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px4-firmware/EKF/mag_fusion.cpp

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/****************************************************************************
*
* Copyright (c) 2015 Estimation and Control Library (ECL). All rights reserved.
*
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****************************************************************************/
/**
* @file heading_fusion.cpp
* Magnetometer fusion methods.
*
* @author Roman Bast <bapstroman@gmail.com>
* @author Paul Riseborough <p_riseborough@live.com.au>
*
*/
#include "ekf.h"
#include <mathlib/mathlib.h>
void Ekf::fuseMag()
{
// assign intermediate 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 magN = _state.mag_I(0);
float magE = _state.mag_I(1);
float magD = _state.mag_I(2);
// XYZ Measurement uncertainty. Need to consider timing errors for fast rotations
float R_MAG = fmaxf(_params.mag_noise, 1.0e-3f);
R_MAG = R_MAG * R_MAG;
// intermediate variables from algebraic optimisation
float SH_MAG[9];
SH_MAG[0] = sq(q0) - sq(q1) + sq(q2) - sq(q3);
SH_MAG[1] = sq(q0) + sq(q1) - sq(q2) - sq(q3);
SH_MAG[2] = sq(q0) - sq(q1) - sq(q2) + sq(q3);
SH_MAG[3] = 2 * q0 * q1 + 2 * q2 * q3;
SH_MAG[4] = 2 * q0 * q3 + 2 * q1 * q2;
SH_MAG[5] = 2 * q0 * q2 + 2 * q1 * q3;
SH_MAG[6] = magE * (2 * q0 * q1 - 2 * q2 * q3);
SH_MAG[7] = 2 * q1 * q3 - 2 * q0 * q2;
SH_MAG[8] = 2 * q0 * q3;
// rotate magnetometer earth field state into body frame
matrix::Dcm<float> R_to_body(_state.quat_nominal);
R_to_body = R_to_body.transpose();
Vector3f mag_I_rot = R_to_body * _state.mag_I;
// compute magnetometer innovations
_mag_innov[0] = (mag_I_rot(0) + _state.mag_B(0)) - _mag_sample_delayed.mag(0);
_mag_innov[1] = (mag_I_rot(1) + _state.mag_B(1)) - _mag_sample_delayed.mag(1);
_mag_innov[2] = (mag_I_rot(2) + _state.mag_B(2)) - _mag_sample_delayed.mag(2);
// Note that although the observation jacobians and kalman gains are decalred as arrays
// sequential fusion of the X,Y and Z components is used.
float H_MAG[3][24] = {};
float Kfusion[24] = {};
// Calculate observation Jacobians and kalman gains for each magentoemter axis
// X Axis
H_MAG[0][1] = SH_MAG[6] - magD * SH_MAG[2] - magN * SH_MAG[5];
H_MAG[0][2] = magE * SH_MAG[0] + magD * SH_MAG[3] - magN * (SH_MAG[8] - 2 * q1 * q2);
H_MAG[0][16] = SH_MAG[1];
H_MAG[0][17] = SH_MAG[4];
H_MAG[0][18] = SH_MAG[7];
H_MAG[0][19] = 1;
// intermediate variables
float SK_MX[4] = {};
// innovation variance
_mag_innov_var[0] = (P[19][19] + R_MAG - P[1][19] * (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) + P[16][19] *
SH_MAG[1]
+ P[17][19] * SH_MAG[4] + P[18][19] * SH_MAG[7] + P[2][19] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN *
(SH_MAG[8] - 2 * q1 * q2)) - (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) * (P[19][1] - P[1][1] *
(magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) + P[16][1] * SH_MAG[1] + P[17][1] * SH_MAG[4] + P[18][1] * SH_MAG[7] +
P[2][1] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN * (SH_MAG[8] - 2 * q1 * q2))) + SH_MAG[1] *
(P[19][16] - P[1][16] * (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) + P[16][16] * SH_MAG[1] + P[17][16] *
SH_MAG[4] + P[18][16] * SH_MAG[7] + P[2][16] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN *
(SH_MAG[8] - 2 * q1 * q2))) + SH_MAG[4] * (P[19][17] - P[1][17] * (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) +
P[16][17] * SH_MAG[1] + P[17][17] * SH_MAG[4] + P[18][17] * SH_MAG[7] + P[2][17] * (magE * SH_MAG[0] + magD * SH_MAG[3]
- magN * (SH_MAG[8] - 2 * q1 * q2))) + SH_MAG[7] * (P[19][18] - P[1][18] * (magD * SH_MAG[2] - SH_MAG[6] + magN *
SH_MAG[5]) + P[16][18] * SH_MAG[1] + P[17][18] * SH_MAG[4] + P[18][18] * SH_MAG[7] + P[2][18] *
(magE * SH_MAG[0] + magD * SH_MAG[3] - magN * (SH_MAG[8] - 2 * q1 * q2))) + (magE * SH_MAG[0] + magD * SH_MAG[3] -
magN * (SH_MAG[8] - 2 * q1 * q2)) * (P[19][2] - P[1][2] * (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) + P[16][2] *
SH_MAG[1] + P[17][2] * SH_MAG[4] + P[18][2] * SH_MAG[7] + P[2][2] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN *
(SH_MAG[8] - 2 * q1 * q2))));
// check for a badly conditioned covariance matrix
if (_mag_innov_var[0] >= R_MAG) {
// the innovation variance contribution from the state covariances is non-negative - no fault
_fault_status.bad_mag_x = false;
} else {
// the innovation variance contribution from the state covariances is negtive which means the covariance matrix is badly conditioned
_fault_status.bad_mag_x = true;
// we need to reinitialise the covariance matrix and abort this fusion step
initialiseCovariance();
return;
}
// Y axis
H_MAG[1][0] = magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5];
H_MAG[1][2] = - magE * SH_MAG[4] - magD * SH_MAG[7] - magN * SH_MAG[1];
H_MAG[1][16] = 2 * q1 * q2 - SH_MAG[8];
H_MAG[1][17] = SH_MAG[0];
H_MAG[1][18] = SH_MAG[3];
H_MAG[1][20] = 1;
// intermediate variables - note SK_MY[0] is 1/(innovation variance)
