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px4_autopilot/EKF/mag_fusion.cpp

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/****************************************************************************
*
* Copyright (c) 2015 Estimation and Control Library (ECL). 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 ECL nor the names of its contributors may be
* used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
****************************************************************************/
/**
* @file 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.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]);
// Don't update wind states unless we are doing wind estimation
if (_control_status.flags.wind) {
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 {
Kfusion[22] = 0.0f;
Kfusion[23] = 0.0f;
}
} 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]);
// Don't update wind states unless we are doing wind estimation
if (_control_status.flags.wind) {
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 {
Kfusion[22] = 0.0f;
Kfusion[23] = 0.0f;
}
} 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]);
// Don't update wind states unless we are doing wind estimation
if (_control_status.flags.wind) {
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 {
Kfusion[22] = 0.0f;
Kfusion[23] = 0.0f;
}
} 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
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column <= 2; column++) {
KH[row][column] = Kfusion[row] * H_MAG[index][column];
}
for (unsigned column = 16; column <= 21; column++) {
KH[row][column] = Kfusion[row] * H_MAG[index][column];
}
}
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 R_YAW = fmaxf(_params.mag_heading_noise, 1.0e-2f);
R_YAW = R_YAW * R_YAW;
float predicted_hdg;
float H_YAW[3];
matrix::Vector3f mag_earth_pred;
// determine if a 321 or 312 Euler sequence is best
if (fabsf(_R_prev(0, 2)) < fabsf(_R_prev(1, 2))) {
// calculate observation jacobian when we are observing the first rotation in a 321 sequence
float t2 = q0 * q0;
float t3 = q1 * q1;
float t4 = q2 * q2;
float t5 = q3 * q3;
float t6 = t2 + t3 - t4 - t5;
float t7 = q0 * q3 * 2.0f;
float t8 = q1 * q2 * 2.0f;
float t9 = t7 + t8;
float t10 = sq(t6);
if (t10 > 1e-6f) {
t10 = 1.0f / t10;
} else {
return;
}
float t11 = t9 * t9;
float t12 = t10 * t11;
float t13 = t12 + 1.0f;
float t14;
if (fabsf(t13) > 1e-3f) {
t14 = 1.0f / t13;
} else {
return;
}
float t15 = 1.0f / t6;
H_YAW[0] = 0.0f;
H_YAW[1] = t14 * (t15 * (q0 * q1 * 2.0f - q2 * q3 * 2.0f) + t9 * t10 * (q0 * q2 * 2.0f + q1 * q3 * 2.0f));
H_YAW[2] = t14 * (t15 * (t2 - t3 + t4 - t5) + t9 * t10 * (t7 - t8));
// rotate the magnetometer measurement into earth frame
matrix::Euler<float> euler321(_state.quat_nominal);
predicted_hdg = euler321(2); // we will need the predicted heading to calculate the innovation
// Set the yaw angle to zero and rotate the measurements into earth frame using the zero yaw angle
euler321(2) = 0.0f;
matrix::Dcm<float> R_to_earth(euler321);
// rotate the magnetometer measurements into earth frame using a zero yaw angle
mag_earth_pred = R_to_earth * _mag_sample_delayed.mag;
} else {
// calculate observaton jacobian when we are observing a rotation in a 312 sequence
float t2 = q0 * q0;
float t3 = q1 * q1;
float t4 = q2 * q2;
float t5 = q3 * q3;
float t6 = t2 - t3 + t4 - t5;
float t7 = q0 * q3 * 2.0f;
float t10 = q1 * q2 * 2.0f;
