
_H(1, 0) = _tmp7;
_H(2, 0) = _tmp8;
_H(3, 0) = _tmp9;
}
} // NOLINT(readability/fn_size)
// NOLINTNEXTLINE(readability/fn_size)
} // namespace sym
@@ -0,0 +1,75 @@
// -----------------------------------------------------------------------------
// This file was autogenerated by symforce from template:
// backends/cpp/templates/function/FUNCTION.h.jinja
// Do NOT modify by hand.
// -----------------------------------------------------------------------------
#pragma once
#include <matrix/math.hpp>
namespace sym {
/**
* This function was autogenerated from a symbolic function. Do not modify by hand.
*
* Symbolic function: compute_yaw_312_innov_var_and_h_alternate
*
* Args:
* state: Matrix24_1
* P: Matrix24_24
* R: Scalar
* epsilon: Scalar
*
* Outputs:
* innov_var: Scalar
* H: Matrix24_1
*/
template <typename Scalar>
void ComputeYaw312InnovVarAndHAlternate(const matrix::Matrix<Scalar, 24, 1>& state,
const matrix::Matrix<Scalar, 24, 24>& P, const Scalar R,
const Scalar epsilon, Scalar* const innov_var = nullptr,
matrix::Matrix<Scalar, 24, 1>* const H = nullptr) {
// Total ops: 83
// Input arrays
// Intermediate terms (11)
const Scalar _tmp0 = std::pow(state(0, 0), Scalar(2)) - std::pow(state(1, 0), Scalar(2)) +
std::pow(state(2, 0), Scalar(2)) - std::pow(state(3, 0), Scalar(2));
const Scalar _tmp1 = -state(0, 0) * state(3, 0) + state(1, 0) * state(2, 0);
const Scalar _tmp2 = 2 * _tmp1 + epsilon * ((((_tmp1) > 0) - ((_tmp1) < 0)) + Scalar(0.5));
const Scalar _tmp3 = std::pow(_tmp2, Scalar(2));
const Scalar _tmp4 = 2 * _tmp0 / _tmp3;
const Scalar _tmp5 = 2 / _tmp2;
const Scalar _tmp6 = _tmp3 / (std::pow(_tmp0, Scalar(2)) + _tmp3);
const Scalar _tmp7 = _tmp6 * (_tmp4 * state(1, 0) - _tmp5 * state(2, 0));
const Scalar _tmp8 = _tmp6 * (_tmp4 * state(2, 0) + _tmp5 * state(1, 0));
const Scalar _tmp9 = _tmp6 * (-_tmp4 * state(0, 0) + _tmp5 * state(3, 0));
const Scalar _tmp10 = _tmp6 * (-_tmp4 * state(3, 0) - _tmp5 * state(0, 0));
// Output terms (2)
if (innov_var != nullptr) {
Scalar& _innov_var = (*innov_var);
_innov_var =
R - _tmp10 * (-P(0, 0) * _tmp10 - P(1, 0) * _tmp8 - P(2, 0) * _tmp7 - P(3, 0) * _tmp9) -
_tmp7 * (-P(0, 2) * _tmp10 - P(1, 2) * _tmp8 - P(2, 2) * _tmp7 - P(3, 2) * _tmp9) -
_tmp8 * (-P(0, 1) * _tmp10 - P(1, 1) * _tmp8 - P(2, 1) * _tmp7 - P(3, 1) * _tmp9) -
_tmp9 * (-P(0, 3) * _tmp10 - P(1, 3) * _tmp8 - P(2, 3) * _tmp7 - P(3, 3) * _tmp9);
}
if (H != nullptr) {
matrix::Matrix<Scalar, 24, 1>& _H = (*H);
_H.setZero();
_H(0, 0) = -_tmp10;
_H(1, 0) = -_tmp8;
_H(2, 0) = -_tmp7;
_H(3, 0) = -_tmp9;
}
} // NOLINT(readability/fn_size)
// NOLINTNEXTLINE(readability/fn_size)
} // namespace sym
@@ -0,0 +1,75 @@
// -----------------------------------------------------------------------------
// This file was autogenerated by symforce from template:
// backends/cpp/templates/function/FUNCTION.h.jinja
// Do NOT modify by hand.