float SK_MY[4];
_mag_innov_var[1] = (P[20][20] + R_MAG + P[0][20] * (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) + P[17][20] *
SH_MAG[0]
+ P[18][20] * SH_MAG[3] - (SH_MAG[8] - 2 * q1 * q2) * (P[20][16] + P[0][16] * (magD * SH_MAG[2] - SH_MAG[6] + magN *
SH_MAG[5]) + P[17][16] * SH_MAG[0] + P[18][16] * SH_MAG[3] - P[2][16] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN *
SH_MAG[1]) - P[16][16] * (SH_MAG[8] - 2 * q1 * q2)) - P[2][20] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN *
SH_MAG[1]) + (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) * (P[20][0] + P[0][0] *
(magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) + P[17][0] * SH_MAG[0] + P[18][0] * SH_MAG[3] - P[2][0] *
(magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) - P[16][0] * (SH_MAG[8] - 2 * q1 * q2)) + SH_MAG[0] *
(P[20][17] + P[0][17] * (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) + P[17][17] * SH_MAG[0] + P[18][17] *
SH_MAG[3] - P[2][17] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) - P[16][17] *
(SH_MAG[8] - 2 * q1 * q2)) + SH_MAG[3] * (P[20][18] + P[0][18] * (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) +
P[17][18] * SH_MAG[0] + P[18][18] * SH_MAG[3] - P[2][18] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) -
P[16][18] * (SH_MAG[8] - 2 * q1 * q2)) - P[16][20] * (SH_MAG[8] - 2 * q1 * q2) - (magE * SH_MAG[4] + magD * SH_MAG[7] +
magN * SH_MAG[1]) * (P[20][2] + P[0][2] * (magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5]) + P[17][2] * SH_MAG[0] +
P[18][2] * SH_MAG[3] - P[2][2] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) - P[16][2] *
(SH_MAG[8] - 2 * q1 * q2)));
// check for a badly conditioned covariance matrix
if (_mag_innov_var[1] >= R_MAG) {
// the innovation variance contribution from the state covariances is non-negative - no fault
_fault_status.bad_mag_y = false;
} else {
// the innovation variance contribution from the state covariances is negtive which means the covariance matrix is badly conditioned
_fault_status.bad_mag_y = true;
// we need to reinitialise the covariance matrix and abort this fusion step
initialiseCovariance();
return;
}
// Z axis
H_MAG[2][0] = magN * (SH_MAG[8] - 2 * q1 * q2) - magD * SH_MAG[3] - magE * SH_MAG[0];
H_MAG[2][1] = magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1];
H_MAG[2][16] = SH_MAG[5];
H_MAG[2][17] = 2 * q2 * q3 - 2 * q0 * q1;
H_MAG[2][18] = SH_MAG[2];
H_MAG[2][21] = 1;
// intermediate variables
float SK_MZ[4];
_mag_innov_var[2] = (P[21][21] + R_MAG + P[16][21] * SH_MAG[5] + P[18][21] * SH_MAG[2] - (2 * q0 * q1 - 2 * q2 * q3) *
(P[21][17] + P[16][17] * SH_MAG[5] + P[18][17] * SH_MAG[2] - P[0][17] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN *
(SH_MAG[8] - 2 * q1 * q2)) + P[1][17] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) - P[17][17] *
(2 * q0 * q1 - 2 * q2 * q3)) - P[0][21] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN *
(SH_MAG[8] - 2 * q1 * q2)) + P[1][21] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) + SH_MAG[5] *
(P[21][16] + P[16][16] * SH_MAG[5] + P[18][16] * SH_MAG[2] - P[0][16] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN *
(SH_MAG[8] - 2 * q1 * q2)) + P[1][16] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) - P[17][16] *
(2 * q0 * q1 - 2 * q2 * q3)) + SH_MAG[2] * (P[21][18] + P[16][18] * SH_MAG[5] + P[18][18] * SH_MAG[2] - P[0][18] *
(magE * SH_MAG[0] + magD * SH_MAG[3] - magN * (SH_MAG[8] - 2 * q1 * q2)) + P[1][18] *
(magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) - P[17][18] * (2 * q0 * q1 - 2 * q2 * q3)) -
(magE * SH_MAG[0] + magD * SH_MAG[3] - magN * (SH_MAG[8] - 2 * q1 * q2)) * (P[21][0] + P[16][0] * SH_MAG[5] + P[18][0] *
SH_MAG[2] - P[0][0] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN * (SH_MAG[8] - 2 * q1 * q2)) + P[1][0] *
(magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) - P[17][0] * (2 * q0 * q1 - 2 * q2 * q3)) - P[17][21] *
(2 * q0 * q1 - 2 * q2 * q3) + (magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) *
(P[21][1] + P[16][1] * SH_MAG[5] + P[18][1] * SH_MAG[2] - P[0][1] * (magE * SH_MAG[0] + magD * SH_MAG[3] - magN *
(SH_MAG[8] - 2 * q1 * q2)) + P[1][1] * (magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1]) - P[17][1] *
(2 * q0 * q1 - 2 * q2 * q3)));
// check for a badly conditioned covariance matrix
if (_mag_innov_var[2] >= R_MAG) {
// the innovation variance contribution from the state covariances is non-negative - no fault
_fault_status.bad_mag_z = false;
} else {
// the innovation variance contribution from the state covariances is negtive which means the covariance matrix is badly conditioned
_fault_status.bad_mag_z = true;
// we need to reinitialise the covariance matrix and abort this fusion step
initialiseCovariance();
return;
}
// Perform an innovation consistency check on each measurement and if one axis fails
// do not fuse any data from the sensor because the most common errors affect multiple axes.
