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px4-firmware/EKF/covariance.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
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
****************************************************************************/
/**
* @file covariance.cpp
* Contains functions for initialising, predicting and updating the state
* covariance matrix
*
* @author Roman Bast <bastroman@gmail.com>
*
*/
#include "ekf.h"
#include <math.h>
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#include "mathlib.h"
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void Ekf::initialiseCovariance()
{
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for (unsigned i = 0; i < _k_num_states; i++) {
for (unsigned j = 0; j < _k_num_states; j++) {
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P[i][j] = 0.0f;
}
}
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// calculate average prediction time step in sec
float dt = 0.001f * (float)FILTER_UPDATE_PERRIOD_MS;
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// XXX use initial guess for the diagonal elements for the covariance matrix
// angle error
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P[0][0] = 0.1f;
P[1][1] = 0.1f;
P[2][2] = 0.1f;
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// velocity
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P[3][3] = sq(fmaxf(_params.gps_vel_noise, 0.01f));
P[4][4] = P[3][3];
P[5][5] = sq(1.5f) * P[3][3];
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// position
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P[6][6] = sq(fmaxf(_params.gps_pos_noise, 0.01f));
P[7][7] = P[6][6];
P[8][8] = sq(fmaxf(_params.baro_noise, 0.01f));
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// gyro bias
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P[9][9] = sq(0.035f * dt);
P[10][10] = P[9][9];
P[11][11] = P[9][9];
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// gyro scale
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P[12][12] = sq(0.001f);
P[13][13] = P[12][12];
P[14][14] = P[12][12];
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// accel z bias
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P[15][15] = sq(0.2f * dt);
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EKF: Initialise variances to zero for un-used states Setting these variances to zero makes it less likely that these states will be modified by fusion processing.
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// variances for optional states
// these state variances are set to zero until the states are required, then they must be initialised
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// earth magnetic field
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P[16][16] = 0.0f;
P[17][17] = 0.0f;
P[18][18] = 0.0f;
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// body magnetic field
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P[19][19] = 0.0f;
P[20][20] = 0.0f;
P[21][21] = 0.0f;
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// wind
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P[22][22] = 0.0f;
P[23][23] = 0.0f;
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}
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void Ekf::get_pos_var(Vector3f &pos_var)
{
pos_var(0) = P[6][6];
pos_var(1) = P[7][7];
pos_var(2) = P[8][8];
}
void Ekf::get_vel_var(Vector3f &vel_var)
{
vel_var(0) = P[3][3];
vel_var(1) = P[4][4];
vel_var(2) = P[5][5];
}
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void Ekf::predictCovariance()
{
// 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 dax = _imu_sample_delayed.delta_ang(0);
float day = _imu_sample_delayed.delta_ang(1);
float daz = _imu_sample_delayed.delta_ang(2);
float dvx = _imu_sample_delayed.delta_vel(0);
float dvy = _imu_sample_delayed.delta_vel(1);
float dvz = _imu_sample_delayed.delta_vel(2);
float dax_b = _state.gyro_bias(0);
float day_b = _state.gyro_bias(1);
float daz_b = _state.gyro_bias(2);
float dax_s = _state.gyro_scale(0);
float day_s = _state.gyro_scale(1);
float daz_s = _state.gyro_scale(2);
float dvz_b = _state.accel_z_bias;
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float dt = _imu_sample_delayed.delta_vel_dt;
// compute process noise
float process_noise[_k_num_states] = {};
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float d_ang_bias_sig = dt * math::constrain(_params.gyro_bias_p_noise, 0.0f, 1e-4f);
float d_vel_bias_sig = dt * math::constrain(_params.accel_bias_p_noise, 0.0f, 1e-2f);
float d_ang_scale_sig = dt * math::constrain(_params.gyro_scale_p_noise, 0.0f, 1e-2f);
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float mag_I_sig, mag_B_sig;
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// Don't continue to grow the earth field variances if they are becoming too large or we are not doing 3-axis fusion as this can make the covariance matrix badly conditioned
EKF: Improve variance limiting for stationary states Turn off the process noise if they grow too large and use the hard variance limit as a backup. This is numerically more stable than relying on a hard variance limit which does not deal with the covariances.
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if (_control_status.flags.mag_3D && (P[16][16] + P[17][17] + P[18][8]) < 0.1f) {
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mag_I_sig = dt * math::constrain(_params.mage_p_noise, 0.0f, 1e-1f);
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} else {
mag_I_sig = 0.0f;
}
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// Don't continue to grow the body field variances if they is becoming too large or we are not doing 3-axis fusion as this can make the covariance matrix badly conditioned
EKF: Improve variance limiting for stationary states Turn off the process noise if they grow too large and use the hard variance limit as a backup. This is numerically more stable than relying on a hard variance limit which does not deal with the covariances.
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if (_control_status.flags.mag_3D && (P[19][19] + P[20][20] + P[21][21]) < 0.1f) {
