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829 lines
26 KiB
C
829 lines
26 KiB
C
/**
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******************************************************************************
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* @addtogroup AHRS
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* @{
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* @addtogroup INSGPS
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* @{
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* @brief INSGPS is a joint attitude and position estimation EKF
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*
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* @file insgps.c
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* @author The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
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* @brief An INS/GPS algorithm implemented with an EKF.
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*
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* @see The GNU Public License (GPL) Version 3
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*
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*****************************************************************************/
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/*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*/
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#include "insgps.h"
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#include <math.h>
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#include <stdint.h>
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#include <pios_math.h>
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// constants/macros/typdefs
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#define NUMX 13 // number of states, X is the state vector
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#define NUMW 9 // number of plant noise inputs, w is disturbance noise vector
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#define NUMV 10 // number of measurements, v is the measurement noise vector
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#define NUMU 6 // number of deterministic inputs, U is the input vector
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// Private functions
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void CovariancePrediction(float F[NUMX][NUMX], float G[NUMX][NUMW],
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float Q[NUMW], float dT, float P[NUMX][NUMX]);
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void SerialUpdate(float H[NUMV][NUMX], float R[NUMV], float Z[NUMV],
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float Y[NUMV], float P[NUMX][NUMX], float X[NUMX],
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uint16_t SensorsUsed);
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void RungeKutta(float X[NUMX], float U[NUMU], float dT);
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void StateEq(float X[NUMX], float U[NUMU], float Xdot[NUMX]);
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void LinearizeFG(float X[NUMX], float U[NUMU], float F[NUMX][NUMX],
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float G[NUMX][NUMW]);
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void MeasurementEq(float X[NUMX], float Be[3], float Y[NUMV]);
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void LinearizeH(float X[NUMX], float Be[3], float H[NUMV][NUMX]);
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// Private variables
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// speed optimizations, describe matrix sparsity
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// derived from state equations in
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// LinearizeFG() and LinearizeH():
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//
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// usage F: usage G: usage H:
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// 0123456789abc 012345678 0123456789abc
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// 0...X......... ......... X............
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// 1....X........ ......... .X...........
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// 2.....X....... ......... ..X..........
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// 3......XXXX... ...XXX... ...X.........
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// 4......XXXX... ...XXX... ....X........
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// 5......XXXX... ...XXX... .....X.......
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// 6.......XXXXXX XXX...... ......XXXX...
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// 7......X.XXXXX XXX...... ......XXXX...
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// 8......XX.XXXX XXX...... ......XXXX...
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// 9......XXX.XXX XXX...... ..X..........
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// a............. ......X..
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// b............. .......X.
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// c............. ........X
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static const int8_t FrowMin[NUMX] = { 3, 4, 5, 6, 6, 6, 7, 6, 6, 6, 13, 13, 13 };
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static const int8_t FrowMax[NUMX] = { 3, 4, 5, 9, 9, 9, 12, 12, 12, 12, -1, -1, -1 };
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static const int8_t GrowMin[NUMX] = { 9, 9, 9, 3, 3, 3, 0, 0, 0, 0, 6, 7, 8 };
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static const int8_t GrowMax[NUMX] = { -1, -1, -1, 5, 5, 5, 2, 2, 2, 2, 6, 7, 8 };
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static const int8_t HrowMin[NUMV] = { 0, 1, 2, 3, 4, 5, 6, 6, 6, 2 };
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static const int8_t HrowMax[NUMV] = { 0, 1, 2, 3, 4, 5, 9, 9, 9, 2 };
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static struct EKFData {
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// linearized system matrices
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float F[NUMX][NUMX];
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float G[NUMX][NUMW];
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float H[NUMV][NUMX];
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// local magnetic unit vector in NED frame
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float Be[3];
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// covariance matrix and state vector
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float P[NUMX][NUMX];
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float X[NUMX];
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// input noise and measurement noise variances
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float Q[NUMW];
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float R[NUMV];
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} ekf;
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// Global variables
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struct NavStruct Nav;
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// ************* Exposed Functions ****************
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// *************************************************
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uint16_t ins_get_num_states()
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{
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return NUMX;
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}