// -----------------------------------------------------------------------------
#pragma once
#include <matrix/math.hpp>
namespace sym {
/**
* This function was autogenerated from a symbolic function. Do not modify by hand.
*
* Symbolic function: compute_yaw_321_innov_var_and_h
*
* Args:
* state: Matrix24_1
* P: Matrix24_24
* R: Scalar
* epsilon: Scalar
*
* Outputs:
* innov_var: Scalar
* H: Matrix24_1
*/
template <typename Scalar>
void ComputeYaw321InnovVarAndH(const matrix::Matrix<Scalar, 24, 1>& state,
const matrix::Matrix<Scalar, 24, 24>& P, const Scalar R,
const Scalar epsilon, Scalar* const innov_var = nullptr,
matrix::Matrix<Scalar, 24, 1>* const H = nullptr) {
// Total ops: 74
// Input arrays
// Intermediate terms (11)
const Scalar _tmp0 = state(0, 0) * state(3, 0) + state(1, 0) * state(2, 0);
const Scalar _tmp1 = std::pow(state(0, 0), Scalar(2)) + std::pow(state(1, 0), Scalar(2)) -
std::pow(state(2, 0), Scalar(2)) - std::pow(state(3, 0), Scalar(2));
const Scalar _tmp2 = _tmp1 + epsilon * ((((_tmp1) > 0) - ((_tmp1) < 0)) + Scalar(0.5));
const Scalar _tmp3 = std::pow(_tmp2, Scalar(2));
const Scalar _tmp4 = 4 * _tmp0 / _tmp3;
const Scalar _tmp5 = 2 / _tmp2;
const Scalar _tmp6 = _tmp3 / (4 * std::pow(_tmp0, Scalar(2)) + _tmp3);
const Scalar _tmp7 = _tmp6 * (_tmp4 * state(2, 0) + _tmp5 * state(1, 0));
const Scalar _tmp8 = _tmp6 * (-_tmp4 * state(1, 0) + _tmp5 * state(2, 0));
const Scalar _tmp9 = _tmp6 * (-_tmp4 * state(0, 0) + _tmp5 * state(3, 0));
const Scalar _tmp10 = _tmp6 * (_tmp4 * state(3, 0) + _tmp5 * state(0, 0));
// Output terms (2)
if (innov_var != nullptr) {
Scalar& _innov_var = (*innov_var);
_innov_var = R +
_tmp10 * (P(0, 3) * _tmp9 + P(1, 3) * _tmp8 + P(2, 3) * _tmp7 + P(3, 3) * _tmp10) +
_tmp7 * (P(0, 2) * _tmp9 + P(1, 2) * _tmp8 + P(2, 2) * _tmp7 + P(3, 2) * _tmp10) +
_tmp8 * (P(0, 1) * _tmp9 + P(1, 1) * _tmp8 + P(2, 1) * _tmp7 + P(3, 1) * _tmp10) +
_tmp9 * (P(0, 0) * _tmp9 + P(1, 0) * _tmp8 + P(2, 0) * _tmp7 + P(3, 0) * _tmp10);
}
if (H != nullptr) {
matrix::Matrix<Scalar, 24, 1>& _H = (*H);
_H.setZero();
_H(0, 0) = _tmp9;
_H(1, 0) = _tmp8;
_H(2, 0) = _tmp7;
_H(3, 0) = _tmp10;
}
} // NOLINT(readability/fn_size)
// NOLINTNEXTLINE(readability/fn_size)
} // namespace sym
@@ -0,0 +1,75 @@
// -----------------------------------------------------------------------------
// This file was autogenerated by symforce from template:
// backends/cpp/templates/function/FUNCTION.h.jinja
// Do NOT modify by hand.