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mag_B_sig = dt * math::constrain(_params.magb_p_noise, 0.0f, 1e-1f);
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} else {
mag_B_sig = 0.0f;
}
float wind_vel_sig;
// Don't continue to grow wind velocity state variances if they are becoming too large or we are not using wind velocity states as this can make the covariance matrix badly conditioned
if (_control_status.flags.wind && (P[22][22] + P[22][22]) < 1000.0f) {
wind_vel_sig = dt * math::constrain(_params.wind_vel_p_noise, 0.0f, 1.0f);
} else {
wind_vel_sig = 0.0f;
}
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for (unsigned i = 0; i < 9; i++) {
process_noise[i] = 0.0f;
}
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for (unsigned i = 9; i < 12; i++) {
process_noise[i] = sq(d_ang_bias_sig);
}
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for (unsigned i = 12; i < 15; i++) {
process_noise[i] = sq(d_ang_scale_sig);
}
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process_noise[15] = sq(d_vel_bias_sig);
for (unsigned i = 16; i < 19; i++) {
process_noise[i] = sq(mag_I_sig);
}
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for (unsigned i = 19; i < 22; i++) {
process_noise[i] = sq(mag_B_sig);
}
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for (unsigned i = 22; i < 24; i++) {
process_noise[i] = sq(wind_vel_sig);
}
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// assign input noise
// inputs to the system are 3 delta angles and 3 delta velocities
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float daxNoise, dayNoise, dazNoise;
float dvxNoise, dvyNoise, dvzNoise;
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float gyro_noise = math::constrain(_params.gyro_noise, 1e-4f, 1e-1f);
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daxNoise = dayNoise = dazNoise = dt * gyro_noise;
float accel_noise = math::constrain(_params.accel_noise, 1e-2f, 1.0f);
dvxNoise = dvyNoise = dvzNoise = dt * accel_noise;
// predict covarinace matrix
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// intermediate calculations
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float SF[25] = {};
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SF[0] = daz_b / 2 + dazNoise / 2 - (daz * daz_s) / 2;
SF[1] = day_b / 2 + dayNoise / 2 - (day * day_s) / 2;
SF[2] = dax_b / 2 + daxNoise / 2 - (dax * dax_s) / 2;
SF[3] = q3 / 2 - (q0 * SF[0]) / 2 + (q1 * SF[1]) / 2 - (q2 * SF[2]) / 2;
SF[4] = q0 / 2 - (q1 * SF[2]) / 2 - (q2 * SF[1]) / 2 + (q3 * SF[0]) / 2;
SF[5] = q1 / 2 + (q0 * SF[2]) / 2 - (q2 * SF[0]) / 2 - (q3 * SF[1]) / 2;
SF[6] = q3 / 2 + (q0 * SF[0]) / 2 - (q1 * SF[1]) / 2 - (q2 * SF[2]) / 2;
SF[7] = q0 / 2 - (q1 * SF[2]) / 2 + (q2 * SF[1]) / 2 - (q3 * SF[0]) / 2;
SF[8] = q0 / 2 + (q1 * SF[2]) / 2 - (q2 * SF[1]) / 2 - (q3 * SF[0]) / 2;
SF[9] = q2 / 2 + (q0 * SF[1]) / 2 + (q1 * SF[0]) / 2 + (q3 * SF[2]) / 2;
SF[10] = q2 / 2 - (q0 * SF[1]) / 2 - (q1 * SF[0]) / 2 + (q3 * SF[2]) / 2;
SF[11] = q2 / 2 + (q0 * SF[1]) / 2 - (q1 * SF[0]) / 2 - (q3 * SF[2]) / 2;
SF[12] = q1 / 2 + (q0 * SF[2]) / 2 + (q2 * SF[0]) / 2 + (q3 * SF[1]) / 2;
SF[13] = q1 / 2 - (q0 * SF[2]) / 2 + (q2 * SF[0]) / 2 - (q3 * SF[1]) / 2;
SF[14] = q3 / 2 + (q0 * SF[0]) / 2 + (q1 * SF[1]) / 2 + (q2 * SF[2]) / 2;
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SF[15] = - sq(q0) - sq(q1) - sq(q2) - sq(q3);
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SF[16] = dvz_b - dvz + dvzNoise;
SF[17] = dvx - dvxNoise;
SF[18] = dvy - dvyNoise;
SF[19] = sq(q2);
SF[20] = SF[19] - sq(q0) + sq(q1) - sq(q3);
SF[21] = SF[19] + sq(q0) - sq(q1) - sq(q3);
SF[22] = 2 * q0 * q1 - 2 * q2 * q3;
SF[23] = SF[19] - sq(q0) - sq(q1) + sq(q3);
SF[24] = 2 * q1 * q2;
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float SG[5] = {};
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SG[0] = - sq(q0) - sq(q1) - sq(q2) - sq(q3);
SG[1] = sq(q3);
SG[2] = sq(q2);
SG[3] = sq(q1);
SG[4] = sq(q0);
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float SQ[10] = {};
SQ[0] = - sq(dvyNoise)*(2*q0*q1 + 2*q2*q3)*(SG[1] - SG[2] + SG[3] - SG[4]) - sq(dvzNoise)*(2*q0*q1 - 2*q2*q3)*(SG[1] - SG[2] - SG[3] + SG[4]) - sq(dvxNoise)*(2*q0*q2 - 2*q1*q3)*(2*q0*q3 + 2*q1*q2);
SQ[1] = sq(dvxNoise)*(2*q0*q2 - 2*q1*q3)*(SG[1] + SG[2] - SG[3] - SG[4]) + sq(dvzNoise)*(2*q0*q2 + 2*q1*q3)*(SG[1] - SG[2] - SG[3] + SG[4]) - sq(dvyNoise)*(2*q0*q1 + 2*q2*q3)*(2*q0*q3 - 2*q1*q2);
SQ[2] = sq(dvyNoise)*(2*q0*q3 - 2*q1*q2)*(SG[1] - SG[2] + SG[3] - SG[4]) - sq(dvxNoise)*(2*q0*q3 + 2*q1*q2)*(SG[1] + SG[2] - SG[3] - SG[4]) - sq(dvzNoise)*(2*q0*q1 - 2*q2*q3)*(2*q0*q2 + 2*q1*q3);
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SQ[3] = sq(SG[0]);
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SQ[4] = sq(dvyNoise);
SQ[5] = sq(dvzNoise);
SQ[6] = sq(dvxNoise);
SQ[7] = 2*q2*q3;
SQ[8] = 2*q1*q3;
SQ[9] = 2*q1*q2;
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float SPP[23] = {};
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SPP[0] = SF[17]*(2*q0*q1 + 2*q2*q3) + SF[18]*(2*q0*q2 - 2*q1*q3);
SPP[1] = SF[18]*(2*q0*q2 + 2*q1*q3) + SF[16]*(SF[24] - 2*q0*q3);
SPP[2] = 2*q3*SF[8] + 2*q1*SF[11] - 2*q0*SF[14] - 2*q2*SF[13];
SPP[3] = 2*q1*SF[7] + 2*q2*SF[6] - 2*q0*SF[12] - 2*q3*SF[10];
SPP[4] = 2*q0*SF[6] - 2*q3*SF[7] - 2*q1*SF[10] + 2*q2*SF[12];
SPP[5] = 2*q0*SF[8] + 2*q2*SF[11] + 2*q1*SF[13] + 2*q3*SF[14];
SPP[6] = 2*q0*SF[7] + 2*q3*SF[6] + 2*q2*SF[10] + 2*q1*SF[12];
SPP[7] = 2*q1*SF[3] - 2*q2*SF[4] - 2*q3*SF[5] + 2*q0*SF[9];
SPP[8] = 2*q0*SF[5] - 2*q1*SF[4] - 2*q2*SF[3] + 2*q3*SF[9];
SPP[9] = SF[18]*SF[20] - SF[16]*(2*q0*q1 + 2*q2*q3);
SPP[10] = SF[17]*SF[20] + SF[16]*(2*q0*q2 - 2*q1*q3);
SPP[11] = SF[17]*SF[21] - SF[18]*(SF[24] + 2*q0*q3);
SPP[12] = SF[17]*SF[22] - SF[16]*(SF[24] + 2*q0*q3);
SPP[13] = 2*q0*SF[4] + 2*q1*SF[5] + 2*q3*SF[3] + 2*q2*SF[9];
SPP[14] = 2*q2*SF[8] - 2*q0*SF[11] - 2*q1*SF[14] + 2*q3*SF[13];
SPP[15] = SF[18]*SF[23] + SF[17]*(SF[24] - 2*q0*q3);
SPP[16] = daz*SF[19] + daz*sq(q0) + daz*sq(q1) + daz*sq(q3);
SPP[17] = day*SF[19] + day*sq(q0) + day*sq(q1) + day*sq(q3);
SPP[18] = dax*SF[19] + dax*sq(q0) + dax*sq(q1) + dax*sq(q3);