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void INSGPSInit() // pretty much just a place holder for now
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{
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ekf.Be[0] = 1.0f;
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ekf.Be[1] = 0.0f;
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ekf.Be[2] = 0.0f; // local magnetic unit vector
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for (int i = 0; i < NUMX; i++) {
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for (int j = 0; j < NUMX; j++) {
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ekf.P[i][j] = 0.0f; // zero all terms
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ekf.F[i][j] = 0.0f;
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}
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for (int j = 0; j < NUMW; j++) {
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ekf.G[i][j] = 0.0f;
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}
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for (int j = 0; j < NUMV; j++) {
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ekf.H[j][i] = 0.0f;
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}
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ekf.X[i] = 0.0f;
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}
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for (int i = 0; i < NUMW; i++) {
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ekf.Q[i] = 0.0f;
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}
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for (int i = 0; i < NUMV; i++) {
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ekf.R[i] = 0.0f;
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}
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ekf.P[0][0] = ekf.P[1][1] = ekf.P[2][2] = 25.0f; // initial position variance (m^2)
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ekf.P[3][3] = ekf.P[4][4] = ekf.P[5][5] = 5.0f; // initial velocity variance (m/s)^2
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ekf.P[6][6] = ekf.P[7][7] = ekf.P[8][8] = ekf.P[9][9] = 1e-5f; // initial quaternion variance
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ekf.P[10][10] = ekf.P[11][11] = ekf.P[12][12] = 1e-9f; // initial gyro bias variance (rad/s)^2
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ekf.X[0] = ekf.X[1] = ekf.X[2] = ekf.X[3] = ekf.X[4] = ekf.X[5] = 0.0f; // initial pos and vel (m)
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ekf.X[6] = 1.0f;
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ekf.X[7] = ekf.X[8] = ekf.X[9] = 0.0f; // initial quaternion (level and North) (m/s)
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ekf.X[10] = ekf.X[11] = ekf.X[12] = 0.0f; // initial gyro bias (rad/s)
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ekf.Q[0] = ekf.Q[1] = ekf.Q[2] = 50e-4f; // gyro noise variance (rad/s)^2
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ekf.Q[3] = ekf.Q[4] = ekf.Q[5] = 0.00001f; // accelerometer noise variance (m/s^2)^2
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ekf.Q[6] = ekf.Q[7] = ekf.Q[8] = 2e-8f; // gyro bias random walk variance (rad/s^2)^2
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ekf.R[0] = ekf.R[1] = 0.004f; // High freq GPS horizontal position noise variance (m^2)
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ekf.R[2] = 0.036f; // High freq GPS vertical position noise variance (m^2)
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ekf.R[3] = ekf.R[4] = 0.004f; // High freq GPS horizontal velocity noise variance (m/s)^2
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ekf.R[5] = 100.0f; // High freq GPS vertical velocity noise variance (m/s)^2
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ekf.R[6] = ekf.R[7] = ekf.R[8] = 0.005f; // magnetometer unit vector noise variance
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ekf.R[9] = .25f; // High freq altimeter noise variance (m^2)
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}
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void INSResetP(float PDiag[NUMX])
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{
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uint8_t i, j;
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// if PDiag[i] nonzero then clear row and column and set diagonal element
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for (i = 0; i < NUMX; i++) {
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if (PDiag != 0) {
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for (j = 0; j < NUMX; j++) {
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ekf.P[i][j] = ekf.P[j][i] = 0.0f;
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}
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ekf.P[i][i] = PDiag[i];
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}
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}
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}
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void INSGetP(float PDiag[NUMX])
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{
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uint8_t i;
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// retrieve diagonal elements (aka state variance)
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for (i = 0; i < NUMX; i++) {
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if (PDiag != 0) {
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PDiag[i] = ekf.P[i][i];
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}
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}
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}
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void INSSetState(float pos[3], float vel[3], float q[4], float gyro_bias[3], __attribute__((unused)) float accel_bias[3])
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{
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/* Note: accel_bias not used in 13 state INS */
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ekf.X[0] = pos[0];
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ekf.X[1] = pos[1];
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ekf.X[2] = pos[2];
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ekf.X[3] = vel[0];
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ekf.X[4] = vel[1];
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ekf.X[5] = vel[2];
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ekf.X[6] = q[0];
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ekf.X[7] = q[1];
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ekf.X[8] = q[2];
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ekf.X[9] = q[3];
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ekf.X[10] = gyro_bias[0];
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ekf.X[11] = gyro_bias[1];
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ekf.X[12] = gyro_bias[2];
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}
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void INSPosVelReset(float pos[3], float vel[3])
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{
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for (int i = 0; i < 6; i++) {
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for (int j = i; j < NUMX; j++) {
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ekf.P[i][j] = 0; // zero the first 6 rows and columns
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ekf.P[j][i] = 0;
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}
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}
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ekf.P[0][0] = ekf.P[1][1] = ekf.P[2][2] = 25; // initial position variance (m^2)