_mag_healthy = true;
for (uint8_t index = 0; index <= 2; index++) {
_mag_test_ratio[index] = sq(_mag_innov[index]) / (sq(math::max(_params.mag_innov_gate, 1.0f)) * _mag_innov_var[index]);
if (_mag_test_ratio[index] > 1.0f) {
_mag_healthy = false;
}
}
if (!_mag_healthy) {
return;
}
// update the states and covariance usinng sequential fusion of the magnetometer components
for (uint8_t index = 0; index <= 2; index++) {
// Calculate Kalman gains
if (index == 0) {
// Calculate X axis Kalman gains
SK_MX[0] = 1.0f / _mag_innov_var[0];
SK_MX[1] = magE * SH_MAG[0] + magD * SH_MAG[3] - magN * (SH_MAG[8] - 2 * q1 * q2);
SK_MX[2] = magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5];
SK_MX[3] = SH_MAG[7];
Kfusion[0] = SK_MX[0] * (P[0][19] + P[0][16] * SH_MAG[1] + P[0][17] * SH_MAG[4] - P[0][1] * SK_MX[2] + P[0][2] *
SK_MX[1] + P[0][18] * SK_MX[3]);
Kfusion[1] = SK_MX[0] * (P[1][19] + P[1][16] * SH_MAG[1] + P[1][17] * SH_MAG[4] - P[1][1] * SK_MX[2] + P[1][2] *
SK_MX[1] + P[1][18] * SK_MX[3]);
Kfusion[2] = SK_MX[0] * (P[2][19] + P[2][16] * SH_MAG[1] + P[2][17] * SH_MAG[4] - P[2][1] * SK_MX[2] + P[2][2] *
SK_MX[1] + P[2][18] * SK_MX[3]);
Kfusion[3] = SK_MX[0] * (P[3][19] + P[3][16] * SH_MAG[1] + P[3][17] * SH_MAG[4] - P[3][1] * SK_MX[2] + P[3][2] *
SK_MX[1] + P[3][18] * SK_MX[3]);
Kfusion[4] = SK_MX[0] * (P[4][19] + P[4][16] * SH_MAG[1] + P[4][17] * SH_MAG[4] - P[4][1] * SK_MX[2] + P[4][2] *
SK_MX[1] + P[4][18] * SK_MX[3]);
Kfusion[5] = SK_MX[0] * (P[5][19] + P[5][16] * SH_MAG[1] + P[5][17] * SH_MAG[4] - P[5][1] * SK_MX[2] + P[5][2] *
SK_MX[1] + P[5][18] * SK_MX[3]);
Kfusion[6] = SK_MX[0] * (P[6][19] + P[6][16] * SH_MAG[1] + P[6][17] * SH_MAG[4] - P[6][1] * SK_MX[2] + P[6][2] *
SK_MX[1] + P[6][18] * SK_MX[3]);
Kfusion[7] = SK_MX[0] * (P[7][19] + P[7][16] * SH_MAG[1] + P[7][17] * SH_MAG[4] - P[7][1] * SK_MX[2] + P[7][2] *
SK_MX[1] + P[7][18] * SK_MX[3]);
Kfusion[8] = SK_MX[0] * (P[8][19] + P[8][16] * SH_MAG[1] + P[8][17] * SH_MAG[4] - P[8][1] * SK_MX[2] + P[8][2] *
SK_MX[1] + P[8][18] * SK_MX[3]);
Kfusion[9] = SK_MX[0] * (P[9][19] + P[9][16] * SH_MAG[1] + P[9][17] * SH_MAG[4] - P[9][1] * SK_MX[2] + P[9][2] *
SK_MX[1] + P[9][18] * SK_MX[3]);
Kfusion[10] = SK_MX[0] * (P[10][19] + P[10][16] * SH_MAG[1] + P[10][17] * SH_MAG[4] - P[10][1] * SK_MX[2] + P[10][2] *
SK_MX[1] + P[10][18] * SK_MX[3]);
Kfusion[11] = SK_MX[0] * (P[11][19] + P[11][16] * SH_MAG[1] + P[11][17] * SH_MAG[4] - P[11][1] * SK_MX[2] + P[11][2] *
SK_MX[1] + P[11][18] * SK_MX[3]);
Kfusion[12] = SK_MX[0] * (P[12][19] + P[12][16] * SH_MAG[1] + P[12][17] * SH_MAG[4] - P[12][1] * SK_MX[2] + P[12][2] *
SK_MX[1] + P[12][18] * SK_MX[3]);
Kfusion[13] = SK_MX[0] * (P[13][19] + P[13][16] * SH_MAG[1] + P[13][17] * SH_MAG[4] - P[13][1] * SK_MX[2] + P[13][2] *
SK_MX[1] + P[13][18] * SK_MX[3]);
Kfusion[14] = SK_MX[0] * (P[14][19] + P[14][16] * SH_MAG[1] + P[14][17] * SH_MAG[4] - P[14][1] * SK_MX[2] + P[14][2] *
SK_MX[1] + P[14][18] * SK_MX[3]);
Kfusion[15] = SK_MX[0] * (P[15][19] + P[15][16] * SH_MAG[1] + P[15][17] * SH_MAG[4] - P[15][1] * SK_MX[2] + P[15][2] *
SK_MX[1] + P[15][18] * SK_MX[3]);
Kfusion[16] = SK_MX[0] * (P[16][19] + P[16][16] * SH_MAG[1] + P[16][17] * SH_MAG[4] - P[16][1] * SK_MX[2] + P[16][2] *
SK_MX[1] + P[16][18] * SK_MX[3]);
Kfusion[17] = SK_MX[0] * (P[17][19] + P[17][16] * SH_MAG[1] + P[17][17] * SH_MAG[4] - P[17][1] * SK_MX[2] + P[17][2] *
SK_MX[1] + P[17][18] * SK_MX[3]);
Kfusion[18] = SK_MX[0] * (P[18][19] + P[18][16] * SH_MAG[1] + P[18][17] * SH_MAG[4] - P[18][1] * SK_MX[2] + P[18][2] *
SK_MX[1] + P[18][18] * SK_MX[3]);