float t8 = t7 - t10;
float t9 = sq(t6);
if (t9 > 1e-6f) {
t9 = 1.0f / t9;
} else {
return;
}
float t11 = t8 * t8;
float t12 = t9 * t11;
float t13 = t12 + 1.0f;
float t14;
if (fabsf(t13) > 1e-3f) {
t14 = 1.0f / t13;
} else {
return;
}
float t15 = 1.0f / t6;
H_YAW[0] = -t14 * (t15 * (q0 * q2 * 2.0f + q1 * q3 * 2.0f) - t8 * t9 * (q0 * q1 * 2.0f - q2 * q3 * 2.0f));
H_YAW[1] = 0.0f;
H_YAW[2] = t14 * (t15 * (t2 + t3 - t4 - t5) + t8 * t9 * (t7 + t10));
// Calculate the 312 sequence euler angles that rotate from earth to body frame
// See http://www.atacolorado.com/eulersequences.doc
Vector3f euler312;
euler312(0) = atan2f(-_R_prev(1, 0) , _R_prev(1, 1)); // first rotation (yaw)
euler312(1) = asinf(_R_prev(1, 2)); // second rotation (roll)
euler312(2) = atan2f(-_R_prev(0, 2) , _R_prev(2, 2)); // third rotation (pitch)
predicted_hdg = euler312(0); // we will need the predicted heading to calculate the innovation
// Set the first rotation (yaw) to zero and rotate the measurements into earth frame
euler312(0) = 0.0f;
// Calculate the body to earth frame rotation matrix from the euler angles using a 312 rotation sequence
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));
matrix::Dcm<float> 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;
// rotate the magnetometer measurements into earth frame using a zero yaw angle
mag_earth_pred = R_to_earth * _mag_sample_delayed.mag;
}
// Calculate innovation variance and Kalman gains, taking advantage of the fact that only the first 3 elements in H are non zero
// calculate the innovaton variance
float PH[3];
_heading_innov_var = R_YAW;
for (unsigned row = 0; row <= 2; row++) {
PH[row] = 0.0f;
for (uint8_t col = 0; col <= 2; 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.bad_mag_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.bad_mag_hdg = true;
// we reinitialise the covariance matrix and abort this fusion step
initialiseCovariance();
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 <= 2; 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 <= 2; col++) {
Kfusion[row] += P[row][col] * H_YAW[col];
}
Kfusion[row] *= heading_innov_var_inv;
}
}
// Use the difference between the horizontal projection of the mag field and declination to give the measured heading
float measured_hdg = -atan2f(mag_earth_pred(1), mag_earth_pred(0)) + _mag_declination;
// wrap the heading to the interval between +-pi
measured_hdg = matrix::wrap_pi(measured_hdg);
// calculate the innovation
_heading_innov = predicted_hdg - measured_hdg;
// wrap the innovation to the interval between +-pi
_heading_innov = matrix::wrap_pi(_heading_innov);
// innovation test ratio
_yaw_test_ratio = sq(_heading_innov) / (sq(math::max(_params.heading_innov_gate, 1.0f)) * _heading_innov_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 {
// constrain the innovation to the maximum set by the gate
float gate_limit = sqrtf((sq(math::max(_params.heading_innov_gate, 1.0f)) * _heading_innov_var));
_heading_innov = math::constrain(_heading_innov, -gate_limit, gate_limit);
}
} else {
_mag_healthy = true;
}
// zero the attitude error states and use the kalman gain vector and innovation to update the states
_state.ang_error.setZero();
fuse(Kfusion, _heading_innov);
// correct the nominal 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
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column <= 2; column++) {
KH[row][column] = Kfusion[row] * H_YAW[column];