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ekf.P[3][3] = ekf.P[4][4] = ekf.P[5][5] = 5; // initial velocity variance (m/s)^2
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ekf.X[0] = pos[0];
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ekf.X[1] = pos[1];
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ekf.X[2] = pos[2];
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ekf.X[3] = vel[0];
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ekf.X[4] = vel[1];
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ekf.X[5] = vel[2];
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}
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void INSSetPosVelVar(float PosVar[3], float VelVar[3])
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{
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ekf.R[0] = PosVar[0];
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ekf.R[1] = PosVar[1];
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ekf.R[2] = PosVar[2];
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ekf.R[3] = VelVar[0];
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ekf.R[4] = VelVar[1];
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ekf.R[5] = VelVar[2];
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}
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void INSSetGyroBias(float gyro_bias[3])
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{
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ekf.X[10] = gyro_bias[0];
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ekf.X[11] = gyro_bias[1];
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ekf.X[12] = gyro_bias[2];
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}
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void INSSetAccelVar(float accel_var[3])
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{
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ekf.Q[3] = accel_var[0];
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ekf.Q[4] = accel_var[1];
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ekf.Q[5] = accel_var[2];
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}
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void INSSetGyroVar(float gyro_var[3])
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{
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ekf.Q[0] = gyro_var[0];
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ekf.Q[1] = gyro_var[1];
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ekf.Q[2] = gyro_var[2];
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}
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void INSSetGyroBiasVar(float gyro_bias_var[3])
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{
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ekf.Q[6] = gyro_bias_var[0];
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ekf.Q[7] = gyro_bias_var[1];
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ekf.Q[8] = gyro_bias_var[2];
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}
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void INSSetMagVar(float scaled_mag_var[3])
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{
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ekf.R[6] = scaled_mag_var[0];
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ekf.R[7] = scaled_mag_var[1];
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ekf.R[8] = scaled_mag_var[2];
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}
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void INSSetBaroVar(float baro_var)
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{
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ekf.R[9] = baro_var;
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}
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void INSSetMagNorth(float B[3])
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{
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float mag = sqrtf(B[0] * B[0] + B[1] * B[1] + B[2] * B[2]);
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ekf.Be[0] = B[0] / mag;
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ekf.Be[1] = B[1] / mag;
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ekf.Be[2] = B[2] / mag;
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}
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void INSStatePrediction(float gyro_data[3], float accel_data[3], float dT)
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{
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float U[6];
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float qmag;
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// rate gyro inputs in units of rad/s
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U[0] = gyro_data[0];
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U[1] = gyro_data[1];
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U[2] = gyro_data[2];
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// accelerometer inputs in units of m/s
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U[3] = accel_data[0];
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U[4] = accel_data[1];
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U[5] = accel_data[2];
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// EKF prediction step
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LinearizeFG(ekf.X, U, ekf.F, ekf.G);
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RungeKutta(ekf.X, U, dT);
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qmag = sqrtf(ekf.X[6] * ekf.X[6] + ekf.X[7] * ekf.X[7] + ekf.X[8] * ekf.X[8] + ekf.X[9] * ekf.X[9]);
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ekf.X[6] /= qmag;
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ekf.X[7] /= qmag;
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ekf.X[8] /= qmag;
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ekf.X[9] /= qmag;
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// CovariancePrediction(ekf.F,ekf.G,ekf.Q,dT,ekf.P);
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// Update Nav solution structure
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Nav.Pos[0] = ekf.X[0];
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Nav.Pos[1] = ekf.X[1];
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Nav.Pos[2] = ekf.X[2];
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Nav.Vel[0] = ekf.X[3];
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Nav.Vel[1] = ekf.X[4];
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Nav.Vel[2] = ekf.X[5];
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Nav.q[0] = ekf.X[6];
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Nav.q[1] = ekf.X[7];
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Nav.q[2] = ekf.X[8];
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Nav.q[3] = ekf.X[9];
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Nav.gyro_bias[0] = ekf.X[10];
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Nav.gyro_bias[1] = ekf.X[11];
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Nav.gyro_bias[2] = ekf.X[12];
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}
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void INSCovariancePrediction(float dT)
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{
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CovariancePrediction(ekf.F, ekf.G, ekf.Q, dT, ekf.P);
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}
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float zeros[3] = { 0, 0, 0 };
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void MagCorrection(float mag_data[3])
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{
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INSCorrection(mag_data, zeros, zeros, zeros[0], MAG_SENSORS);
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}