Kfusion[19] = SK_MX[0] * (P[19][19] + P[19][16] * SH_MAG[1] + P[19][17] * SH_MAG[4] - P[19][1] * SK_MX[2] + P[19][2] *
SK_MX[1] + P[19][18] * SK_MX[3]);
Kfusion[20] = SK_MX[0] * (P[20][19] + P[20][16] * SH_MAG[1] + P[20][17] * SH_MAG[4] - P[20][1] * SK_MX[2] + P[20][2] *
SK_MX[1] + P[20][18] * SK_MX[3]);
Kfusion[21] = SK_MX[0] * (P[21][19] + P[21][16] * SH_MAG[1] + P[21][17] * SH_MAG[4] - P[21][1] * SK_MX[2] + P[21][2] *
SK_MX[1] + P[21][18] * SK_MX[3]);
Kfusion[22] = SK_MX[0] * (P[22][19] + P[22][16] * SH_MAG[1] + P[22][17] * SH_MAG[4] - P[22][1] * SK_MX[2] + P[22][2] *
SK_MX[1] + P[22][18] * SK_MX[3]);
Kfusion[23] = SK_MX[0] * (P[23][19] + P[23][16] * SH_MAG[1] + P[23][17] * SH_MAG[4] - P[23][1] * SK_MX[2] + P[23][2] *
SK_MX[1] + P[23][18] * SK_MX[3]);
} else if (index == 1) {
// Calculate Y axis Kalman gains
SK_MY[0] = 1.0f / _mag_innov_var[1];
SK_MY[1] = magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1];
SK_MY[2] = magD * SH_MAG[2] - SH_MAG[6] + magN * SH_MAG[5];
SK_MY[3] = SH_MAG[8] - 2 * q1 * q2;
Kfusion[0] = SK_MY[0] * (P[0][20] + P[0][17] * SH_MAG[0] + P[0][18] * SH_MAG[3] + P[0][0] * SK_MY[2] - P[0][2] *
SK_MY[1] - P[0][16] * SK_MY[3]);
Kfusion[1] = SK_MY[0] * (P[1][20] + P[1][17] * SH_MAG[0] + P[1][18] * SH_MAG[3] + P[1][0] * SK_MY[2] - P[1][2] *
SK_MY[1] - P[1][16] * SK_MY[3]);
Kfusion[2] = SK_MY[0] * (P[2][20] + P[2][17] * SH_MAG[0] + P[2][18] * SH_MAG[3] + P[2][0] * SK_MY[2] - P[2][2] *
SK_MY[1] - P[2][16] * SK_MY[3]);
Kfusion[3] = SK_MY[0] * (P[3][20] + P[3][17] * SH_MAG[0] + P[3][18] * SH_MAG[3] + P[3][0] * SK_MY[2] - P[3][2] *
SK_MY[1] - P[3][16] * SK_MY[3]);
Kfusion[4] = SK_MY[0] * (P[4][20] + P[4][17] * SH_MAG[0] + P[4][18] * SH_MAG[3] + P[4][0] * SK_MY[2] - P[4][2] *
SK_MY[1] - P[4][16] * SK_MY[3]);
Kfusion[5] = SK_MY[0] * (P[5][20] + P[5][17] * SH_MAG[0] + P[5][18] * SH_MAG[3] + P[5][0] * SK_MY[2] - P[5][2] *
SK_MY[1] - P[5][16] * SK_MY[3]);
Kfusion[6] = SK_MY[0] * (P[6][20] + P[6][17] * SH_MAG[0] + P[6][18] * SH_MAG[3] + P[6][0] * SK_MY[2] - P[6][2] *
SK_MY[1] - P[6][16] * SK_MY[3]);
Kfusion[7] = SK_MY[0] * (P[7][20] + P[7][17] * SH_MAG[0] + P[7][18] * SH_MAG[3] + P[7][0] * SK_MY[2] - P[7][2] *
SK_MY[1] - P[7][16] * SK_MY[3]);
Kfusion[8] = SK_MY[0] * (P[8][20] + P[8][17] * SH_MAG[0] + P[8][18] * SH_MAG[3] + P[8][0] * SK_MY[2] - P[8][2] *
SK_MY[1] - P[8][16] * SK_MY[3]);
Kfusion[9] = SK_MY[0] * (P[9][20] + P[9][17] * SH_MAG[0] + P[9][18] * SH_MAG[3] + P[9][0] * SK_MY[2] - P[9][2] *
SK_MY[1] - P[9][16] * SK_MY[3]);
Kfusion[10] = SK_MY[0] * (P[10][20] + P[10][17] * SH_MAG[0] + P[10][18] * SH_MAG[3] + P[10][0] * SK_MY[2] - P[10][2] *
SK_MY[1] - P[10][16] * SK_MY[3]);
Kfusion[11] = SK_MY[0] * (P[11][20] + P[11][17] * SH_MAG[0] + P[11][18] * SH_MAG[3] + P[11][0] * SK_MY[2] - P[11][2] *
SK_MY[1] - P[11][16] * SK_MY[3]);
Kfusion[12] = SK_MY[0] * (P[12][20] + P[12][17] * SH_MAG[0] + P[12][18] * SH_MAG[3] + P[12][0] * SK_MY[2] - P[12][2] *
SK_MY[1] - P[12][16] * SK_MY[3]);
Kfusion[13] = SK_MY[0] * (P[13][20] + P[13][17] * SH_MAG[0] + P[13][18] * SH_MAG[3] + P[13][0] * SK_MY[2] - P[13][2] *
SK_MY[1] - P[13][16] * SK_MY[3]);
Kfusion[14] = SK_MY[0] * (P[14][20] + P[14][17] * SH_MAG[0] + P[14][18] * SH_MAG[3] + P[14][0] * SK_MY[2] - P[14][2] *
SK_MY[1] - P[14][16] * SK_MY[3]);
Kfusion[15] = SK_MY[0] * (P[15][20] + P[15][17] * SH_MAG[0] + P[15][18] * SH_MAG[3] + P[15][0] * SK_MY[2] - P[15][2] *
SK_MY[1] - P[15][16] * SK_MY[3]);
Kfusion[16] = SK_MY[0] * (P[16][20] + P[16][17] * SH_MAG[0] + P[16][18] * SH_MAG[3] + P[16][0] * SK_MY[2] - P[16][2] *