// -----------------------------------------------------------------------------
#pragma once
#include <matrix/math.hpp>
namespace sym {
/**
* This function was autogenerated from a symbolic function. Do not modify by hand.
*
* Symbolic function: compute_yaw_321_innov_var_and_h_alternate
*
* Args:
* state: Matrix24_1
* P: Matrix24_24
* R: Scalar
* epsilon: Scalar
*
* Outputs:
* innov_var: Scalar
* H: Matrix24_1
*/
template <typename Scalar>
void ComputeYaw321InnovVarAndHAlternate(const matrix::Matrix<Scalar, 24, 1>& state,
const matrix::Matrix<Scalar, 24, 24>& P, const Scalar R,
const Scalar epsilon, Scalar* const innov_var = nullptr,
matrix::Matrix<Scalar, 24, 1>* const H = nullptr) {
// Total ops: 84
// Input arrays
// Intermediate terms (11)
const Scalar _tmp0 = std::pow(state(0, 0), Scalar(2)) + std::pow(state(1, 0), Scalar(2)) -
std::pow(state(2, 0), Scalar(2)) - std::pow(state(3, 0), Scalar(2));
const Scalar _tmp1 = state(0, 0) * state(3, 0) + state(1, 0) * state(2, 0);
const Scalar _tmp2 = 2 * _tmp1 + epsilon * ((((_tmp1) > 0) - ((_tmp1) < 0)) + Scalar(0.5));
const Scalar _tmp3 = std::pow(_tmp2, Scalar(2));
const Scalar _tmp4 = 2 * _tmp0 / _tmp3;
const Scalar _tmp5 = 2 / _tmp2;
const Scalar _tmp6 = _tmp3 / (std::pow(_tmp0, Scalar(2)) + _tmp3);
const Scalar _tmp7 = _tmp6 * (-_tmp4 * state(0, 0) - _tmp5 * state(3, 0));
const Scalar _tmp8 = _tmp6 * (-_tmp4 * state(2, 0) + _tmp5 * state(1, 0));
const Scalar _tmp9 = _tmp6 * (-_tmp4 * state(3, 0) + _tmp5 * state(0, 0));
const Scalar _tmp10 = _tmp6 * (-_tmp4 * state(1, 0) - _tmp5 * state(2, 0));
// Output terms (2)
if (innov_var != nullptr) {
Scalar& _innov_var = (*innov_var);
_innov_var =
R - _tmp10 * (-P(0, 2) * _tmp9 - P(1, 2) * _tmp8 - P(2, 2) * _tmp10 - P(3, 2) * _tmp7) -
_tmp7 * (-P(0, 3) * _tmp9 - P(1, 3) * _tmp8 - P(2, 3) * _tmp10 - P(3, 3) * _tmp7) -
_tmp8 * (-P(0, 1) * _tmp9 - P(1, 1) * _tmp8 - P(2, 1) * _tmp10 - P(3, 1) * _tmp7) -
_tmp9 * (-P(0, 0) * _tmp9 - P(1, 0) * _tmp8 - P(2, 0) * _tmp10 - P(3, 0) * _tmp7);
}
if (H != nullptr) {
matrix::Matrix<Scalar, 24, 1>& _H = (*H);
_H.setZero();
_H(0, 0) = -_tmp9;
_H(1, 0) = -_tmp8;
_H(2, 0) = -_tmp10;
_H(3, 0) = -_tmp7;
}
} // NOLINT(readability/fn_size)
// NOLINTNEXTLINE(readability/fn_size)
} // namespace sym
+1
View File
@@ -57,4 +57,5 @@ px4_add_unit_gtest(SRC test_EKF_terrain_estimator.cpp LINKLIBS ecl_EKF ecl_senso
px4_add_unit_gtest(SRC test_EKF_utils.cpp LINKLIBS ecl_EKF ecl_sensor_sim)
px4_add_unit_gtest(SRC test_EKF_withReplayData.cpp LINKLIBS ecl_EKF ecl_sensor_sim)
px4_add_unit_gtest(SRC test_EKF_yaw_estimator.cpp LINKLIBS ecl_EKF ecl_sensor_sim ecl_test_helper)
px4_add_unit_gtest(SRC test_EKF_yaw_fusion_generated.cpp LINKLIBS ecl_EKF ecl_test_helper)
px4_add_unit_gtest(SRC test_SensorRangeFinder.cpp LINKLIBS ecl_EKF ecl_sensor_sim)
@@ -0,0 +1,102 @@
/****************************************************************************
*
* Copyright (C) 2022 PX4 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.