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void MagVelBaroCorrection(float mag_data[3], float Vel[3], float BaroAlt)
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{
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INSCorrection(mag_data, zeros, Vel, BaroAlt,
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MAG_SENSORS | HORIZ_SENSORS | VERT_SENSORS |
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BARO_SENSOR);
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}
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void GpsBaroCorrection(float Pos[3], float Vel[3], float BaroAlt)
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{
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INSCorrection(zeros, Pos, Vel, BaroAlt,
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HORIZ_SENSORS | VERT_SENSORS | BARO_SENSOR);
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}
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void FullCorrection(float mag_data[3], float Pos[3], float Vel[3],
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float BaroAlt)
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{
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INSCorrection(mag_data, Pos, Vel, BaroAlt, FULL_SENSORS);
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}
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void GpsMagCorrection(float mag_data[3], float Pos[3], float Vel[3])
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{
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INSCorrection(mag_data, Pos, Vel, zeros[0],
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POS_SENSORS | HORIZ_SENSORS | MAG_SENSORS);
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}
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void VelBaroCorrection(float Vel[3], float BaroAlt)
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{
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INSCorrection(zeros, zeros, Vel, BaroAlt,
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HORIZ_SENSORS | VERT_SENSORS | BARO_SENSOR);
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}
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void INSCorrection(float mag_data[3], float Pos[3], float Vel[3],
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float BaroAlt, uint16_t SensorsUsed)
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{
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float Z[10], Y[10];
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float Bmag, qmag;
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// GPS Position in meters and in local NED frame
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Z[0] = Pos[0];
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Z[1] = Pos[1];
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Z[2] = Pos[2];
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// GPS Velocity in meters and in local NED frame
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Z[3] = Vel[0];
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Z[4] = Vel[1];
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Z[5] = Vel[2];
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// magnetometer data in any units (use unit vector) and in body frame
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Bmag =
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sqrtf(mag_data[0] * mag_data[0] + mag_data[1] * mag_data[1] +
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mag_data[2] * mag_data[2]);
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Z[6] = mag_data[0] / Bmag;
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Z[7] = mag_data[1] / Bmag;
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Z[8] = mag_data[2] / Bmag;
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// barometric altimeter in meters and in local NED frame
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Z[9] = BaroAlt;
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// EKF correction step
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LinearizeH(ekf.X, ekf.Be, ekf.H);
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MeasurementEq(ekf.X, ekf.Be, Y);
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SerialUpdate(ekf.H, ekf.R, Z, Y, ekf.P, ekf.X, SensorsUsed);
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qmag = sqrtf(ekf.X[6] * ekf.X[6] + ekf.X[7] * ekf.X[7] + ekf.X[8] * ekf.X[8] + ekf.X[9] * ekf.X[9]);
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ekf.X[6] /= qmag;
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ekf.X[7] /= qmag;
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ekf.X[8] /= qmag;
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ekf.X[9] /= qmag;
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// Update Nav solution structure
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Nav.Pos[0] = ekf.X[0];
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Nav.Pos[1] = ekf.X[1];
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Nav.Pos[2] = ekf.X[2];
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Nav.Vel[0] = ekf.X[3];
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Nav.Vel[1] = ekf.X[4];
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Nav.Vel[2] = ekf.X[5];
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Nav.q[0] = ekf.X[6];
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Nav.q[1] = ekf.X[7];
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Nav.q[2] = ekf.X[8];
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Nav.q[3] = ekf.X[9];
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Nav.gyro_bias[0] = ekf.X[10];
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Nav.gyro_bias[1] = ekf.X[11];
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Nav.gyro_bias[2] = ekf.X[12];
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}
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// ************* CovariancePrediction *************
|
|
// Does the prediction step of the Kalman filter for the covariance matrix
|
|
// Output, Pnew, overwrites P, the input covariance
|
|
// Pnew = (I+F*T)*P*(I+F*T)' + T^2*G*Q*G'
|
|
// Q is the discrete time covariance of process noise
|
|
// Q is vector of the diagonal for a square matrix with
|
|
// dimensions equal to the number of disturbance noise variables
|
|
// The General Method is very inefficient,not taking advantage of the sparse F and G
|
|
// The first Method is very specific to this implementation
|
|
// ************************************************
|
|
|
|
__attribute__((optimize("O3")))
|
|
void CovariancePrediction(float F[NUMX][NUMX], float G[NUMX][NUMW],
|
|
float Q[NUMW], float dT, float P[NUMX][NUMX])
|
|
{
|
|
// Pnew = (I+F*T)*P*(I+F*T)' + (T^2)*G*Q*G' = (T^2)[(P/T + F*P)*(I/T + F') + G*Q*G')]
|
|
|
|
float dT1 = 1.0f / dT; // multiplication is faster than division on fpu.
|
|
float dTsq = dT * dT;
|
|
|
|
float Dummy[NUMX][NUMX];
|
|
int8_t i;
|
|
|
|
for (i = 0; i < NUMX; i++) { // Calculate Dummy = (P/T +F*P)
|
|
float *Firow = F[i];
|
|
float *Pirow = P[i];
|
|
float *Dirow = Dummy[i];
|
|
int8_t Fistart = FrowMin[i];
|
|
int8_t Fiend = FrowMax[i];
|
|
int8_t j;
|
|
for (j = 0; j < NUMX; j++) {
|
|
Dirow[j] = Pirow[j] * dT1; // Dummy = P / T ...
|
|
int8_t k;
|
|
for (k = Fistart; k <= Fiend; k++) {
|
|
Dirow[j] += Firow[k] * P[k][j]; // [] + F * P
|
|
}
|
|
}
|
|
}
|
|
for (i = 0; i < NUMX; i++) { // Calculate Pnew = (T^2) [Dummy/T + Dummy*F' + G*Qw*G']
|
|
float *Dirow = Dummy[i];
|
|
float *Girow = G[i];
|
|
float *Pirow = P[i];
|
|
int8_t Gistart = GrowMin[i];
|
|
int8_t Giend = GrowMax[i];
|
|
int8_t j;
|
|
for (j = i; j < NUMX; j++) { // Use symmetry, ie only find upper triangular
|
|
float Ptmp = Dirow[j] * dT1; // Pnew = Dummy / T ...