SK_MY[1] - P[16][16] * SK_MY[3]);
Kfusion[17] = SK_MY[0] * (P[17][20] + P[17][17] * SH_MAG[0] + P[17][18] * SH_MAG[3] + P[17][0] * SK_MY[2] - P[17][2] *
SK_MY[1] - P[17][16] * SK_MY[3]);
Kfusion[18] = SK_MY[0] * (P[18][20] + P[18][17] * SH_MAG[0] + P[18][18] * SH_MAG[3] + P[18][0] * SK_MY[2] - P[18][2] *
SK_MY[1] - P[18][16] * SK_MY[3]);
Kfusion[19] = SK_MY[0] * (P[19][20] + P[19][17] * SH_MAG[0] + P[19][18] * SH_MAG[3] + P[19][0] * SK_MY[2] - P[19][2] *
SK_MY[1] - P[19][16] * SK_MY[3]);
Kfusion[20] = SK_MY[0] * (P[20][20] + P[20][17] * SH_MAG[0] + P[20][18] * SH_MAG[3] + P[20][0] * SK_MY[2] - P[20][2] *
SK_MY[1] - P[20][16] * SK_MY[3]);
Kfusion[21] = SK_MY[0] * (P[21][20] + P[21][17] * SH_MAG[0] + P[21][18] * SH_MAG[3] + P[21][0] * SK_MY[2] - P[21][2] *
SK_MY[1] - P[21][16] * SK_MY[3]);
Kfusion[22] = SK_MY[0] * (P[22][20] + P[22][17] * SH_MAG[0] + P[22][18] * SH_MAG[3] + P[22][0] * SK_MY[2] - P[22][2] *
SK_MY[1] - P[22][16] * SK_MY[3]);
Kfusion[23] = SK_MY[0] * (P[23][20] + P[23][17] * SH_MAG[0] + P[23][18] * SH_MAG[3] + P[23][0] * SK_MY[2] - P[23][2] *
SK_MY[1] - P[23][16] * SK_MY[3]);
} else if (index == 2) {
// Calculate Z axis Kalman gains
SK_MZ[0] = 1.0f / _mag_innov_var[2];
SK_MZ[1] = magE * SH_MAG[0] + magD * SH_MAG[3] - magN * (SH_MAG[8] - 2 * q1 * q2);
SK_MZ[2] = magE * SH_MAG[4] + magD * SH_MAG[7] + magN * SH_MAG[1];
SK_MZ[3] = 2 * q0 * q1 - 2 * q2 * q3;
Kfusion[0] = SK_MZ[0] * (P[0][21] + P[0][18] * SH_MAG[2] + P[0][16] * SH_MAG[5] - P[0][0] * SK_MZ[1] + P[0][1] *
SK_MZ[2] - P[0][17] * SK_MZ[3]);
Kfusion[1] = SK_MZ[0] * (P[1][21] + P[1][18] * SH_MAG[2] + P[1][16] * SH_MAG[5] - P[1][0] * SK_MZ[1] + P[1][1] *
SK_MZ[2] - P[1][17] * SK_MZ[3]);
Kfusion[2] = SK_MZ[0] * (P[2][21] + P[2][18] * SH_MAG[2] + P[2][16] * SH_MAG[5] - P[2][0] * SK_MZ[1] + P[2][1] *
SK_MZ[2] - P[2][17] * SK_MZ[3]);
Kfusion[3] = SK_MZ[0] * (P[3][21] + P[3][18] * SH_MAG[2] + P[3][16] * SH_MAG[5] - P[3][0] * SK_MZ[1] + P[3][1] *
SK_MZ[2] - P[3][17] * SK_MZ[3]);
Kfusion[4] = SK_MZ[0] * (P[4][21] + P[4][18] * SH_MAG[2] + P[4][16] * SH_MAG[5] - P[4][0] * SK_MZ[1] + P[4][1] *
SK_MZ[2] - P[4][17] * SK_MZ[3]);
Kfusion[5] = SK_MZ[0] * (P[5][21] + P[5][18] * SH_MAG[2] + P[5][16] * SH_MAG[5] - P[5][0] * SK_MZ[1] + P[5][1] *
SK_MZ[2] - P[5][17] * SK_MZ[3]);
Kfusion[6] = SK_MZ[0] * (P[6][21] + P[6][18] * SH_MAG[2] + P[6][16] * SH_MAG[5] - P[6][0] * SK_MZ[1] + P[6][1] *
SK_MZ[2] - P[6][17] * SK_MZ[3]);
Kfusion[7] = SK_MZ[0] * (P[7][21] + P[7][18] * SH_MAG[2] + P[7][16] * SH_MAG[5] - P[7][0] * SK_MZ[1] + P[7][1] *
SK_MZ[2] - P[7][17] * SK_MZ[3]);
Kfusion[8] = SK_MZ[0] * (P[8][21] + P[8][18] * SH_MAG[2] + P[8][16] * SH_MAG[5] - P[8][0] * SK_MZ[1] + P[8][1] *
SK_MZ[2] - P[8][17] * SK_MZ[3]);
Kfusion[9] = SK_MZ[0] * (P[9][21] + P[9][18] * SH_MAG[2] + P[9][16] * SH_MAG[5] - P[9][0] * SK_MZ[1] + P[9][1] *
SK_MZ[2] - P[9][17] * SK_MZ[3]);
Kfusion[10] = SK_MZ[0] * (P[10][21] + P[10][18] * SH_MAG[2] + P[10][16] * SH_MAG[5] - P[10][0] * SK_MZ[1] + P[10][1] *
SK_MZ[2] - P[10][17] * SK_MZ[3]);
Kfusion[11] = SK_MZ[0] * (P[11][21] + P[11][18] * SH_MAG[2] + P[11][16] * SH_MAG[5] - P[11][0] * SK_MZ[1] + P[11][1] *
SK_MZ[2] - P[11][17] * SK_MZ[3]);
Kfusion[12] = SK_MZ[0] * (P[12][21] + P[12][18] * SH_MAG[2] + P[12][16] * SH_MAG[5] - P[12][0] * SK_MZ[1] + P[12][1] *
SK_MZ[2] - P[12][17] * SK_MZ[3]);
Kfusion[13] = SK_MZ[0] * (P[13][21] + P[13][18] * SH_MAG[2] + P[13][16] * SH_MAG[5] - P[13][0] * SK_MZ[1] + P[13][1] *
SK_MZ[2] - P[13][17] * SK_MZ[3]);
Kfusion[14] = SK_MZ[0] * (P[14][21] + P[14][18] * SH_MAG[2] + P[14][16] * SH_MAG[5] - P[14][0] * SK_MZ[1] + P[14][1] *
