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px4-firmware/EKF/gps_yaw_fusion.cpp

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/****************************************************************************
*
* Copyright (c) 2018 Estimation and Control Library (ECL). All rights reserved.
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/**
* @file gps_yaw_fusion.cpp
* Definition of functions required to use yaw obtained from GPS dual antenna measurements.
*
* @author Paul Riseborough <p_riseborough@live.com.au>
*
*/
#include "ekf.h"
#include <ecl.h>
#include <mathlib/mathlib.h>
#include <cstdlib>
void Ekf::fuseGpsAntYaw()
{
// assign intermediate state variables
float q0 = _state.quat_nominal(0);
float q1 = _state.quat_nominal(1);
float q2 = _state.quat_nominal(2);
float q3 = _state.quat_nominal(3);
float R_YAW = 1.0f;
float predicted_hdg;
float H_YAW[4];
float measured_hdg;
// check if data has been set to NAN indicating no measurement
if (ISFINITE(_gps_sample_delayed.yaw)) {
// calculate the observed yaw angle of antenna array, converting a from body to antenna yaw measurement
measured_hdg = _gps_sample_delayed.yaw + _gps_yaw_offset;
// define the predicted antenna array vector and rotate into earth frame
Vector3f ant_vec_bf = {cosf(_gps_yaw_offset), sinf(_gps_yaw_offset), 0.0f};
Vector3f ant_vec_ef = _R_to_earth * ant_vec_bf;
// check if antenna array vector is within 30 degrees of vertical and therefore unable to provide a reliable heading
if (fabsf(ant_vec_ef(2)) > cosf(math::radians(30.0f))) {
return;
}
// calculate predicted antenna yaw angle
predicted_hdg = atan2f(ant_vec_ef(1),ant_vec_ef(0));
// 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);
if (t18 < 1e-6f) {
return;
}
t18 = 1.0f / t18;
float t21 = t16*t16;
float t22 = sq(t11-t19);
if (t22 < 1e-6f) {
return;
}
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;
if (fabsf(t29) < 1e-6f) {
return;
}
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;
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);
// using magnetic heading tuning parameter
R_YAW = sq(fmaxf(_params.mag_heading_noise, 1.0e-2f));
} else {
// there is nothing to fuse
return;
}
// wrap the heading to the interval between +-pi
measured_hdg = wrap_pi(measured_hdg);
// calculate the innovation and define the innovation gate
float innov_gate = math::max(_params.heading_innov_gate, 1.0f);
_heading_innov = predicted_hdg - measured_hdg;
// wrap the innovation to the interval between +-pi
_heading_innov = wrap_pi(_heading_innov);
// 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];
}
float heading_innov_var_inv;
// check if the innovation variance calculation is badly conditioned
if (_heading_innov_var >= R_YAW) {
// the innovation variance contribution from the state covariances is not negative, no fault
_fault_status.flags.bad_hdg = false;
heading_innov_var_inv = 1.0f / _heading_innov_var;
} else {
// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
_fault_status.flags.bad_hdg = true;
// we reinitialise the covariance matrix and abort this fusion step
initialiseCovariance();
ECL_ERR("EKF GPS yaw fusion numerical error - covariance reset");
return;
}
// calculate the Kalman gains
// only calculate gains for states we are using
float Kfusion[_k_num_states] = {};
for (uint8_t row = 0; row <= 15; row++) {
Kfusion[row] = 0.0f;
for (uint8_t col = 0; col <= 3; col++) {
Kfusion[row] += P[row][col] * H_YAW[col];
}
Kfusion[row] *= heading_innov_var_inv;
}
if (_control_status.flags.wind) {
for (uint8_t row = 22; row <= 23; row++) {