|
|
|
|
{
|
|
float *Fjrow = F[j];
|
|
int8_t Fjstart = FrowMin[j];
|
|
int8_t Fjend = FrowMax[j];
|
|
int8_t k;
|
|
for (k = Fjstart; k <= Fjend; k++) {
|
|
Ptmp += Dirow[k] * Fjrow[k]; // [] + Dummy*F' ...
|
|
}
|
|
}
|
|
|
|
{
|
|
float *Gjrow = G[j];
|
|
int8_t Gjstart = MAX(Gistart, GrowMin[j]);
|
|
int8_t Gjend = MIN(Giend, GrowMax[j]);
|
|
int8_t k;
|
|
for (k = Gjstart; k <= Gjend; k++) {
|
|
Ptmp += Q[k] * Girow[k] * Gjrow[k]; // [] + G*Q*G' ...
|
|
}
|
|
}
|
|
|
|
P[j][i] = Pirow[j] = Ptmp * dTsq; // [] * (T^2)
|
|
}
|
|
}
|
|
}
|
|
|
|
// ************* SerialUpdate *******************
|
|
// Does the update step of the Kalman filter for the covariance and estimate
|
|
// Outputs are Xnew & Pnew, and are written over P and X
|
|
// Z is actual measurement, Y is predicted measurement
|
|
// Xnew = X + K*(Z-Y), Pnew=(I-K*H)*P,
|
|
// where K=P*H'*inv[H*P*H'+R]
|
|
// NOTE the algorithm assumes R (measurement covariance matrix) is diagonal
|
|
// i.e. the measurment noises are uncorrelated.
|
|
// It therefore uses a serial update that requires no matrix inversion by
|
|
// processing the measurements one at a time.
|
|
// Algorithm - see Grewal and Andrews, "Kalman Filtering,2nd Ed" p.121 & p.253
|
|
// - or see Simon, "Optimal State Estimation," 1st Ed, p.150
|
|
// The SensorsUsed variable is a bitwise mask indicating which sensors
|
|
// should be used in the update.
|
|
// ************************************************
|
|
|
|
void SerialUpdate(float H[NUMV][NUMX], float R[NUMV], float Z[NUMV],
|
|
float Y[NUMV], float P[NUMX][NUMX], float X[NUMX],
|
|
uint16_t SensorsUsed)
|
|
{
|
|
float HP[NUMX], HPHR, Error;
|
|
uint8_t i, j, k, m;
|
|
float Km[NUMX];
|
|
|
|
for (m = 0; m < NUMV; m++) {
|
|
if (SensorsUsed & (0x01 << m)) { // use this sensor for update
|
|
for (j = 0; j < NUMX; j++) { // Find Hp = H*P
|
|
HP[j] = 0;
|
|
for (k = HrowMin[m]; k <= HrowMax[m]; k++) {
|
|
HP[j] += H[m][k] * P[k][j];
|
|
}
|
|
}
|
|
HPHR = R[m]; // Find HPHR = H*P*H' + R
|
|
for (k = HrowMin[m]; k <= HrowMax[m]; k++) {
|
|
HPHR += HP[k] * H[m][k];
|
|
}
|
|
|
|
for (k = 0; k < NUMX; k++) {
|
|
Km[k] = HP[k] / HPHR; // find K = HP/HPHR
|
|
}
|
|
for (i = 0; i < NUMX; i++) { // Find P(m)= P(m-1) + K*HP
|
|
for (j = i; j < NUMX; j++) {
|
|
P[i][j] = P[j][i] =
|
|
P[i][j] - Km[i] * HP[j];
|
|
}
|
|
}
|
|
|
|
Error = Z[m] - Y[m];
|
|
for (i = 0; i < NUMX; i++) { // Find X(m)= X(m-1) + K*Error
|
|
X[i] = X[i] + Km[i] * Error;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// ************* RungeKutta **********************
|
|
// Does a 4th order Runge Kutta numerical integration step
|
|
// Output, Xnew, is written over X
|
|
// NOTE the algorithm assumes time invariant state equations and
|
|
// constant inputs over integration step
|
|
// ************************************************
|
|
|
|
void RungeKutta(float X[NUMX], float U[NUMU], float dT)
|
|
{
|
|
float dT2 =
|
|
dT / 2.0f, K1[NUMX], K2[NUMX], K3[NUMX], K4[NUMX], Xlast[NUMX];
|
|
uint8_t i;
|
|
|
|