SK_MZ[2] - P[14][17] * SK_MZ[3]);
Kfusion[15] = SK_MZ[0] * (P[15][21] + P[15][18] * SH_MAG[2] + P[15][16] * SH_MAG[5] - P[15][0] * SK_MZ[1] + P[15][1] *
SK_MZ[2] - P[15][17] * SK_MZ[3]);
Kfusion[16] = SK_MZ[0] * (P[16][21] + P[16][18] * SH_MAG[2] + P[16][16] * SH_MAG[5] - P[16][0] * SK_MZ[1] + P[16][1] *
SK_MZ[2] - P[16][17] * SK_MZ[3]);
Kfusion[17] = SK_MZ[0] * (P[17][21] + P[17][18] * SH_MAG[2] + P[17][16] * SH_MAG[5] - P[17][0] * SK_MZ[1] + P[17][1] *
SK_MZ[2] - P[17][17] * SK_MZ[3]);
Kfusion[18] = SK_MZ[0] * (P[18][21] + P[18][18] * SH_MAG[2] + P[18][16] * SH_MAG[5] - P[18][0] * SK_MZ[1] + P[18][1] *
SK_MZ[2] - P[18][17] * SK_MZ[3]);
Kfusion[19] = SK_MZ[0] * (P[19][21] + P[19][18] * SH_MAG[2] + P[19][16] * SH_MAG[5] - P[19][0] * SK_MZ[1] + P[19][1] *
SK_MZ[2] - P[19][17] * SK_MZ[3]);
Kfusion[20] = SK_MZ[0] * (P[20][21] + P[20][18] * SH_MAG[2] + P[20][16] * SH_MAG[5] - P[20][0] * SK_MZ[1] + P[20][1] *
SK_MZ[2] - P[20][17] * SK_MZ[3]);
Kfusion[21] = SK_MZ[0] * (P[21][21] + P[21][18] * SH_MAG[2] + P[21][16] * SH_MAG[5] - P[21][0] * SK_MZ[1] + P[21][1] *
SK_MZ[2] - P[21][17] * SK_MZ[3]);
Kfusion[22] = SK_MZ[0] * (P[22][21] + P[22][18] * SH_MAG[2] + P[22][16] * SH_MAG[5] - P[22][0] * SK_MZ[1] + P[22][1] *
SK_MZ[2] - P[22][17] * SK_MZ[3]);
Kfusion[23] = SK_MZ[0] * (P[23][21] + P[23][18] * SH_MAG[2] + P[23][16] * SH_MAG[5] - P[23][0] * SK_MZ[1] + P[23][1] *
SK_MZ[2] - P[23][17] * SK_MZ[3]);
} else {
return;
}
// by definition our error state is zero at the time of fusion
_state.ang_error.setZero();
fuse(Kfusion, _mag_innov[index]);
Quaternion q_correction;
q_correction.from_axis_angle(_state.ang_error);
_state.quat_nominal = q_correction * _state.quat_nominal;
_state.quat_nominal.normalize();
_state.ang_error.setZero();
// apply covariance correction via P_new = (I -K*H)*P
// first calculate expression for KHP
// then calculate P - KHP
float KH[_k_num_states][_k_num_states] = {};
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < 3; column++) {
KH[row][column] = Kfusion[row] * H_MAG[index][column];
}
for (unsigned column = 16; column < 22; column++) {
KH[row][column] = Kfusion[row] * H_MAG[index][column];
}
}
float KHP[_k_num_states][_k_num_states] = {};
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < _k_num_states; column++) {
float tmp = KH[row][0] * P[0][column];
tmp += KH[row][1] * P[1][column];
tmp += KH[row][2] * P[2][column];
tmp += KH[row][16] * P[16][column];
tmp += KH[row][17] * P[17][column];
tmp += KH[row][18] * P[18][column];
tmp += KH[row][19] * P[19][column];
tmp += KH[row][20] * P[20][column];
tmp += KH[row][21] * P[21][column];
KHP[row][column] = tmp;
}
}
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < _k_num_states; column++) {
P[row][column] -= KHP[row][column];
}
}
makeSymmetrical();
limitCov();
}
}
void Ekf::fuseHeading()
{
// 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 magX = _mag_sample_delayed.mag(0);
float magY = _mag_sample_delayed.mag(1);
float magZ = _mag_sample_delayed.mag(2);
float R_mag = fmaxf(_params.mag_heading_noise, 1.0e-2f);
R_mag = R_mag * R_mag;
float t2 = q0 * q0;
float t3 = q1 * q1;
float t4 = q2 * q2;
float t5 = q3 * q3;
float t6 = q0 * q2 * 2.0f;
float t7 = q1 * q3 * 2.0f;
float t8 = t6 + t7;
float t9 = q0 * q3 * 2.0f;
float t13 = q1 * q2 * 2.0f;
float t10 = t9 - t13;
float t11 = t2 + t3 - t4 - t5;
float t12 = magX * t11;
float t14 = magZ * t8;
float t19 = magY * t10;
float t15 = t12 + t14 - t19;
float t16 = t2 - t3 + t4 - t5;
float t17 = q0 * q1 * 2.0f;