SPP[19] = SF[16]*SF[23] - SF[17]*(2*q0*q2 + 2*q1*q3);
SPP[20] = SF[16]*SF[21] - SF[18]*SF[22];
SPP[21] = 2*q0*q2 + 2*q1*q3;
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SPP[22] = SF[15];
// covariance update
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float nextP[24][24] = {};
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nextP[0][0] = SPP[5]*(P[0][0]*SPP[5] - P[1][0]*SPP[4] + P[2][0]*SPP[7] + P[9][0]*SPP[22] + P[12][0]*SPP[18]) - SPP[4]*(P[0][1]*SPP[5] - P[1][1]*SPP[4] + P[2][1]*SPP[7] + P[9][1]*SPP[22] + P[12][1]*SPP[18]) + SPP[7]*(P[0][2]*SPP[5] - P[1][2]*SPP[4] + P[2][2]*SPP[7] + P[9][2]*SPP[22] + P[12][2]*SPP[18]) + SPP[22]*(P[0][9]*SPP[5] - P[1][9]*SPP[4] + P[2][9]*SPP[7] + P[9][9]*SPP[22] + P[12][9]*SPP[18]) + SPP[18]*(P[0][12]*SPP[5] - P[1][12]*SPP[4] + P[2][12]*SPP[7] + P[9][12]*SPP[22] + P[12][12]*SPP[18]) + sq(daxNoise)*SQ[3];
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nextP[0][1] = SPP[6] * (P[0][1] * SPP[5] - P[1][1] * SPP[4] + P[2][1] * SPP[7] + P[9][1] * SPP[22] + P[12][1] * SPP[18])
- SPP[2] * (P[0][0] * SPP[5] - P[1][0] * SPP[4] + P[2][0] * SPP[7] + P[9][0] * SPP[22] + P[12][0] * SPP[18]) -
SPP[8] * (P[0][2] * SPP[5] - P[1][2] * SPP[4] + P[2][2] * SPP[7] + P[9][2] * SPP[22] + P[12][2] * SPP[18]) + SPP[22] *
(P[0][10] * SPP[5] - P[1][10] * SPP[4] + P[2][10] * SPP[7] + P[9][10] * SPP[22] + P[12][10] * SPP[18]) + SPP[17] *
(P[0][13] * SPP[5] - P[1][13] * SPP[4] + P[2][13] * SPP[7] + P[9][13] * SPP[22] + P[12][13] * SPP[18]);
EKF: Apply covariance prediction derivation changes
2016-04-01 21:45:22 -03:00
nextP[1][1] = SPP[6]*(P[1][1]*SPP[6] - P[0][1]*SPP[2] - P[2][1]*SPP[8] + P[10][1]*SPP[22] + P[13][1]*SPP[17]) - SPP[2]*(P[1][0]*SPP[6] - P[0][0]*SPP[2] - P[2][0]*SPP[8] + P[10][0]*SPP[22] + P[13][0]*SPP[17]) - SPP[8]*(P[1][2]*SPP[6] - P[0][2]*SPP[2] - P[2][2]*SPP[8] + P[10][2]*SPP[22] + P[13][2]*SPP[17]) + SPP[22]*(P[1][10]*SPP[6] - P[0][10]*SPP[2] - P[2][10]*SPP[8] + P[10][10]*SPP[22] + P[13][10]*SPP[17]) + SPP[17]*(P[1][13]*SPP[6] - P[0][13]*SPP[2] - P[2][13]*SPP[8] + P[10][13]*SPP[22] + P[13][13]*SPP[17]) + sq(dayNoise)*SQ[3];
added file with covariance calculations
2015-12-06 07:18:05 -04:00
nextP[0][2] = SPP[14] * (P[0][0] * SPP[5] - P[1][0] * SPP[4] + P[2][0] * SPP[7] + P[9][0] * SPP[22] + P[12][0] *
SPP[18]) - SPP[3] * (P[0][1] * SPP[5] - P[1][1] * SPP[4] + P[2][1] * SPP[7] + P[9][1] * SPP[22] + P[12][1] * SPP[18]) +
SPP[13] * (P[0][2] * SPP[5] - P[1][2] * SPP[4] + P[2][2] * SPP[7] + P[9][2] * SPP[22] + P[12][2] * SPP[18]) +
SPP[22] * (P[0][11] * SPP[5] - P[1][11] * SPP[4] + P[2][11] * SPP[7] + P[9][11] * SPP[22] + P[12][11] * SPP[18]) +
SPP[16] * (P[0][14] * SPP[5] - P[1][14] * SPP[4] + P[2][14] * SPP[7] + P[9][14] * SPP[22] + P[12][14] * SPP[18]);
nextP[1][2] = SPP[14] * (P[1][0] * SPP[6] - P[0][0] * SPP[2] - P[2][0] * SPP[8] + P[10][0] * SPP[22] + P[13][0] *
SPP[17]) - SPP[3] * (P[1][1] * SPP[6] - P[0][1] * SPP[2] - P[2][1] * SPP[8] + P[10][1] * SPP[22] + P[13][1] * SPP[17]) +
SPP[13] * (P[1][2] * SPP[6] - P[0][2] * SPP[2] - P[2][2] * SPP[8] + P[10][2] * SPP[22] + P[13][2] * SPP[17]) +
SPP[22] * (P[1][11] * SPP[6] - P[0][11] * SPP[2] - P[2][11] * SPP[8] + P[10][11] * SPP[22] + P[13][11] * SPP[17]) +
SPP[16] * (P[1][14] * SPP[6] - P[0][14] * SPP[2] - P[2][14] * SPP[8] + P[10][14] * SPP[22] + P[13][14] * SPP[17]);
EKF: Apply covariance prediction derivation changes
2016-04-01 21:45:22 -03:00
nextP[2][2] = SPP[14]*(P[0][0]*SPP[14] - P[1][0]*SPP[3] + P[2][0]*SPP[13] + P[11][0]*SPP[22] + P[14][0]*SPP[16]) - SPP[3]*(P[0][1]*SPP[14] - P[1][1]*SPP[3] + P[2][1]*SPP[13] + P[11][1]*SPP[22] + P[14][1]*SPP[16]) + SPP[13]*(P[0][2]*SPP[14] - P[1][2]*SPP[3] + P[2][2]*SPP[13] + P[11][2]*SPP[22] + P[14][2]*SPP[16]) + SPP[22]*(P[0][11]*SPP[14] - P[1][11]*SPP[3] + P[2][11]*SPP[13] + P[11][11]*SPP[22] + P[14][11]*SPP[16]) + SPP[16]*(P[0][14]*SPP[14] - P[1][14]*SPP[3] + P[2][14]*SPP[13] + P[11][14]*SPP[22] + P[14][14]*SPP[16]) + sq(dazNoise)*SQ[3];
added file with covariance calculations
2015-12-06 07:18:05 -04:00
nextP[0][3] = P[0][3] * SPP[5] - P[1][3] * SPP[4] + P[2][3] * SPP[7] + P[9][3] * SPP[22] + P[12][3] * SPP[18] +
SPP[1] * (P[0][0] * SPP[5] - P[1][0] * SPP[4] + P[2][0] * SPP[7] + P[9][0] * SPP[22] + P[12][0] * SPP[18]) + SPP[19] *
(P[0][1] * SPP[5] - P[1][1] * SPP[4] + P[2][1] * SPP[7] + P[9][1] * SPP[22] + P[12][1] * SPP[18]) + SPP[15] *
(P[0][2] * SPP[5] - P[1][2] * SPP[4] + P[2][2] * SPP[7] + P[9][2] * SPP[22] + P[12][2] * SPP[18]) - SPP[21] *
(P[0][15] * SPP[5] - P[1][15] * SPP[4] + P[2][15] * SPP[7] + P[9][15] * SPP[22] + P[12][15] * SPP[18]);
nextP[1][3] = P[1][3] * SPP[6] - P[0][3] * SPP[2] - P[2][3] * SPP[8] + P[10][3] * SPP[22] + P[13][3] * SPP[17] +
SPP[1] * (P[1][0] * SPP[6] - P[0][0] * SPP[2] - P[2][0] * SPP[8] + P[10][0] * SPP[22] + P[13][0] * SPP[17]) +
SPP[19] * (P[1][1] * SPP[6] - P[0][1] * SPP[2] - P[2][1] * SPP[8] + P[10][1] * SPP[22] + P[13][1] * SPP[17]) +
SPP[15] * (P[1][2] * SPP[6] - P[0][2] * SPP[2] - P[2][2] * SPP[8] + P[10][2] * SPP[22] + P[13][2] * SPP[17]) -
SPP[21] * (P[1][15] * SPP[6] - P[0][15] * SPP[2] - P[2][15] * SPP[8] + P[10][15] * SPP[22] + P[13][15] * SPP[17]);
nextP[2][3] = P[0][3] * SPP[14] - P[1][3] * SPP[3] + P[2][3] * SPP[13] + P[11][3] * SPP[22] + P[14][3] * SPP[16] +
SPP[1] * (P[0][0] * SPP[14] - P[1][0] * SPP[3] + P[2][0] * SPP[13] + P[11][0] * SPP[22] + P[14][0] * SPP[16]) +
SPP[19] * (P[0][1] * SPP[14] - P[1][1] * SPP[3] + P[2][1] * SPP[13] + P[11][1] * SPP[22] + P[14][1] * SPP[16]) +
SPP[15] * (P[0][2] * SPP[14] - P[1][2] * SPP[3] + P[2][2] * SPP[13] + P[11][2] * SPP[22] + P[14][2] * SPP[16]) -
SPP[21] * (P[0][15] * SPP[14] - P[1][15] * SPP[3] + P[2][15] * SPP[13] + P[11][15] * SPP[22] + P[14][15] * SPP[16]);
EKF: Apply covariance prediction derivation changes
2016-04-01 21:45:22 -03:00
nextP[3][3] = P[3][3] + P[0][3]*SPP[1] + P[1][3]*SPP[19] + P[2][3]*SPP[15] - P[15][3]*SPP[21] + SQ[5]*sq(SQ[8] + 2*q0*q2) + SQ[4]*sq(SQ[9] - 2*q0*q3) + SPP[1]*(P[3][0] + P[0][0]*SPP[1] + P[1][0]*SPP[19] + P[2][0]*SPP[15] - P[15][0]*SPP[21]) + SPP[19]*(P[3][1] + P[0][1]*SPP[1] + P[1][1]*SPP[19] + P[2][1]*SPP[15] - P[15][1]*SPP[21]) + SPP[15]*(P[3][2] + P[0][2]*SPP[1] + P[1][2]*SPP[19] + P[2][2]*SPP[15] - P[15][2]*SPP[21]) - SPP[21]*(P[3][15] + P[0][15]*SPP[1] + P[1][15]*SPP[19] + P[2][15]*SPP[15] - P[15][15]*SPP[21]) + SQ[6]*sq(SG[1] + SG[2] - SG[3] - SG[4]);