Kfusion[row] = 0.0f;
for (uint8_t col = 0; col <= 3; col++) {
Kfusion[row] += P[row][col] * H_YAW[col];
}
Kfusion[row] *= heading_innov_var_inv;
}
}
// innovation test ratio
_yaw_test_ratio = sq(_heading_innov) / (sq(innov_gate) * _heading_innov_var);
// we are no longer using 3-axis fusion so set the reported test levels to zero
memset(_mag_test_ratio, 0, sizeof(_mag_test_ratio));
// set the magnetometer unhealthy if the test fails
if (_yaw_test_ratio > 1.0f) {
_innov_check_fail_status.flags.reject_yaw = true;
// if we are in air we don't want to fuse the measurement
// we allow to use it when on the ground because the large innovation could be caused
// by interference or a large initial gyro bias
if (_control_status.flags.in_air) {
return;
} else {
// constrain the innovation to the maximum set by the gate
float gate_limit = sqrtf((sq(innov_gate) * _heading_innov_var));
_heading_innov = math::constrain(_heading_innov, -gate_limit, gate_limit);
}
} else {
_innov_check_fail_status.flags.reject_yaw = false;
}
// apply covariance correction via P_new = (I -K*H)*P
// first calculate expression for KHP
// then calculate P - KHP
float KHP[_k_num_states][_k_num_states];
float KH[4];
for (unsigned row = 0; row < _k_num_states; row++) {
KH[0] = Kfusion[row] * H_YAW[0];
KH[1] = Kfusion[row] * H_YAW[1];
KH[2] = Kfusion[row] * H_YAW[2];
KH[3] = Kfusion[row] * H_YAW[3];
for (unsigned column = 0; column < _k_num_states; column++) {
float tmp = KH[0] * P[0][column];
tmp += KH[1] * P[1][column];
tmp += KH[2] * P[2][column];
tmp += KH[3] * P[3][column];
KHP[row][column] = tmp;
}
}
// if the covariance correction will result in a negative variance, then
// the covariance matrix is unhealthy and must be corrected
bool healthy = true;
_fault_status.flags.bad_hdg = false;
for (int i = 0; i < _k_num_states; i++) {
if (P[i][i] < KHP[i][i]) {
// zero rows and columns
zeroRows(P, i, i);
zeroCols(P, i, i);
//flag as unhealthy
healthy = false;
// update individual measurement health status
_fault_status.flags.bad_hdg = true;
}
}
// only apply covariance and state corrections if healthy
if (healthy) {
// apply the covariance corrections
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < _k_num_states; column++) {
P[row][column] = P[row][column] - KHP[row][column];
}
}
// correct the covariance matrix for gross errors
fixCovarianceErrors();
// apply the state corrections
fuse(Kfusion, _heading_innov);
}
}
bool Ekf::resetGpsAntYaw()
{
// check if data has been set to NAN indicating no measurement
if (ISFINITE(_gps_sample_delayed.yaw)) {
// define the predicted antenna array vector and rotate into earth frame
Vector3f ant_vec_bf = {cosf(_gps_yaw_offset), sinf(_gps_yaw_offset), 0.0f};
Vector3f ant_vec_ef = _R_to_earth * ant_vec_bf;
// check if antenna array vector is within 30 degrees of vertical and therefore unable to provide a reliable heading
if (fabsf(ant_vec_ef(2)) > cosf(math::radians(30.0f))) {
return false;
}
float predicted_yaw = atan2f(ant_vec_ef(1),ant_vec_ef(0));
// get measurement and correct for antenna array yaw offset
float measured_yaw = _gps_sample_delayed.yaw + _gps_yaw_offset;
// calculate the amount the yaw needs to be rotated by
float yaw_delta = wrap_pi(measured_yaw - predicted_yaw);
// save a copy of the quaternion state for later use in calculating the amount of reset change
Quatf quat_before_reset = _state.quat_nominal;
Quatf quat_after_reset = _state.quat_nominal;
// obtain the yaw angle using the best conditioned from either a Tait-Bryan 321 or 312 sequence