*
****************************************************************************/
#include <gtest/gtest.h>
#include "EKF/ekf.h"
#include "test_helper/comparison_helper.h"
#include "../EKF/python/ekf_derivation/generated/compute_yaw_321_innov_var_and_h.h"
#include "../EKF/python/ekf_derivation/generated/compute_yaw_321_innov_var_and_h_alternate.h"
#include "../EKF/python/ekf_derivation/generated/compute_yaw_312_innov_var_and_h.h"
#include "../EKF/python/ekf_derivation/generated/compute_yaw_312_innov_var_and_h_alternate.h"
using namespace matrix;
TEST(YawFusionGenerated, singularityYawEquivalence)
{
// GIVEN: an attitude that should give a singularity when transforming the
// rotation matrix to Euler yaw
const Quatf q(Eulerf(M_PI_F, 0.f, M_PI_F));
Vector24f state_vector{};
state_vector(0) = q(0);
state_vector(1) = q(1);
state_vector(2) = q(2);
state_vector(3) = q(3);
const float R = sq(radians(10.f));
SquareMatrix24f P = createRandomCovarianceMatrix24f();
Vector24f H_a;
Vector24f H_b;
float innov_var_a;
float innov_var_b;
// WHEN: computing the innovation variance and H using two different
// alternate forms (one is singular at pi/2 and the other one at 0)
sym::ComputeYaw321InnovVarAndH(state_vector, P, R, FLT_EPSILON, &innov_var_a, &H_a);
sym::ComputeYaw321InnovVarAndHAlternate(state_vector, P, R, FLT_EPSILON, &innov_var_b, &H_b);
// THEN: Even at the singularity point, the result is still correct, thanks to epsilon
EXPECT_TRUE(isEqual(H_a, H_b));
EXPECT_NEAR(innov_var_a, innov_var_b, 1e-5f);
EXPECT_TRUE(innov_var_a < 5.f && innov_var_a > R) << "innov_var = " << innov_var_a;
}
TEST(YawFusionGenerated, gimbalLock321vs312)
{
// GIVEN: an attitude at gimbal lock position
const Quatf q(Eulerf(0.f, -M_PI_F / 2.f, M_PI_F));
Vector24f state_vector{};
state_vector(0) = q(0);
state_vector(1) = q(1);
state_vector(2) = q(2);
state_vector(3) = q(3);
const float R = sq(radians(10.f));
SquareMatrix24f P = createRandomCovarianceMatrix24f();
Vector24f H_321;
Vector24f H_312;
float innov_var_321;
float innov_var_312;
sym::ComputeYaw321InnovVarAndH(state_vector, P, R, FLT_EPSILON, &innov_var_321, &H_321);
sym::ComputeYaw312InnovVarAndH(state_vector, P, R, FLT_EPSILON, &innov_var_312, &H_312);
// THEN: both computation are not equivalent, 321 is undefined but 312 is valid
EXPECT_FALSE(isEqual(H_321, H_312));
EXPECT_GT(fabsf(innov_var_321 - innov_var_312), 1e6f);
EXPECT_TRUE(innov_var_312 < 5.f && innov_var_312 > R) << "innov_var = " << innov_var_312;
}