added file with covariance calculations
2015-12-06 07:18:05 -04:00
nextP[0][4] = P[0][4] * SPP[5] - P[1][4] * SPP[4] + P[2][4] * SPP[7] + P[9][4] * SPP[22] + P[12][4] * SPP[18] +
SF[22] * (P[0][15] * SPP[5] - P[1][15] * SPP[4] + P[2][15] * SPP[7] + P[9][15] * SPP[22] + P[12][15] * SPP[18]) +
SPP[12] * (P[0][1] * SPP[5] - P[1][1] * SPP[4] + P[2][1] * SPP[7] + P[9][1] * SPP[22] + P[12][1] * SPP[18]) +
SPP[20] * (P[0][0] * SPP[5] - P[1][0] * SPP[4] + P[2][0] * SPP[7] + P[9][0] * SPP[22] + P[12][0] * SPP[18]) +
SPP[11] * (P[0][2] * SPP[5] - P[1][2] * SPP[4] + P[2][2] * SPP[7] + P[9][2] * SPP[22] + P[12][2] * SPP[18]);
nextP[1][4] = P[1][4] * SPP[6] - P[0][4] * SPP[2] - P[2][4] * SPP[8] + P[10][4] * SPP[22] + P[13][4] * SPP[17] +
SF[22] * (P[1][15] * SPP[6] - P[0][15] * SPP[2] - P[2][15] * SPP[8] + P[10][15] * SPP[22] + P[13][15] * SPP[17]) +
SPP[12] * (P[1][1] * SPP[6] - P[0][1] * SPP[2] - P[2][1] * SPP[8] + P[10][1] * SPP[22] + P[13][1] * SPP[17]) +
SPP[20] * (P[1][0] * SPP[6] - P[0][0] * SPP[2] - P[2][0] * SPP[8] + P[10][0] * SPP[22] + P[13][0] * SPP[17]) +
SPP[11] * (P[1][2] * SPP[6] - P[0][2] * SPP[2] - P[2][2] * SPP[8] + P[10][2] * SPP[22] + P[13][2] * SPP[17]);
nextP[2][4] = P[0][4] * SPP[14] - P[1][4] * SPP[3] + P[2][4] * SPP[13] + P[11][4] * SPP[22] + P[14][4] * SPP[16] +
SF[22] * (P[0][15] * SPP[14] - P[1][15] * SPP[3] + P[2][15] * SPP[13] + P[11][15] * SPP[22] + P[14][15] * SPP[16]) +
SPP[12] * (P[0][1] * SPP[14] - P[1][1] * SPP[3] + P[2][1] * SPP[13] + P[11][1] * SPP[22] + P[14][1] * SPP[16]) +
SPP[20] * (P[0][0] * SPP[14] - P[1][0] * SPP[3] + P[2][0] * SPP[13] + P[11][0] * SPP[22] + P[14][0] * SPP[16]) +
SPP[11] * (P[0][2] * SPP[14] - P[1][2] * SPP[3] + P[2][2] * SPP[13] + P[11][2] * SPP[22] + P[14][2] * SPP[16]);
nextP[3][4] = P[3][4] + SQ[2] + P[0][4] * SPP[1] + P[1][4] * SPP[19] + P[2][4] * SPP[15] - P[15][4] * SPP[21] +
SF[22] * (P[3][15] + P[0][15] * SPP[1] + P[1][15] * SPP[19] + P[2][15] * SPP[15] - P[15][15] * SPP[21]) + SPP[12] *
(P[3][1] + P[0][1] * SPP[1] + P[1][1] * SPP[19] + P[2][1] * SPP[15] - P[15][1] * SPP[21]) + SPP[20] *
(P[3][0] + P[0][0] * SPP[1] + P[1][0] * SPP[19] + P[2][0] * SPP[15] - P[15][0] * SPP[21]) + SPP[11] *
(P[3][2] + P[0][2] * SPP[1] + P[1][2] * SPP[19] + P[2][2] * SPP[15] - P[15][2] * SPP[21]);
EKF: Apply covariance prediction derivation changes
2016-04-01 21:45:22 -03:00
nextP[4][4] = P[4][4] + P[15][4]*SF[22] + P[0][4]*SPP[20] + P[1][4]*SPP[12] + P[2][4]*SPP[11] + SQ[5]*sq(SQ[7] - 2*q0*q1) + SQ[6]*sq(SQ[9] + 2*q0*q3) + SF[22]*(P[4][15] + P[15][15]*SF[22] + P[0][15]*SPP[20] + P[1][15]*SPP[12] + P[2][15]*SPP[11]) + SPP[12]*(P[4][1] + P[15][1]*SF[22] + P[0][1]*SPP[20] + P[1][1]*SPP[12] + P[2][1]*SPP[11]) + SPP[20]*(P[4][0] + P[15][0]*SF[22] + P[0][0]*SPP[20] + P[1][0]*SPP[12] + P[2][0]*SPP[11]) + SPP[11]*(P[4][2] + P[15][2]*SF[22] + P[0][2]*SPP[20] + P[1][2]*SPP[12] + P[2][2]*SPP[11]) + SQ[4]*sq(SG[1] - SG[2] + SG[3] - SG[4]);
added file with covariance calculations
2015-12-06 07:18:05 -04:00
nextP[0][5] = P[0][5] * SPP[5] - P[1][5] * SPP[4] + P[2][5] * SPP[7] + P[9][5] * SPP[22] + P[12][5] * SPP[18] +
SF[20] * (P[0][15] * SPP[5] - P[1][15] * SPP[4] + P[2][15] * SPP[7] + P[9][15] * SPP[22] + P[12][15] * SPP[18]) -
SPP[9] * (P[0][0] * SPP[5] - P[1][0] * SPP[4] + P[2][0] * SPP[7] + P[9][0] * SPP[22] + P[12][0] * SPP[18]) + SPP[0] *
(P[0][2] * SPP[5] - P[1][2] * SPP[4] + P[2][2] * SPP[7] + P[9][2] * SPP[22] + P[12][2] * SPP[18]) + SPP[10] *
(P[0][1] * SPP[5] - P[1][1] * SPP[4] + P[2][1] * SPP[7] + P[9][1] * SPP[22] + P[12][1] * SPP[18]);
nextP[1][5] = P[1][5] * SPP[6] - P[0][5] * SPP[2] - P[2][5] * SPP[8] + P[10][5] * SPP[22] + P[13][5] * SPP[17] +
SF[20] * (P[1][15] * SPP[6] - P[0][15] * SPP[2] - P[2][15] * SPP[8] + P[10][15] * SPP[22] + P[13][15] * SPP[17]) -
SPP[9] * (P[1][0] * SPP[6] - P[0][0] * SPP[2] - P[2][0] * SPP[8] + P[10][0] * SPP[22] + P[13][0] * SPP[17]) + SPP[0] *
(P[1][2] * SPP[6] - P[0][2] * SPP[2] - P[2][2] * SPP[8] + P[10][2] * SPP[22] + P[13][2] * SPP[17]) + SPP[10] *
(P[1][1] * SPP[6] - P[0][1] * SPP[2] - P[2][1] * SPP[8] + P[10][1] * SPP[22] + P[13][1] * SPP[17]);
nextP[2][5] = P[0][5] * SPP[14] - P[1][5] * SPP[3] + P[2][5] * SPP[13] + P[11][5] * SPP[22] + P[14][5] * SPP[16] +
SF[20] * (P[0][15] * SPP[14] - P[1][15] * SPP[3] + P[2][15] * SPP[13] + P[11][15] * SPP[22] + P[14][15] * SPP[16]) -
SPP[9] * (P[0][0] * SPP[14] - P[1][0] * SPP[3] + P[2][0] * SPP[13] + P[11][0] * SPP[22] + P[14][0] * SPP[16]) +
SPP[0] * (P[0][2] * SPP[14] - P[1][2] * SPP[3] + P[2][2] * SPP[13] + P[11][2] * SPP[22] + P[14][2] * SPP[16]) +
SPP[10] * (P[0][1] * SPP[14] - P[1][1] * SPP[3] + P[2][1] * SPP[13] + P[11][1] * SPP[22] + P[14][1] * SPP[16]);
nextP[3][5] = P[3][5] + SQ[1] + P[0][5] * SPP[1] + P[1][5] * SPP[19] + P[2][5] * SPP[15] - P[15][5] * SPP[21] +
SF[20] * (P[3][15] + P[0][15] * SPP[1] + P[1][15] * SPP[19] + P[2][15] * SPP[15] - P[15][15] * SPP[21]) - SPP[9] *
(P[3][0] + P[0][0] * SPP[1] + P[1][0] * SPP[19] + P[2][0] * SPP[15] - P[15][0] * SPP[21]) + SPP[0] *
(P[3][2] + P[0][2] * SPP[1] + P[1][2] * SPP[19] + P[2][2] * SPP[15] - P[15][2] * SPP[21]) + SPP[10] *
(P[3][1] + P[0][1] * SPP[1] + P[1][1] * SPP[19] + P[2][1] * SPP[15] - P[15][1] * SPP[21]);
nextP[4][5] = P[4][5] + SQ[0] + P[15][5] * SF[22] + P[0][5] * SPP[20] + P[1][5] * SPP[12] + P[2][5] * SPP[11] +
SF[20] * (P[4][15] + P[15][15] * SF[22] + P[0][15] * SPP[20] + P[1][15] * SPP[12] + P[2][15] * SPP[11]) - SPP[9] *
(P[4][0] + P[15][0] * SF[22] + P[0][0] * SPP[20] + P[1][0] * SPP[12] + P[2][0] * SPP[11]) + SPP[0] *
(P[4][2] + P[15][2] * SF[22] + P[0][2] * SPP[20] + P[1][2] * SPP[12] + P[2][2] * SPP[11]) + SPP[10] *
(P[4][1] + P[15][1] * SF[22] + P[0][1] * SPP[20] + P[1][1] * SPP[12] + P[2][1] * SPP[11]);
EKF: Apply covariance prediction derivation changes
2016-04-01 21:45:22 -03:00