float t24 = q2 * q3 * 2.0f;
float t18 = t17 - t24;
float t20 = 1.0f / t15;
float t21 = magY * t16;
float t22 = t9 + t13;
float t23 = magX * t22;
float t28 = magZ * t18;
float t25 = t21 + t23 - t28;
float t29 = t20 * t25;
float t26 = tan(t29);
float t27 = 1.0f / (t15 * t15);
float t30 = t26 * t26;
float t31 = t30 + 1.0f;
float H_HDG[3] = {};
H_HDG[0] = -t31 * (t20 * (magZ * t16 + magY * t18) + t25 * t27 * (magY * t8 + magZ * t10));
H_HDG[1] = t31 * (t20 * (magX * t18 + magZ * t22) + t25 * t27 * (magX * t8 - magZ * t11));
H_HDG[2] = t31 * (t20 * (magX * t16 - magY * t22) + t25 * t27 * (magX * t10 + magY * t11));
// calculate innovation
matrix::Dcm<float> R_to_earth(_state.quat_nominal);
matrix::Vector3f mag_earth_pred = R_to_earth * _mag_sample_delayed.mag;
float innovation = atan2f(mag_earth_pred(1), mag_earth_pred(0)) - math::radians(_params.mag_declination_deg);
innovation = math::constrain(innovation, -0.5f, 0.5f);
_heading_innov = innovation;
float innovation_var = R_mag;
_heading_innov_var = innovation_var;
// calculate innovation variance
float PH[3] = {};
for (unsigned row = 0; row < 3; row++) {
for (unsigned column = 0; column < 3; column++) {
PH[row] += P[row][column] * H_HDG[column];
}
innovation_var += H_HDG[row] * PH[row];
}
if (innovation_var >= R_mag) {
// the innovation variance contribution from the state covariances is not negative, no fault
_fault_status.bad_mag_hdg = false;
} else {
// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
_fault_status.bad_mag_hdg = true;
// we reinitialise the covariance matrix and abort this fusion step
initialiseCovariance();
return;
}
float innovation_var_inv = 1 / innovation_var;
// calculate kalman gain
float Kfusion[_k_num_states] = {};
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < 3; column++) {
Kfusion[row] += P[row][column] * H_HDG[column];
}
Kfusion[row] *= innovation_var_inv;
}
// innovation test ratio
_yaw_test_ratio = sq(innovation) / (sq(math::max(_params.heading_innov_gate, 1.0f)) * innovation_var);
// set the magnetometer unhealthy if the test fails
if (_yaw_test_ratio > 1.0f) {
_mag_healthy = false;
// 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 {
_mag_healthy = true;
}
_state.ang_error.setZero();
fuse(Kfusion, innovation);
// correct the nominal quaternion
Quaternion dq;
dq.from_axis_angle(_state.ang_error);
_state.quat_nominal = dq * _state.quat_nominal;
_state.quat_nominal.normalize();
float HP[_k_num_states] = {};
for (unsigned column = 0; column < _k_num_states; column++) {
for (unsigned row = 0; row < 3; row++) {
HP[column] += H_HDG[row] * P[row][column];
}
}
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < _k_num_states; column++) {
P[row][column] -= Kfusion[row] * HP[column];
}
}
makeSymmetrical();
limitCov();
}
void Ekf::fuseDeclination()
{
// assign intermediate state variables
float magN = _state.mag_I(0);
float magE = _state.mag_I(1);
float R_DECL = sq(0.5f);
// Calculate intermediate variables
// if the horizontal magnetic field is too small, this calculation will be badly conditioned
if (fabsf(magN) < 0.001f) {
return;
}
float t2 = 1.0f/magN;
float t4 = magE*t2;
float t3 = tanf(t4);
float t5 = t3*t3;
float t6 = t5+1.0f;
float t25 = t2*t6;
float t7 = 1.0f/(magN*magN);
float t26 = magE*t6*t7;
float t8 = P[17][17]*t25;
float t15 = P[16][17]*t26;
float t9 = t8-t15;
float t10 = t25*t9;
float t11 = P[17][16]*t25;
float t16 = P[16][16]*t26;
float t12 = t11-t16;
float t17 = t26*t12;
float t13 = R_DECL+t10-t17; // innovation variance
// check the innovation variance calculation for a badly conditioned covariance matrix