for (i = 0; i < NUMX; i++) {
|
|
Xlast[i] = X[i]; // make a working copy
|
|
}
|
|
StateEq(X, U, K1); // k1 = f(x,u)
|
|
for (i = 0; i < NUMX; i++) {
|
|
X[i] = Xlast[i] + dT2 * K1[i];
|
|
}
|
|
StateEq(X, U, K2); // k2 = f(x+0.5*dT*k1,u)
|
|
for (i = 0; i < NUMX; i++) {
|
|
X[i] = Xlast[i] + dT2 * K2[i];
|
|
}
|
|
StateEq(X, U, K3); // k3 = f(x+0.5*dT*k2,u)
|
|
for (i = 0; i < NUMX; i++) {
|
|
X[i] = Xlast[i] + dT * K3[i];
|
|
}
|
|
StateEq(X, U, K4); // k4 = f(x+dT*k3,u)
|
|
|
|
// Xnew = X + dT*(k1+2*k2+2*k3+k4)/6
|
|
for (i = 0; i < NUMX; i++) {
|
|
X[i] =
|
|
Xlast[i] + dT * (K1[i] + 2.0f * K2[i] + 2.0f * K3[i] +
|
|
K4[i]) / 6.0f;
|
|
}
|
|
}
|
|
|
|
// ************* Model Specific Stuff ***************************
|
|
// *** StateEq, MeasurementEq, LinerizeFG, and LinearizeH ********
|
|
//
|
|
// State Variables = [Pos Vel Quaternion GyroBias NO-AccelBias]
|
|
// Deterministic Inputs = [AngularVel Accel]
|
|
// Disturbance Noise = [GyroNoise AccelNoise GyroRandomWalkNoise NO-AccelRandomWalkNoise]
|
|
//
|
|
// Measurement Variables = [Pos Vel BodyFrameMagField Altimeter]
|
|
// Inputs to Measurement = [EarthFrameMagField]
|
|
//
|
|
// Notes: Pos and Vel in earth frame
|
|
// AngularVel and Accel in body frame
|
|
// MagFields are unit vectors
|
|
// Xdot is output of StateEq()
|
|
// F and G are outputs of LinearizeFG(), all elements not set should be zero
|
|
// y is output of OutputEq()
|
|
// H is output of LinearizeH(), all elements not set should be zero
|
|
// ************************************************
|
|
|
|
void StateEq(float X[NUMX], float U[NUMU], float Xdot[NUMX])
|
|
{
|
|
float ax, ay, az, wx, wy, wz, q0, q1, q2, q3;
|
|
|
|
// ax=U[3]-X[13]; ay=U[4]-X[14]; az=U[5]-X[15]; // subtract the biases on accels
|
|
ax = U[3];
|
|
ay = U[4];
|
|
az = U[5]; // NO BIAS STATES ON ACCELS
|
|
wx = U[0] - X[10];
|
|
wy = U[1] - X[11];
|
|
wz = U[2] - X[12]; // subtract the biases on gyros
|
|
q0 = X[6];
|
|
q1 = X[7];
|
|
q2 = X[8];
|
|
q3 = X[9];
|
|
|
|
// Pdot = V
|
|
Xdot[0] = X[3];
|
|
Xdot[1] = X[4];
|
|
Xdot[2] = X[5];
|
|
|
|
// Vdot = Reb*a
|
|
Xdot[3] =
|
|
(q0 * q0 + q1 * q1 - q2 * q2 - q3 * q3) * ax + 2.0f * (q1 * q2 -
|
|
q0 * q3) *
|
|
ay + 2.0f * (q1 * q3 + q0 * q2) * az;
|
|
Xdot[4] =
|
|
2.0f * (q1 * q2 + q0 * q3) * ax + (q0 * q0 - q1 * q1 + q2 * q2 -
|
|
q3 * q3) * ay + 2 * (q2 * q3 -
|
|
q0 * q1) *
|
|
az;
|
|
Xdot[5] =
|
|
2.0f * (q1 * q3 - q0 * q2) * ax + 2 * (q2 * q3 + q0 * q1) * ay +
|
|
(q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3) * az + 9.81f;
|
|
|
|
// qdot = Q*w
|
|
Xdot[6] = (-q1 * wx - q2 * wy - q3 * wz) / 2.0f;
|
|
Xdot[7] = (q0 * wx - q3 * wy + q2 * wz) / 2.0f;
|
|
Xdot[8] = (q3 * wx + q0 * wy - q1 * wz) / 2.0f;
|
|
Xdot[9] = (-q2 * wx + q1 * wy + q0 * wz) / 2.0f;
|
|
|
|
// best guess is that bias stays constant
|
|
Xdot[10] = Xdot[11] = Xdot[12] = 0;
|
|
}
|
|
|
|
void LinearizeFG(float X[NUMX], float U[NUMU], float F[NUMX][NUMX],
|
|
float G[NUMX][NUMW])
|
|
{
|
|
float ax, ay, az, wx, wy, wz, q0, q1, q2, q3;
|
|
|
|