nextP[5][5] = P[5][5] + P[15][5]*SF[20] - P[0][5]*SPP[9] + P[1][5]*SPP[10] + P[2][5]*SPP[0] + SQ[4]*sq(SQ[7] + 2*q0*q1) + SQ[6]*sq(SQ[8] - 2*q0*q2) + SF[20]*(P[5][15] + P[15][15]*SF[20] - P[0][15]*SPP[9] + P[1][15]*SPP[10] + P[2][15]*SPP[0]) - SPP[9]*(P[5][0] + P[15][0]*SF[20] - P[0][0]*SPP[9] + P[1][0]*SPP[10] + P[2][0]*SPP[0]) + SPP[0]*(P[5][2] + P[15][2]*SF[20] - P[0][2]*SPP[9] + P[1][2]*SPP[10] + P[2][2]*SPP[0]) + SPP[10]*(P[5][1] + P[15][1]*SF[20] - P[0][1]*SPP[9] + P[1][1]*SPP[10] + P[2][1]*SPP[0]) + SQ[5]*sq(SG[1] - SG[2] - SG[3] + SG[4]);
added file with covariance calculations
2015-12-06 07:18:05 -04:00
nextP[0][6] = P[0][6] * SPP[5] - P[1][6] * SPP[4] + P[2][6] * SPP[7] + P[9][6] * SPP[22] + P[12][6] * SPP[18] + dt *
(P[0][3] * SPP[5] - P[1][3] * SPP[4] + P[2][3] * SPP[7] + P[9][3] * SPP[22] + P[12][3] * SPP[18]);
nextP[1][6] = P[1][6] * SPP[6] - P[0][6] * SPP[2] - P[2][6] * SPP[8] + P[10][6] * SPP[22] + P[13][6] * SPP[17] + dt *
(P[1][3] * SPP[6] - P[0][3] * SPP[2] - P[2][3] * SPP[8] + P[10][3] * SPP[22] + P[13][3] * SPP[17]);
nextP[2][6] = P[0][6] * SPP[14] - P[1][6] * SPP[3] + P[2][6] * SPP[13] + P[11][6] * SPP[22] + P[14][6] * SPP[16] +
dt * (P[0][3] * SPP[14] - P[1][3] * SPP[3] + P[2][3] * SPP[13] + P[11][3] * SPP[22] + P[14][3] * SPP[16]);
nextP[3][6] = P[3][6] + P[0][6] * SPP[1] + P[1][6] * SPP[19] + P[2][6] * SPP[15] - P[15][6] * SPP[21] + dt *
(P[3][3] + P[0][3] * SPP[1] + P[1][3] * SPP[19] + P[2][3] * SPP[15] - P[15][3] * SPP[21]);
nextP[4][6] = P[4][6] + P[15][6] * SF[22] + P[0][6] * SPP[20] + P[1][6] * SPP[12] + P[2][6] * SPP[11] + dt *
(P[4][3] + P[15][3] * SF[22] + P[0][3] * SPP[20] + P[1][3] * SPP[12] + P[2][3] * SPP[11]);
nextP[5][6] = P[5][6] + P[15][6] * SF[20] - P[0][6] * SPP[9] + P[1][6] * SPP[10] + P[2][6] * SPP[0] + dt *
(P[5][3] + P[15][3] * SF[20] - P[0][3] * SPP[9] + P[1][3] * SPP[10] + P[2][3] * SPP[0]);
nextP[6][6] = P[6][6] + P[3][6] * dt + dt * (P[6][3] + P[3][3] * dt);
nextP[0][7] = P[0][7] * SPP[5] - P[1][7] * SPP[4] + P[2][7] * SPP[7] + P[9][7] * SPP[22] + P[12][7] * SPP[18] + dt *
(P[0][4] * SPP[5] - P[1][4] * SPP[4] + P[2][4] * SPP[7] + P[9][4] * SPP[22] + P[12][4] * SPP[18]);
nextP[1][7] = P[1][7] * SPP[6] - P[0][7] * SPP[2] - P[2][7] * SPP[8] + P[10][7] * SPP[22] + P[13][7] * SPP[17] + dt *
(P[1][4] * SPP[6] - P[0][4] * SPP[2] - P[2][4] * SPP[8] + P[10][4] * SPP[22] + P[13][4] * SPP[17]);
nextP[2][7] = P[0][7] * SPP[14] - P[1][7] * SPP[3] + P[2][7] * SPP[13] + P[11][7] * SPP[22] + P[14][7] * SPP[16] +
dt * (P[0][4] * SPP[14] - P[1][4] * SPP[3] + P[2][4] * SPP[13] + P[11][4] * SPP[22] + P[14][4] * SPP[16]);
nextP[3][7] = P[3][7] + P[0][7] * SPP[1] + P[1][7] * SPP[19] + P[2][7] * SPP[15] - P[15][7] * SPP[21] + dt *
(P[3][4] + P[0][4] * SPP[1] + P[1][4] * SPP[19] + P[2][4] * SPP[15] - P[15][4] * SPP[21]);
nextP[4][7] = P[4][7] + P[15][7] * SF[22] + P[0][7] * SPP[20] + P[1][7] * SPP[12] + P[2][7] * SPP[11] + dt *
(P[4][4] + P[15][4] * SF[22] + P[0][4] * SPP[20] + P[1][4] * SPP[12] + P[2][4] * SPP[11]);
nextP[5][7] = P[5][7] + P[15][7] * SF[20] - P[0][7] * SPP[9] + P[1][7] * SPP[10] + P[2][7] * SPP[0] + dt *
(P[5][4] + P[15][4] * SF[20] - P[0][4] * SPP[9] + P[1][4] * SPP[10] + P[2][4] * SPP[0]);
nextP[6][7] = P[6][7] + P[3][7] * dt + dt * (P[6][4] + P[3][4] * dt);
nextP[7][7] = P[7][7] + P[4][7] * dt + dt * (P[7][4] + P[4][4] * dt);
nextP[0][8] = P[0][8] * SPP[5] - P[1][8] * SPP[4] + P[2][8] * SPP[7] + P[9][8] * SPP[22] + P[12][8] * SPP[18] + dt *
(P[0][5] * SPP[5] - P[1][5] * SPP[4] + P[2][5] * SPP[7] + P[9][5] * SPP[22] + P[12][5] * SPP[18]);
nextP[1][8] = P[1][8] * SPP[6] - P[0][8] * SPP[2] - P[2][8] * SPP[8] + P[10][8] * SPP[22] + P[13][8] * SPP[17] + dt *
(P[1][5] * SPP[6] - P[0][5] * SPP[2] - P[2][5] * SPP[8] + P[10][5] * SPP[22] + P[13][5] * SPP[17]);
nextP[2][8] = P[0][8] * SPP[14] - P[1][8] * SPP[3] + P[2][8] * SPP[13] + P[11][8] * SPP[22] + P[14][8] * SPP[16] +
dt * (P[0][5] * SPP[14] - P[1][5] * SPP[3] + P[2][5] * SPP[13] + P[11][5] * SPP[22] + P[14][5] * SPP[16]);
nextP[3][8] = P[3][8] + P[0][8] * SPP[1] + P[1][8] * SPP[19] + P[2][8] * SPP[15] - P[15][8] * SPP[21] + dt *
(P[3][5] + P[0][5] * SPP[1] + P[1][5] * SPP[19] + P[2][5] * SPP[15] - P[15][5] * SPP[21]);
nextP[4][8] = P[4][8] + P[15][8] * SF[22] + P[0][8] * SPP[20] + P[1][8] * SPP[12] + P[2][8] * SPP[11] + dt *
(P[4][5] + P[15][5] * SF[22] + P[0][5] * SPP[20] + P[1][5] * SPP[12] + P[2][5] * SPP[11]);
nextP[5][8] = P[5][8] + P[15][8] * SF[20] - P[0][8] * SPP[9] + P[1][8] * SPP[10] + P[2][8] * SPP[0] + dt *
(P[5][5] + P[15][5] * SF[20] - P[0][5] * SPP[9] + P[1][5] * SPP[10] + P[2][5] * SPP[0]);
nextP[6][8] = P[6][8] + P[3][8] * dt + dt * (P[6][5] + P[3][5] * dt);
nextP[7][8] = P[7][8] + P[4][8] * dt + dt * (P[7][5] + P[4][5] * dt);
nextP[8][8] = P[8][8] + P[5][8] * dt + dt * (P[8][5] + P[5][5] * dt);
nextP[0][9] = P[0][9] * SPP[5] - P[1][9] * SPP[4] + P[2][9] * SPP[7] + P[9][9] * SPP[22] + P[12][9] * SPP[18];
nextP[1][9] = P[1][9] * SPP[6] - P[0][9] * SPP[2] - P[2][9] * SPP[8] + P[10][9] * SPP[22] + P[13][9] * SPP[17];
nextP[2][9] = P[0][9] * SPP[14] - P[1][9] * SPP[3] + P[2][9] * SPP[13] + P[11][9] * SPP[22] + P[14][9] * SPP[16];
nextP[3][9] = P[3][9] + P[0][9] * SPP[1] + P[1][9] * SPP[19] + P[2][9] * SPP[15] - P[15][9] * SPP[21];
nextP[4][9] = P[4][9] + P[15][9] * SF[22] + P[0][9] * SPP[20] + P[1][9] * SPP[12] + P[2][9] * SPP[11];
nextP[5][9] = P[5][9] + P[15][9] * SF[20] - P[0][9] * SPP[9] + P[1][9] * SPP[10] + P[2][9] * SPP[0];
nextP[6][9] = P[6][9] + P[3][9] * dt;
nextP[7][9] = P[7][9] + P[4][9] * dt;
nextP[8][9] = P[8][9] + P[5][9] * dt;
nextP[9][9] = P[9][9];
nextP[0][10] = P[0][10] * SPP[5] - P[1][10] * SPP[4] + P[2][10] * SPP[7] + P[9][10] * SPP[22] + P[12][10] * SPP[18];
nextP[1][10] = P[1][10] * SPP[6] - P[0][10] * SPP[2] - P[2][10] * SPP[8] + P[10][10] * SPP[22] + P[13][10] * SPP[17];
nextP[2][10] = P[0][10] * SPP[14] - P[1][10] * SPP[3] + P[2][10] * SPP[13] + P[11][10] * SPP[22] + P[14][10] * SPP[16];
nextP[3][10] = P[3][10] + P[0][10] * SPP[1] + P[1][10] * SPP[19] + P[2][10] * SPP[15] - P[15][10] * SPP[21];
nextP[4][10] = P[4][10] + P[15][10] * SF[22] + P[0][10] * SPP[20] + P[1][10] * SPP[12] + P[2][10] * SPP[11];
nextP[5][10] = P[5][10] + P[15][10] * SF[20] - P[0][10] * SPP[9] + P[1][10] * SPP[10] + P[2][10] * SPP[0];