}
}
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];
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::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 (magN < 0.001f) {
return;
}
float t2 = magE * magE;
float t3 = magN * magN;
float t4 = t2 + t3;
float t5 = 1.0f / t4;
float t22 = magE * t5;
float t23 = magN * t5;
float t6 = P[16][16] * t22;
float t13 = P[17][16] * t23;
float t7 = t6 - t13;
float t8 = t22 * t7;
float t9 = P[16][17] * t22;
float t14 = P[17][17] * t23;
float t10 = t9 - t14;
float t15 = t23 * t10;
float t11 = R_DECL + t8 - t15; // innovation variance
// check the innovation variance calculation for a badly conditioned covariance matrix
if (t11 >= 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 t12 = 1.0f / t11;
// 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] = -magE * t5;
H_DECL[17] = magN * t5;
// Calculate the Kalman gains
float Kfusion[_k_num_states] = {};
Kfusion[0] = -t12 * (P[0][16] * t22 - P[0][17] * t23);
Kfusion[1] = -t12 * (P[1][16] * t22 - P[1][17] * t23);
Kfusion[2] = -t12 * (P[2][16] * t22 - P[2][17] * t23);
Kfusion[3] = -t12 * (P[3][16] * t22 - P[3][17] * t23);
Kfusion[4] = -t12 * (P[4][16] * t22 - P[4][17] * t23);
Kfusion[5] = -t12 * (P[5][16] * t22 - P[5][17] * t23);
Kfusion[6] = -t12 * (P[6][16] * t22 - P[6][17] * t23);
Kfusion[7] = -t12 * (P[7][16] * t22 - P[7][17] * t23);
Kfusion[8] = -t12 * (P[8][16] * t22 - P[8][17] * t23);
Kfusion[9] = -t12 * (P[9][16] * t22 - P[9][17] * t23);
Kfusion[10] = -t12 * (P[10][16] * t22 - P[10][17] * t23);
Kfusion[11] = -t12 * (P[11][16] * t22 - P[11][17] * t23);
Kfusion[12] = -t12 * (P[12][16] * t22 - P[12][17] * t23);
Kfusion[13] = -t12 * (P[13][16] * t22 - P[13][17] * t23);
Kfusion[14] = -t12 * (P[14][16] * t22 - P[14][17] * t23);
Kfusion[15] = -t12 * (P[15][16] * t22 - P[15][17] * t23);
// We only do declination fusion when we are using all the field states, so no logic required here
Kfusion[16] = -t12 * (t6 - P[16][17] * t23);
Kfusion[17] = t12 * (t14 - P[17][16] * t22);
Kfusion[18] = -t12 * (P[18][16] * t22 - P[18][17] * t23);
Kfusion[19] = -t12 * (P[19][16] * t22 - P[19][17] * t23);
Kfusion[20] = -t12 * (P[20][16] * t22 - P[20][17] * t23);
Kfusion[21] = -t12 * (P[21][16] * t22 - P[21][17] * t23);
// Don't update wind states unless we are doing wind estimation
if (_control_status.flags.wind) {
Kfusion[22] = -t12 * (P[22][16] * t22 - P[22][17] * t23);
Kfusion[23] = -t12 * (P[23][16] * t22 - P[23][17] * t23);
} else {
Kfusion[22] = 0.0f;
Kfusion[23] = 0.0f;
}
// calculate innovation and constrain
float innovation = atanf(magE / magN) - _mag_declination;
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
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 16; column <= 17; column++) {
KH[row][column] = Kfusion[row] * H_DECL[column];
}
}
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column < _k_num_states; column++) {
float 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();
}
void Ekf::fuseMag2D()
{
// 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_DECL = fmaxf(_params.mag_heading_noise, 1.0e-2f);
R_DECL = R_DECL * R_DECL;
// calculate intermediate variables for observation jacobian
float t2 = q0 * q0;
float t3 = q1 * q1;
float t4 = q2 * q2;
float t5 = q3 * q3;
float t6 = q0 * q3 * 2.0f;
float t8 = t2 - t3 + t4 - t5;
float t9 = q0 * q1 * 2.0f;
float t10 = q2 * q3 * 2.0f;
float t11 = t9 - t10;
float t14 = q1 * q2 * 2.0f;