// ax=U[3]-X[13]; ay=U[4]-X[14]; az=U[5]-X[15]; // subtract the biases on accels
|
|
ax = U[3];
|
|
ay = U[4];
|
|
az = U[5]; // NO BIAS STATES ON ACCELS
|
|
wx = U[0] - X[10];
|
|
wy = U[1] - X[11];
|
|
wz = U[2] - X[12]; // subtract the biases on gyros
|
|
q0 = X[6];
|
|
q1 = X[7];
|
|
q2 = X[8];
|
|
q3 = X[9];
|
|
|
|
// Pdot = V
|
|
F[0][3] = F[1][4] = F[2][5] = 1.0f;
|
|
|
|
// dVdot/dq
|
|
F[3][6] = 2.0f * (q0 * ax - q3 * ay + q2 * az);
|
|
F[3][7] = 2.0f * (q1 * ax + q2 * ay + q3 * az);
|
|
F[3][8] = 2.0f * (-q2 * ax + q1 * ay + q0 * az);
|
|
F[3][9] = 2.0f * (-q3 * ax - q0 * ay + q1 * az);
|
|
F[4][6] = 2.0f * (q3 * ax + q0 * ay - q1 * az);
|
|
F[4][7] = 2.0f * (q2 * ax - q1 * ay - q0 * az);
|
|
F[4][8] = 2.0f * (q1 * ax + q2 * ay + q3 * az);
|
|
F[4][9] = 2.0f * (q0 * ax - q3 * ay + q2 * az);
|
|
F[5][6] = 2.0f * (-q2 * ax + q1 * ay + q0 * az);
|
|
F[5][7] = 2.0f * (q3 * ax + q0 * ay - q1 * az);
|
|
F[5][8] = 2.0f * (-q0 * ax + q3 * ay - q2 * az);
|
|
F[5][9] = 2.0f * (q1 * ax + q2 * ay + q3 * az);
|
|
|
|
// dVdot/dabias & dVdot/dna - NO BIAS STATES ON ACCELS - S0 REPEAT FOR G BELOW
|
|
// F[3][13]=G[3][3]=-q0*q0-q1*q1+q2*q2+q3*q3; F[3][14]=G[3][4]=2*(-q1*q2+q0*q3); F[3][15]=G[3][5]=-2*(q1*q3+q0*q2);
|
|
// F[4][13]=G[4][3]=-2*(q1*q2+q0*q3); F[4][14]=G[4][4]=-q0*q0+q1*q1-q2*q2+q3*q3; F[4][15]=G[4][5]=2*(-q2*q3+q0*q1);
|
|
// F[5][13]=G[5][3]=2*(-q1*q3+q0*q2); F[5][14]=G[5][4]=-2*(q2*q3+q0*q1); F[5][15]=G[5][5]=-q0*q0+q1*q1+q2*q2-q3*q3;
|
|
|
|
// dqdot/dq
|
|
F[6][6] = 0;
|
|
F[6][7] = -wx / 2.0f;
|
|
F[6][8] = -wy / 2.0f;
|
|
F[6][9] = -wz / 2.0f;
|
|
F[7][6] = wx / 2.0f;
|
|
F[7][7] = 0;
|
|
F[7][8] = wz / 2.0f;
|
|
F[7][9] = -wy / 2.0f;
|
|
F[8][6] = wy / 2.0f;
|
|
F[8][7] = -wz / 2.0f;
|
|
F[8][8] = 0;
|
|
F[8][9] = wx / 2.0f;
|
|
F[9][6] = wz / 2.0f;
|
|
F[9][7] = wy / 2.0f;
|
|
F[9][8] = -wx / 2.0f;
|
|
F[9][9] = 0;
|
|
|
|
// dqdot/dwbias
|
|
F[6][10] = q1 / 2.0f;
|
|
F[6][11] = q2 / 2.0f;
|
|
F[6][12] = q3 / 2.0f;
|
|
F[7][10] = -q0 / 2.0f;
|
|
F[7][11] = q3 / 2.0f;
|
|
F[7][12] = -q2 / 2.0f;
|
|
F[8][10] = -q3 / 2.0f;
|
|
F[8][11] = -q0 / 2.0f;
|
|
F[8][12] = q1 / 2.0f;
|
|
F[9][10] = q2 / 2.0f;
|
|
F[9][11] = -q1 / 2.0f;
|
|
F[9][12] = -q0 / 2.0f;
|
|
|
|
// dVdot/dna - NO BIAS STATES ON ACCELS - S0 REPEAT FOR G HERE
|
|
G[3][3] = -q0 * q0 - q1 * q1 + q2 * q2 + q3 * q3;
|
|
G[3][4] = 2.0f * (-q1 * q2 + q0 * q3);
|
|
G[3][5] = -2.0f * (q1 * q3 + q0 * q2);
|
|
G[4][3] = -2.0f * (q1 * q2 + q0 * q3);
|
|
G[4][4] = -q0 * q0 + q1 * q1 - q2 * q2 + q3 * q3;
|
|
G[4][5] = 2.0f * (-q2 * q3 + q0 * q1);
|
|
G[5][3] = 2.0f * (-q1 * q3 + q0 * q2);
|
|
G[5][4] = -2.0f * (q2 * q3 + q0 * q1);
|
|
G[5][5] = -q0 * q0 + q1 * q1 + q2 * q2 - q3 * q3;
|
|
|
|
// dqdot/dnw
|
|
G[6][0] = q1 / 2.0f;
|
|
G[6][1] = q2 / 2.0f;
|
|
G[6][2] = q3 / 2.0f;
|
|
G[7][0] = -q0 / 2.0f;
|
|
G[7][1] = q3 / 2.0f;
|
|
G[7][2] = -q2 / 2.0f;
|
|
G[8][0] = -q3 / 2.0f;
|
|
G[8][1] = -q0 / 2.0f;
|
|
G[8][2] = q1 / 2.0f;
|
|
G[9][0] = q2 / 2.0f;
|
|
G[9][1] = -q1 / 2.0f;
|
|
G[9][2] = -q0 / 2.0f;
|
|
|