nextP[6][10] = P[6][10] + P[3][10] * dt;
nextP[7][10] = P[7][10] + P[4][10] * dt;
nextP[8][10] = P[8][10] + P[5][10] * dt;
nextP[9][10] = P[9][10];
nextP[10][10] = P[10][10];
nextP[0][11] = P[0][11] * SPP[5] - P[1][11] * SPP[4] + P[2][11] * SPP[7] + P[9][11] * SPP[22] + P[12][11] * SPP[18];
nextP[1][11] = P[1][11] * SPP[6] - P[0][11] * SPP[2] - P[2][11] * SPP[8] + P[10][11] * SPP[22] + P[13][11] * SPP[17];
nextP[2][11] = P[0][11] * SPP[14] - P[1][11] * SPP[3] + P[2][11] * SPP[13] + P[11][11] * SPP[22] + P[14][11] * SPP[16];
nextP[3][11] = P[3][11] + P[0][11] * SPP[1] + P[1][11] * SPP[19] + P[2][11] * SPP[15] - P[15][11] * SPP[21];
nextP[4][11] = P[4][11] + P[15][11] * SF[22] + P[0][11] * SPP[20] + P[1][11] * SPP[12] + P[2][11] * SPP[11];
nextP[5][11] = P[5][11] + P[15][11] * SF[20] - P[0][11] * SPP[9] + P[1][11] * SPP[10] + P[2][11] * SPP[0];
nextP[6][11] = P[6][11] + P[3][11] * dt;
nextP[7][11] = P[7][11] + P[4][11] * dt;
nextP[8][11] = P[8][11] + P[5][11] * dt;
nextP[9][11] = P[9][11];
nextP[10][11] = P[10][11];
nextP[11][11] = P[11][11];
nextP[0][12] = P[0][12] * SPP[5] - P[1][12] * SPP[4] + P[2][12] * SPP[7] + P[9][12] * SPP[22] + P[12][12] * SPP[18];
nextP[1][12] = P[1][12] * SPP[6] - P[0][12] * SPP[2] - P[2][12] * SPP[8] + P[10][12] * SPP[22] + P[13][12] * SPP[17];
nextP[2][12] = P[0][12] * SPP[14] - P[1][12] * SPP[3] + P[2][12] * SPP[13] + P[11][12] * SPP[22] + P[14][12] * SPP[16];
nextP[3][12] = P[3][12] + P[0][12] * SPP[1] + P[1][12] * SPP[19] + P[2][12] * SPP[15] - P[15][12] * SPP[21];
nextP[4][12] = P[4][12] + P[15][12] * SF[22] + P[0][12] * SPP[20] + P[1][12] * SPP[12] + P[2][12] * SPP[11];
nextP[5][12] = P[5][12] + P[15][12] * SF[20] - P[0][12] * SPP[9] + P[1][12] * SPP[10] + P[2][12] * SPP[0];
nextP[6][12] = P[6][12] + P[3][12] * dt;
nextP[7][12] = P[7][12] + P[4][12] * dt;
nextP[8][12] = P[8][12] + P[5][12] * dt;
nextP[9][12] = P[9][12];
nextP[10][12] = P[10][12];
nextP[11][12] = P[11][12];
nextP[12][12] = P[12][12];
nextP[0][13] = P[0][13] * SPP[5] - P[1][13] * SPP[4] + P[2][13] * SPP[7] + P[9][13] * SPP[22] + P[12][13] * SPP[18];
nextP[1][13] = P[1][13] * SPP[6] - P[0][13] * SPP[2] - P[2][13] * SPP[8] + P[10][13] * SPP[22] + P[13][13] * SPP[17];
nextP[2][13] = P[0][13] * SPP[14] - P[1][13] * SPP[3] + P[2][13] * SPP[13] + P[11][13] * SPP[22] + P[14][13] * SPP[16];
nextP[3][13] = P[3][13] + P[0][13] * SPP[1] + P[1][13] * SPP[19] + P[2][13] * SPP[15] - P[15][13] * SPP[21];
nextP[4][13] = P[4][13] + P[15][13] * SF[22] + P[0][13] * SPP[20] + P[1][13] * SPP[12] + P[2][13] * SPP[11];
nextP[5][13] = P[5][13] + P[15][13] * SF[20] - P[0][13] * SPP[9] + P[1][13] * SPP[10] + P[2][13] * SPP[0];
nextP[6][13] = P[6][13] + P[3][13] * dt;
nextP[7][13] = P[7][13] + P[4][13] * dt;
nextP[8][13] = P[8][13] + P[5][13] * dt;
nextP[9][13] = P[9][13];
nextP[10][13] = P[10][13];
nextP[11][13] = P[11][13];
nextP[12][13] = P[12][13];
nextP[13][13] = P[13][13];
nextP[0][14] = P[0][14] * SPP[5] - P[1][14] * SPP[4] + P[2][14] * SPP[7] + P[9][14] * SPP[22] + P[12][14] * SPP[18];
nextP[1][14] = P[1][14] * SPP[6] - P[0][14] * SPP[2] - P[2][14] * SPP[8] + P[10][14] * SPP[22] + P[13][14] * SPP[17];
nextP[2][14] = P[0][14] * SPP[14] - P[1][14] * SPP[3] + P[2][14] * SPP[13] + P[11][14] * SPP[22] + P[14][14] * SPP[16];
nextP[3][14] = P[3][14] + P[0][14] * SPP[1] + P[1][14] * SPP[19] + P[2][14] * SPP[15] - P[15][14] * SPP[21];
nextP[4][14] = P[4][14] + P[15][14] * SF[22] + P[0][14] * SPP[20] + P[1][14] * SPP[12] + P[2][14] * SPP[11];
nextP[5][14] = P[5][14] + P[15][14] * SF[20] - P[0][14] * SPP[9] + P[1][14] * SPP[10] + P[2][14] * SPP[0];
nextP[6][14] = P[6][14] + P[3][14] * dt;
nextP[7][14] = P[7][14] + P[4][14] * dt;
nextP[8][14] = P[8][14] + P[5][14] * dt;
nextP[9][14] = P[9][14];
nextP[10][14] = P[10][14];
nextP[11][14] = P[11][14];
nextP[12][14] = P[12][14];
nextP[13][14] = P[13][14];
nextP[14][14] = P[14][14];
nextP[0][15] = P[0][15] * SPP[5] - P[1][15] * SPP[4] + P[2][15] * SPP[7] + P[9][15] * SPP[22] + P[12][15] * SPP[18];
nextP[1][15] = P[1][15] * SPP[6] - P[0][15] * SPP[2] - P[2][15] * SPP[8] + P[10][15] * SPP[22] + P[13][15] * SPP[17];
nextP[2][15] = P[0][15] * SPP[14] - P[1][15] * SPP[3] + P[2][15] * SPP[13] + P[11][15] * SPP[22] + P[14][15] * SPP[16];
nextP[3][15] = P[3][15] + P[0][15] * SPP[1] + P[1][15] * SPP[19] + P[2][15] * SPP[15] - P[15][15] * SPP[21];
nextP[4][15] = P[4][15] + P[15][15] * SF[22] + P[0][15] * SPP[20] + P[1][15] * SPP[12] + P[2][15] * SPP[11];
nextP[5][15] = P[5][15] + P[15][15] * SF[20] - P[0][15] * SPP[9] + P[1][15] * SPP[10] + P[2][15] * SPP[0];
nextP[6][15] = P[6][15] + P[3][15] * dt;
nextP[7][15] = P[7][15] + P[4][15] * dt;
nextP[8][15] = P[8][15] + P[5][15] * dt;
nextP[9][15] = P[9][15];
nextP[10][15] = P[10][15];
nextP[11][15] = P[11][15];
nextP[12][15] = P[12][15];
nextP[13][15] = P[13][15];
nextP[14][15] = P[14][15];
nextP[15][15] = P[15][15];
EKF: Set covariances to zero for un-used states
2016-02-15 20:06:54 -04:00
// Don't do covariance prediction on magnetic field states unless we are using 3-axis fusion
if (_control_status.flags.mag_3D) {
// Check if we have just transitioned into 3-axis fusion and set the state variances
if (!_control_status_prev.flags.mag_3D) {
for (uint8_t index = 16; index <= 21; index++) {
P[index][index] = sq(fmaxf(_params.mag_noise, 0.001f));
}
}
nextP[0][16] = P[0][16] * SPP[5] - P[1][16] * SPP[4] + P[2][16] * SPP[7] + P[9][16] * SPP[22] + P[12][16] * SPP[18];
nextP[1][16] = P[1][16] * SPP[6] - P[0][16] * SPP[2] - P[2][16] * SPP[8] + P[10][16] * SPP[22] + P[13][16] * SPP[17];
nextP[2][16] = P[0][16] * SPP[14] - P[1][16] * SPP[3] + P[2][16] * SPP[13] + P[11][16] * SPP[22] + P[14][16] * SPP[16];
nextP[3][16] = P[3][16] + P[0][16] * SPP[1] + P[1][16] * SPP[19] + P[2][16] * SPP[15] - P[15][16] * SPP[21];
nextP[4][16] = P[4][16] + P[15][16] * SF[22] + P[0][16] * SPP[20] + P[1][16] * SPP[12] + P[2][16] * SPP[11];
nextP[5][16] = P[5][16] + P[15][16] * SF[20] - P[0][16] * SPP[9] + P[1][16] * SPP[10] + P[2][16] * SPP[0];
nextP[6][16] = P[6][16] + P[3][16] * dt;
nextP[7][16] = P[7][16] + P[4][16] * dt;
nextP[8][16] = P[8][16] + P[5][16] * dt;