float t21 = magY * t8;
float t22 = t6 + t14;
float t23 = magX * t22;
float t24 = magZ * t11;
float t7 = t21 + t23 - t24;
float t12 = t2 + t3 - t4 - t5;
float t13 = magX * t12;
float t15 = q0 * q2 * 2.0f;
float t16 = q1 * q3 * 2.0f;
float t17 = t15 + t16;
float t18 = magZ * t17;
float t19 = t6 - t14;
float t25 = magY * t19;
float t20 = t13 + t18 - t25;
if (fabsf(t20) < 1e-6f) {
return;
}
float t26 = 1.0f / (t20 * t20);
float t27 = t7 * t7;
float t28 = t26 * t27;
float t29 = t28 + 1.0f;
if (fabsf(t29) < 1e-12f) {
return;
}
float t30 = 1.0f / t29;
if (fabsf(t20) < 1e-12f) {
return;
}
float t31 = 1.0f / t20;
// calculate observation jacobian
float H_DECL[3] = {};
H_DECL[0] = -t30 * (t31 * (magZ * t8 + magY * t11) + t7 * t26 * (magY * t17 + magZ * t19));
H_DECL[1] = t30 * (t31 * (magX * t11 + magZ * t22) - t7 * t26 * (magZ * t12 - magX * t17));
H_DECL[2] = t30 * (t31 * (magX * t8 - magY * t22) + t7 * t26 * (magY * t12 + magX * t19));
// rotate the magnetometer measurement into earth frame
matrix::Dcm<float> R_to_earth(_state.quat_nominal);
matrix::Vector3f mag_earth_pred = R_to_earth * _mag_sample_delayed.mag;
// check if there is enough magnetic field length to use and exit if too small
float magLength2 = sq(mag_earth_pred(0) + mag_earth_pred(1));
if (magLength2 < sq(_params.mag_noise)) {
return;
}
// Adjust the measurement variance upwards if thehorizontal strength to magnetometer noise ratio make the value unrealistic
R_DECL = fmaxf(R_DECL, sq(_params.mag_noise) / magLength2);
// Calculate the innovation, using the declination angle of the projection onto the horizontal as the measurement
_heading_innov = atan2f(mag_earth_pred(1), mag_earth_pred(0)) - _mag_declination;
// wrap the innovation to the interval between +-pi
_heading_innov = matrix::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
float PH[3];
_heading_innov_var = R_DECL;
for (unsigned row = 0; row <= 2; row++) {
PH[row] = 0.0f;
for (unsigned col = 0; col <= 2; col++) {
PH[row] += P[row][col] * H_DECL[col];
}
_heading_innov_var += H_DECL[row] * PH[row];
}
float varInnovInv;
if (_heading_innov_var >= R_DECL) {
// 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;
}
// innovation test ratio
_yaw_test_ratio = sq(_heading_innov) / (sq(math::max(_params.heading_innov_gate, 1.0f)) * _heading_innov_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 {
// constrain the innovation to the maximum set by the gate
float gate_limit = sqrtf((sq(math::max(_params.heading_innov_gate, 1.0f)) * _heading_innov_var));
_heading_innov = math::constrain(_heading_innov, -gate_limit, gate_limit);
}
} else {
_mag_healthy = true;
}
varInnovInv = 1.0f / _heading_innov_var;
// calculate the Kalman gains
float Kfusion[24] = {};
for (unsigned row = 0; row < 16; row++) {
Kfusion[row] = 0.0f;
for (unsigned col = 0; col <= 2; col++) {
Kfusion[row] += P[row][col] * H_DECL[col];
}
Kfusion[row] *= varInnovInv;
}
// by definition our error state is zero at the time of fusion
_state.ang_error.setZero();
// correct the states
fuse(Kfusion, _heading_innov);
// correct the quaternon using the attitude error estimate
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
for (unsigned row = 0; row < _k_num_states; row++) {
for (unsigned column = 0; column <= 2; column++) {
KH[row][column] = Kfusion[row] * H_DECL[column];
}
}
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];
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();
}