|
// dwbias = random walk noise
|
|
G[10][6] = G[11][7] = G[12][8] = 1.0f;
|
|
// dabias = random walk noise
|
|
// G[13][9]=G[14][10]=G[15][11]=1; // NO BIAS STATES ON ACCELS
|
|
}
|
|
|
|
void MeasurementEq(float X[NUMX], float Be[3], float Y[NUMV])
|
|
{
|
|
float q0, q1, q2, q3;
|
|
|
|
q0 = X[6];
|
|
q1 = X[7];
|
|
q2 = X[8];
|
|
q3 = X[9];
|
|
|
|
// first six outputs are P and V
|
|
Y[0] = X[0];
|
|
Y[1] = X[1];
|
|
Y[2] = X[2];
|
|
Y[3] = X[3];
|
|
Y[4] = X[4];
|
|
Y[5] = X[5];
|
|
|
|
// Bb=Rbe*Be
|
|
Y[6] =
|
|
(q0 * q0 + q1 * q1 - q2 * q2 - q3 * q3) * Be[0] +
|
|
2.0f * (q1 * q2 + q0 * q3) * Be[1] + 2.0f * (q1 * q3 -
|
|
q0 * q2) * Be[2];
|
|
Y[7] =
|
|
2.0f * (q1 * q2 - q0 * q3) * Be[0] + (q0 * q0 - q1 * q1 +
|
|
q2 * q2 - q3 * q3) * Be[1] +
|
|
2.0f * (q2 * q3 + q0 * q1) * Be[2];
|
|
Y[8] =
|
|
2.0f * (q1 * q3 + q0 * q2) * Be[0] + 2.0f * (q2 * q3 -
|
|
q0 * q1) * Be[1] +
|
|
(q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3) * Be[2];
|
|
|
|
// Alt = -Pz
|
|
Y[9] = -1.0f * X[2];
|
|
}
|
|
|
|
void LinearizeH(float X[NUMX], float Be[3], float H[NUMV][NUMX])
|
|
{
|
|
float q0, q1, q2, q3;
|
|
|
|
q0 = X[6];
|
|
q1 = X[7];
|
|
q2 = X[8];
|
|
q3 = X[9];
|
|
|
|
// dP/dP=I;
|
|
H[0][0] = H[1][1] = H[2][2] = 1.0f;
|
|
// dV/dV=I;
|
|
H[3][3] = H[4][4] = H[5][5] = 1.0f;
|
|
|
|
// dBb/dq
|
|
H[6][6] = 2.0f * (q0 * Be[0] + q3 * Be[1] - q2 * Be[2]);
|
|
H[6][7] = 2.0f * (q1 * Be[0] + q2 * Be[1] + q3 * Be[2]);
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H[6][8] = 2.0f * (-q2 * Be[0] + q1 * Be[1] - q0 * Be[2]);
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H[6][9] = 2.0f * (-q3 * Be[0] + q0 * Be[1] + q1 * Be[2]);
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H[7][6] = 2.0f * (-q3 * Be[0] + q0 * Be[1] + q1 * Be[2]);
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H[7][7] = 2.0f * (q2 * Be[0] - q1 * Be[1] + q0 * Be[2]);
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H[7][8] = 2.0f * (q1 * Be[0] + q2 * Be[1] + q3 * Be[2]);
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H[7][9] = 2.0f * (-q0 * Be[0] - q3 * Be[1] + q2 * Be[2]);
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H[8][6] = 2.0f * (q2 * Be[0] - q1 * Be[1] + q0 * Be[2]);
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H[8][7] = 2.0f * (q3 * Be[0] - q0 * Be[1] - q1 * Be[2]);
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H[8][8] = 2.0f * (q0 * Be[0] + q3 * Be[1] - q2 * Be[2]);
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H[8][9] = 2.0f * (q1 * Be[0] + q2 * Be[1] + q3 * Be[2]);
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// dAlt/dPz = -1
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H[9][2] = -1.0f;
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}
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/**
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* @}
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* @}
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*/
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