nextP[9][16] = P[9][16];
nextP[10][16] = P[10][16];
nextP[11][16] = P[11][16];
nextP[12][16] = P[12][16];
nextP[13][16] = P[13][16];
nextP[14][16] = P[14][16];
nextP[15][16] = P[15][16];
nextP[16][16] = P[16][16];
nextP[0][17] = P[0][17] * SPP[5] - P[1][17] * SPP[4] + P[2][17] * SPP[7] + P[9][17] * SPP[22] + P[12][17] * SPP[18];
nextP[1][17] = P[1][17] * SPP[6] - P[0][17] * SPP[2] - P[2][17] * SPP[8] + P[10][17] * SPP[22] + P[13][17] * SPP[17];
nextP[2][17] = P[0][17] * SPP[14] - P[1][17] * SPP[3] + P[2][17] * SPP[13] + P[11][17] * SPP[22] + P[14][17] * SPP[16];
nextP[3][17] = P[3][17] + P[0][17] * SPP[1] + P[1][17] * SPP[19] + P[2][17] * SPP[15] - P[15][17] * SPP[21];
nextP[4][17] = P[4][17] + P[15][17] * SF[22] + P[0][17] * SPP[20] + P[1][17] * SPP[12] + P[2][17] * SPP[11];
nextP[5][17] = P[5][17] + P[15][17] * SF[20] - P[0][17] * SPP[9] + P[1][17] * SPP[10] + P[2][17] * SPP[0];
nextP[6][17] = P[6][17] + P[3][17] * dt;
nextP[7][17] = P[7][17] + P[4][17] * dt;
nextP[8][17] = P[8][17] + P[5][17] * dt;
nextP[9][17] = P[9][17];
nextP[10][17] = P[10][17];
nextP[11][17] = P[11][17];
nextP[12][17] = P[12][17];
nextP[13][17] = P[13][17];
nextP[14][17] = P[14][17];
nextP[15][17] = P[15][17];
nextP[16][17] = P[16][17];
nextP[17][17] = P[17][17];
nextP[0][18] = P[0][18] * SPP[5] - P[1][18] * SPP[4] + P[2][18] * SPP[7] + P[9][18] * SPP[22] + P[12][18] * SPP[18];
nextP[1][18] = P[1][18] * SPP[6] - P[0][18] * SPP[2] - P[2][18] * SPP[8] + P[10][18] * SPP[22] + P[13][18] * SPP[17];
nextP[2][18] = P[0][18] * SPP[14] - P[1][18] * SPP[3] + P[2][18] * SPP[13] + P[11][18] * SPP[22] + P[14][18] * SPP[16];
nextP[3][18] = P[3][18] + P[0][18] * SPP[1] + P[1][18] * SPP[19] + P[2][18] * SPP[15] - P[15][18] * SPP[21];
nextP[4][18] = P[4][18] + P[15][18] * SF[22] + P[0][18] * SPP[20] + P[1][18] * SPP[12] + P[2][18] * SPP[11];
nextP[5][18] = P[5][18] + P[15][18] * SF[20] - P[0][18] * SPP[9] + P[1][18] * SPP[10] + P[2][18] * SPP[0];
nextP[6][18] = P[6][18] + P[3][18] * dt;
nextP[7][18] = P[7][18] + P[4][18] * dt;
nextP[8][18] = P[8][18] + P[5][18] * dt;
nextP[9][18] = P[9][18];
nextP[10][18] = P[10][18];
nextP[11][18] = P[11][18];
nextP[12][18] = P[12][18];
nextP[13][18] = P[13][18];
nextP[14][18] = P[14][18];
nextP[15][18] = P[15][18];
nextP[16][18] = P[16][18];
nextP[17][18] = P[17][18];
nextP[18][18] = P[18][18];
nextP[0][19] = P[0][19] * SPP[5] - P[1][19] * SPP[4] + P[2][19] * SPP[7] + P[9][19] * SPP[22] + P[12][19] * SPP[18];
nextP[1][19] = P[1][19] * SPP[6] - P[0][19] * SPP[2] - P[2][19] * SPP[8] + P[10][19] * SPP[22] + P[13][19] * SPP[17];
nextP[2][19] = P[0][19] * SPP[14] - P[1][19] * SPP[3] + P[2][19] * SPP[13] + P[11][19] * SPP[22] + P[14][19] * SPP[16];
nextP[3][19] = P[3][19] + P[0][19] * SPP[1] + P[1][19] * SPP[19] + P[2][19] * SPP[15] - P[15][19] * SPP[21];
nextP[4][19] = P[4][19] + P[15][19] * SF[22] + P[0][19] * SPP[20] + P[1][19] * SPP[12] + P[2][19] * SPP[11];
nextP[5][19] = P[5][19] + P[15][19] * SF[20] - P[0][19] * SPP[9] + P[1][19] * SPP[10] + P[2][19] * SPP[0];
nextP[6][19] = P[6][19] + P[3][19] * dt;
nextP[7][19] = P[7][19] + P[4][19] * dt;
nextP[8][19] = P[8][19] + P[5][19] * dt;
nextP[9][19] = P[9][19];
nextP[10][19] = P[10][19];
nextP[11][19] = P[11][19];
nextP[12][19] = P[12][19];
nextP[13][19] = P[13][19];
nextP[14][19] = P[14][19];
nextP[15][19] = P[15][19];
nextP[16][19] = P[16][19];
nextP[17][19] = P[17][19];
nextP[18][19] = P[18][19];
nextP[19][19] = P[19][19];
nextP[0][20] = P[0][20] * SPP[5] - P[1][20] * SPP[4] + P[2][20] * SPP[7] + P[9][20] * SPP[22] + P[12][20] * SPP[18];
nextP[1][20] = P[1][20] * SPP[6] - P[0][20] * SPP[2] - P[2][20] * SPP[8] + P[10][20] * SPP[22] + P[13][20] * SPP[17];
nextP[2][20] = P[0][20] * SPP[14] - P[1][20] * SPP[3] + P[2][20] * SPP[13] + P[11][20] * SPP[22] + P[14][20] * SPP[16];
nextP[3][20] = P[3][20] + P[0][20] * SPP[1] + P[1][20] * SPP[19] + P[2][20] * SPP[15] - P[15][20] * SPP[21];
nextP[4][20] = P[4][20] + P[15][20] * SF[22] + P[0][20] * SPP[20] + P[1][20] * SPP[12] + P[2][20] * SPP[11];
nextP[5][20] = P[5][20] + P[15][20] * SF[20] - P[0][20] * SPP[9] + P[1][20] * SPP[10] + P[2][20] * SPP[0];
nextP[6][20] = P[6][20] + P[3][20] * dt;
nextP[7][20] = P[7][20] + P[4][20] * dt;
nextP[8][20] = P[8][20] + P[5][20] * dt;
nextP[9][20] = P[9][20];
nextP[10][20] = P[10][20];
nextP[11][20] = P[11][20];
nextP[12][20] = P[12][20];
nextP[13][20] = P[13][20];
nextP[14][20] = P[14][20];
nextP[15][20] = P[15][20];
nextP[16][20] = P[16][20];
nextP[17][20] = P[17][20];
nextP[18][20] = P[18][20];
nextP[19][20] = P[19][20];
nextP[20][20] = P[20][20];
nextP[0][21] = P[0][21] * SPP[5] - P[1][21] * SPP[4] + P[2][21] * SPP[7] + P[9][21] * SPP[22] + P[12][21] * SPP[18];
nextP[1][21] = P[1][21] * SPP[6] - P[0][21] * SPP[2] - P[2][21] * SPP[8] + P[10][21] * SPP[22] + P[13][21] * SPP[17];
nextP[2][21] = P[0][21] * SPP[14] - P[1][21] * SPP[3] + P[2][21] * SPP[13] + P[11][21] * SPP[22] + P[14][21] * SPP[16];
nextP[3][21] = P[3][21] + P[0][21] * SPP[1] + P[1][21] * SPP[19] + P[2][21] * SPP[15] - P[15][21] * SPP[21];
nextP[4][21] = P[4][21] + P[15][21] * SF[22] + P[0][21] * SPP[20] + P[1][21] * SPP[12] + P[2][21] * SPP[11];
nextP[5][21] = P[5][21] + P[15][21] * SF[20] - P[0][21] * SPP[9] + P[1][21] * SPP[10] + P[2][21] * SPP[0];
nextP[6][21] = P[6][21] + P[3][21] * dt;
nextP[7][21] = P[7][21] + P[4][21] * dt;
nextP[8][21] = P[8][21] + P[5][21] * dt;
nextP[9][21] = P[9][21];
nextP[10][21] = P[10][21];
nextP[11][21] = P[11][21];
nextP[12][21] = P[12][21];
nextP[13][21] = P[13][21];
nextP[14][21] = P[14][21];
nextP[15][21] = P[15][21];
nextP[16][21] = P[16][21];
nextP[17][21] = P[17][21];
nextP[18][21] = P[18][21];
nextP[19][21] = P[19][21];
nextP[20][21] = P[20][21];
nextP[21][21] = P[21][21];
}
// Don't do covariance prediction on wind states unless we are using them
if (_control_status.flags.wind) {
// Check if we have jsut transitioned to using wind states and set the variances accordingly
if (!_control_status_prev.flags.mag_3D) {
for (uint8_t index = 22; index <= 23; index++) {
// TODO initialise wind states using ground speed and airspeed and set initial variance using sum of ground speed and airspeed variances