if (t13 >= R_DECL) {
// the innovation variance contribution from the state covariances is not negative, no fault
_fault_status.bad_mag_decl = false;
} else {
// the innovation variance contribution from the state covariances is negtive which means the covariance matrix is badly conditioned
_fault_status.bad_mag_decl = true;
// we reinitialise the covariance matrix and abort this fusion step
initialiseCovariance();
return;
}
float t14 = 1.0f/t13;
float t18 = magE;
float t19 = magN;
float t21 = 1.0f/t19;
float t22 = t18*t21;
float t20 = tanf(t22);
float t23 = t20*t20;
float t24 = t23+1.0f;
// Calculate the observation Jacobian
// Note only 2 terms are non-zero which can be used in matrix operations for calculation of Kalman gains and covariance update to significantly reduce cost
float H_DECL[24] = {};
H_DECL[16] = -t18*1.0f/(t19*t19)*t24;
H_DECL[17] = t21*t24;
// Calculate the Kalman gains
float Kfusion[_k_num_states] = {};
Kfusion[0] = t14*(P[0][17]*t25-P[0][16]*t26);
Kfusion[1] = t14*(P[1][17]*t25-P[1][16]*t26);
Kfusion[2] = t14*(P[2][17]*t25-P[2][16]*t26);
Kfusion[3] = t14*(P[3][17]*t25-P[3][16]*t26);
Kfusion[4] = t14*(P[4][17]*t25-P[4][16]*t26);
Kfusion[5] = t14*(P[5][17]*t25-P[5][16]*t26);
Kfusion[6] = t14*(P[6][17]*t25-P[6][16]*t26);
Kfusion[7] = t14*(P[7][17]*t25-P[7][16]*t26);
Kfusion[8] = t14*(P[8][17]*t25-P[8][16]*t26);
Kfusion[9] = t14*(P[9][17]*t25-P[9][16]*t26);
Kfusion[10] = t14*(P[10][17]*t25-P[10][16]*t26);
Kfusion[11] = t14*(P[11][17]*t25-P[11][16]*t26);
Kfusion[12] = t14*(P[12][17]*t25-P[12][16]*t26);
Kfusion[13] = t14*(P[13][17]*t25-P[13][16]*t26);
Kfusion[14] = t14*(P[14][17]*t25-P[14][16]*t26);
Kfusion[15] = t14*(P[15][17]*t25-P[15][16]*t26);
Kfusion[16] = -t14*(t16-P[16][17]*t25);
Kfusion[17] = t14*(t8-P[17][16]*t26);
Kfusion[18] = t14*(P[18][17]*t25-P[18][16]*t26);
Kfusion[19] = t14*(P[19][17]*t25-P[19][16]*t26);
Kfusion[20] = t14*(P[20][17]*t25-P[20][16]*t26);
Kfusion[21] = t14*(P[21][17]*t25-P[21][16]*t26);
Kfusion[22] = t14*(P[22][17]*t25-P[22][16]*t26);
Kfusion[23] = t14*(P[23][17]*t25-P[23][16]*t26);
// calculate innovation and constrain
float innovation = atanf(t4) - math::radians(_params.mag_declination_deg);
innovation = math::constrain(innovation, -0.5f, 0.5f);
// zero attitude error states and perform the state correction
_state.ang_error.setZero();
fuse(Kfusion, innovation);
// use the attitude error estimate to correct the quaternion
Quaternion dq;
dq.from_axis_angle(_state.ang_error);
_state.quat_nominal = dq * _state.quat_nominal;
_state.quat_nominal.normalize();
// apply covariance correction via P_new = (I -K*H)*P
// first calculate expression for KHP
// then calculate P - KHP
// take advantage of the empty columns in KH to reduce the number of operations
float KH[_k_num_states][_k_num_states] = {};
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 16; column < 17; column++) {
KH[row][column] = Kfusion[row] * H_DECL[column];
}
}
float KHP[_k_num_states][_k_num_states] = {};
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < _k_num_states; column++) {
float tmp = KH[row][0] * P[0][column];
tmp += KH[row][16] * P[16][column];
tmp += KH[row][17] * P[17][column];
KHP[row][column] = tmp;
}
}
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < _k_num_states; column++) {
P[row][column] -= KHP[row][column];
}
}
// force the covariance matrix to be symmetrical and don't allow the variances to be negative.
makeSymmetrical();
limitCov();
}
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