// to avoid gimbal lock
if (fabsf(_R_to_earth(2, 0)) < fabsf(_R_to_earth(2, 1))) {
// get the roll, pitch, yaw estimates from the quaternion states using a 321 Tait-Bryan rotation sequence
Quatf q_init(_state.quat_nominal);
Eulerf euler_init(q_init);
// correct the yaw angle
euler_init(2) += yaw_delta;
euler_init(2) = wrap_pi(euler_init(2));
// update the quaternions
quat_after_reset = Quatf(euler_init);
} else {
// Calculate the 312 Tait-Bryan sequence euler angles that rotate from earth to body frame
// PX4 math library does not support this so are using equations from
// http://www.atacolorado.com/eulersequences.doc
Vector3f euler312;
euler312(0) = atan2f(-_R_to_earth(0, 1), _R_to_earth(1, 1)); // first rotation (yaw)
euler312(1) = asinf(_R_to_earth(2, 1)); // second rotation (roll)
euler312(2) = atan2f(-_R_to_earth(2, 0), _R_to_earth(2, 2)); // third rotation (pitch)
// correct the yaw angle
euler312(0) += yaw_delta;
euler312(0) = wrap_pi(euler312(0));
// Calculate the body to earth frame rotation matrix from the corrected euler angles
float c2 = cosf(euler312(2));
float s2 = sinf(euler312(2));
float s1 = sinf(euler312(1));
float c1 = cosf(euler312(1));
float s0 = sinf(euler312(0));
float c0 = cosf(euler312(0));
Dcmf R_to_earth;
R_to_earth(0, 0) = c0 * c2 - s0 * s1 * s2;
R_to_earth(1, 1) = c0 * c1;
R_to_earth(2, 2) = c2 * c1;
R_to_earth(0, 1) = -c1 * s0;
R_to_earth(0, 2) = s2 * c0 + c2 * s1 * s0;
R_to_earth(1, 0) = c2 * s0 + s2 * s1 * c0;
R_to_earth(1, 2) = s0 * s2 - s1 * c0 * c2;
R_to_earth(2, 0) = -s2 * c1;
R_to_earth(2, 1) = s1;
// update the quaternions
quat_after_reset = Quatf(R_to_earth);
}
// calculate the amount that the quaternion has changed by
Quatf q_error = quat_before_reset.inversed() * _state.quat_nominal;
q_error.normalize();
// convert the quaternion delta to a delta angle
Vector3f delta_ang_error;
float scalar;
if (q_error(0) >= 0.0f) {
scalar = -2.0f;
} else {
scalar = 2.0f;
}
delta_ang_error(0) = scalar * q_error(1);
delta_ang_error(1) = scalar * q_error(2);
delta_ang_error(2) = scalar * q_error(3);
// update the quaternion state estimates and corresponding covariances only if the change in angle has been large or the yaw is not yet aligned
if (delta_ang_error.norm() > math::radians(15.0f) || !_control_status.flags.yaw_align) {
// update quaternion states
_state.quat_nominal = quat_after_reset;
uncorrelateQuatStates();
// record the state change
_state_reset_status.quat_change = q_error;
// update transformation matrix from body to world frame using the current estimate
_R_to_earth = quat_to_invrotmat(_state.quat_nominal);
// reset the rotation from the EV to EKF frame of reference if it is being used
if ((_params.fusion_mode & MASK_ROTATE_EV) && (_params.fusion_mode & MASK_USE_EVPOS)) {
resetExtVisRotMat();
}
// update the yaw angle variance using the variance of the measurement
increaseQuatYawErrVariance(sq(fmaxf(_params.mag_heading_noise, 1.0e-2f)));
// add the reset amount to the output observer buffered data
for (uint8_t i = 0; i < _output_buffer.get_length(); i++) {
// Note q1 *= q2 is equivalent to q1 = q2 * q1
_output_buffer[i].quat_nominal *= _state_reset_status.quat_change;
}
// apply the change in attitude quaternion to our newest quaternion estimate
// which was already taken out from the output buffer
_output_new.quat_nominal = _state_reset_status.quat_change * _output_new.quat_nominal;
// capture the reset event
_state_reset_status.quat_counter++;
}
return true;
}
return false;
}
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