P[index][index] = sq(5.0f);
}
}
nextP[0][22] = P[0][22] * SPP[5] - P[1][22] * SPP[4] + P[2][22] * SPP[7] + P[9][22] * SPP[22] + P[12][22] * SPP[18];
nextP[1][22] = P[1][22] * SPP[6] - P[0][22] * SPP[2] - P[2][22] * SPP[8] + P[10][22] * SPP[22] + P[13][22] * SPP[17];
nextP[2][22] = P[0][22] * SPP[14] - P[1][22] * SPP[3] + P[2][22] * SPP[13] + P[11][22] * SPP[22] + P[14][22] * SPP[16];
nextP[3][22] = P[3][22] + P[0][22] * SPP[1] + P[1][22] * SPP[19] + P[2][22] * SPP[15] - P[15][22] * SPP[21];
nextP[4][22] = P[4][22] + P[15][22] * SF[22] + P[0][22] * SPP[20] + P[1][22] * SPP[12] + P[2][22] * SPP[11];
nextP[5][22] = P[5][22] + P[15][22] * SF[20] - P[0][22] * SPP[9] + P[1][22] * SPP[10] + P[2][22] * SPP[0];
nextP[6][22] = P[6][22] + P[3][22] * dt;
nextP[7][22] = P[7][22] + P[4][22] * dt;
nextP[8][22] = P[8][22] + P[5][22] * dt;
nextP[9][22] = P[9][22];
nextP[10][22] = P[10][22];
nextP[11][22] = P[11][22];
nextP[12][22] = P[12][22];
nextP[13][22] = P[13][22];
nextP[14][22] = P[14][22];
nextP[15][22] = P[15][22];
nextP[16][22] = P[16][22];
nextP[17][22] = P[17][22];
nextP[18][22] = P[18][22];
nextP[19][22] = P[19][22];
nextP[20][22] = P[20][22];
nextP[21][22] = P[21][22];
nextP[22][22] = P[22][22];
nextP[0][23] = P[0][23] * SPP[5] - P[1][23] * SPP[4] + P[2][23] * SPP[7] + P[9][23] * SPP[22] + P[12][23] * SPP[18];
nextP[1][23] = P[1][23] * SPP[6] - P[0][23] * SPP[2] - P[2][23] * SPP[8] + P[10][23] * SPP[22] + P[13][23] * SPP[17];
nextP[2][23] = P[0][23] * SPP[14] - P[1][23] * SPP[3] + P[2][23] * SPP[13] + P[11][23] * SPP[22] + P[14][23] * SPP[16];
nextP[3][23] = P[3][23] + P[0][23] * SPP[1] + P[1][23] * SPP[19] + P[2][23] * SPP[15] - P[15][23] * SPP[21];
nextP[4][23] = P[4][23] + P[15][23] * SF[22] + P[0][23] * SPP[20] + P[1][23] * SPP[12] + P[2][23] * SPP[11];
nextP[5][23] = P[5][23] + P[15][23] * SF[20] - P[0][23] * SPP[9] + P[1][23] * SPP[10] + P[2][23] * SPP[0];
nextP[6][23] = P[6][23] + P[3][23] * dt;
nextP[7][23] = P[7][23] + P[4][23] * dt;
nextP[8][23] = P[8][23] + P[5][23] * dt;
nextP[9][23] = P[9][23];
nextP[10][23] = P[10][23];
nextP[11][23] = P[11][23];
nextP[12][23] = P[12][23];
nextP[13][23] = P[13][23];
nextP[14][23] = P[14][23];
nextP[15][23] = P[15][23];
nextP[16][23] = P[16][23];
nextP[17][23] = P[17][23];
nextP[18][23] = P[18][23];
nextP[19][23] = P[19][23];
nextP[20][23] = P[20][23];
nextP[21][23] = P[21][23];
nextP[22][23] = P[22][23];
nextP[23][23] = P[23][23];
}
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// add process noise
for (unsigned i = 0; i < _k_num_states; i++) {
nextP[i][i] += process_noise[i];
}
// stop position covariance growth if our total position variance reaches 100m
EKF: miscellaneous formatting and typo updates
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// this can happen if we lose gps for some time
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if ((P[6][6] + P[7][7]) > 1e4f) {
for (uint8_t i = 6; i < 8; i++) {
for (uint8_t j = 0; j < _k_num_states; j++) {
nextP[i][j] = P[i][j];
nextP[j][i] = P[j][i];
}
}
}
// covariance matrix is symmetrical, so copy upper half to lower half
for (unsigned row = 1; row < _k_num_states; row++) {
for (unsigned column = 0 ; column < row; column++) {
nextP[row][column] = nextP[column][row];
}
}
EKF: miscellaneous formatting and typo updates
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// copy variances (diagonals)
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for (unsigned i = 0; i < _k_num_states; i++) {
P[i][i] = nextP[i][i];
}
EKF: miscellaneous formatting and typo updates
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// force symmetry
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for (unsigned row = 1; row < _k_num_states; row++) {
for (unsigned column = 0; column < row; column++) {
P[row][column] = 0.5f * (nextP[row][column] + nextP[column][row]);
P[column][row] = P[row][column];
}
}
limitCov();
}
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void Ekf::limitCov()
{
// Covariance diagonal limits. Use same values for states which
// belong to the same group (e.g. vel_x, vel_y, vel_z)
float P_lim[9] = {};
P_lim[0] = 1.0f; // angle error max var
P_lim[1] = 1000.0f; // velocity max var
P_lim[2] = 1000000.0f; // positiion max var
P_lim[3] = 0.001f; // gyro bias max var
P_lim[4] = 0.01f; // gyro scale max var
P_lim[5] = 0.1f; // delta velocity z bias max var
EKF: Improve variance limiting for stationary states Turn off the process noise if they grow too large and use the hard variance limit as a backup. This is numerically more stable than relying on a hard variance limit which does not deal with the covariances.
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P_lim[6] = 0.1f; // earth mag field max var
P_lim[7] = 0.1f; // body mag field max var
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P_lim[8] = 1000.0f; // wind max var
for (int i = 0; i < 3; i++) {
math::constrain(P[i][i], 0.0f, P_lim[0]);
}
added file with covariance calculations
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for (int i = 3; i < 6; i++) {
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math::constrain(P[i][i], 0.0f, P_lim[1]);
}
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for (int i = 6; i < 9; i++) {
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math::constrain(P[i][i], 0.0f, P_lim[2]);
}
added file with covariance calculations
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for (int i = 9; i < 12; i++) {
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math::constrain(P[i][i], 0.0f, P_lim[3]);
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}
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for (int i = 12; i < 15; i++) {
math::constrain(P[i][i], 0.0f, P_lim[4]);
}
math::constrain(P[15][15], 0.0f, P_lim[5]);
for (int i = 16; i < 19; i++) {
math::constrain(P[i][i], 0.0f, P_lim[6]);
}
for (int i = 19; i < 22; i++) {
math::constrain(P[i][i], 0.0f, P_lim[7]);
}
for (int i = 22; i < 24; i++) {
math::constrain(P[i][i], 0.0f, P_lim[8]);
added file with covariance calculations
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}
}