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ExtendedKalman.cpp
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ExtendedKalman.cpp
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/*
* File: ExtendedKalman.cpp
* Author: matt
*
* Created on 14 March 2013, 17:26
*/
#include "ExtendedKalman.h"
ExtendedKalmanClass::ExtendedKalmanClass() {
Q.Zero();
x.Zero();
F.Zero();
P.Zero();
z.Zero();
h.Zero();
y.Zero();
H.Zero();
S.Zero();
R.Zero();
K.Zero();
I = I.Identity();
P = P.Identity();
P *= 10000;
Q(0,0) = 0;
Q(1,1) = 0;
Q(2,2) = 0;
Q(3,3) = 0;
Q(4,4) = 0.2;
Q(5,5) = 0.2;
Q(6,6) = 0.2;
R(0,0) = 1000000;
R(1,1) = 1000000;
R(2,2) = 1000000;
x(0) = 1;
}
ExtendedKalmanClass::ExtendedKalmanClass(const ExtendedKalmanClass& orig) {
}
ExtendedKalmanClass::~ExtendedKalmanClass() {
}
QuaternionClass ExtendedKalmanClass::predict(s_calibratedData* calibratedData, float dt) {
q0 = x(0);
q1 = x(1);
q2 = x(2);
q3 = x(3);
wxb = x(4);
wyb = x(5);
wzb = x(6);
wx = -calibratedData->p * (pi / 180);
wy = calibratedData->q * (pi / 180);
wz = calibratedData->r * (pi / 180);
//Half dt since dt is only ever used in this form, saves on evaluating dt/2 multiple times
dt /= 2;
//Predicted state estimate, x = f(x,u)
x(0) = q0 + dt * (-q1*(wx-wxb) - q2*(wy-wyb) - q3*(wz-wzb));
x(1) = q1 + dt * ( q0*(wx-wxb) - q3*(wy-wyb) + q2*(wz-wzb));
x(2) = q2 + dt * ( q3*(wx-wxb) + q0*(wy-wyb) - q1*(wz-wzb));
x(3) = q3 + dt * (-q2*(wx-wxb) + q1*(wy-wyb) + q0*(wz-wzb));
//Gyro biases don't change
//Normalise to unit quaternion
norm = sqrt(x(0)*x(0) + x(1)*x(1) + x(2)*x(2) + x(3)*x(3));
x(0) /= norm;
x(1) /= norm;
x(2) /= norm;
x(3) /= norm;
q0 = x(0);
q1 = x(1);
q2 = x(2);
q3 = x(3);
//Build jacobian of f(x,u), F(row,column)
F(0,0) = 1;
F(0,1) = -dt*(wx-wxb);
F(0,2) = -dt*(wy-wyb);
F(0,3) = -dt*(wz-wzb);
F(0,4) = dt*q1;
F(0,5) = dt*q2;
F(0,6) = dt*q3;
F(1,0) = dt*(wx-wxb);
F(1,1) = 1;
F(1,2) = dt*(wz-wzb);
F(1,3) = -dt*(wy-wyb);
F(1,4) = -dt*q0;
F(1,5) = dt*q3;
F(1,6) = -dt*q2;
F(2,0) = dt*(wy-wyb);
F(2,1) = -dt*(wz-wzb);
F(2,2) = 1;
F(2,3) = dt*(wx-wxb);
F(2,4) = -dt*q3;
F(2,5) = -dt*q0;
F(2,6) = dt*q1;
F(3,0) = dt*(wz-wzb);
F(3,1) = dt*(wy-wyb);
F(3,2) = -dt*(wx-wxb);
F(3,3) = 1;
F(3,4) = dt*q2;
F(3,5) = -dt*q1;
F(3,6) = -dt*q0;
F(4,0) = 0;
F(4,1) = 0;
F(4,2) = 0;
F(4,3) = 0;
F(4,4) = 1;
F(4,5) = 0;
F(4,6) = 0;
F(5,0) = 0;
F(5,1) = 0;
F(5,2) = 0;
F(5,3) = 0;
F(5,4) = 0;
F(5,5) = 1;
F(5,6) = 0;
F(6,0) = 0;
F(6,1) = 0;
F(6,2) = 0;
F(6,3) = 0;
F(6,4) = 0;
F(6,5) = 0;
F(6,6) = 1;
//Covariance of estimate
P = F*P*F.transpose() + Q;
QuaternionClass q;
q.w = x(0);
q.x = x(1);
q.y = x(2);
q.z = x(3);
return q;
}
QuaternionClass ExtendedKalmanClass::update(s_calibratedData* calibratedData, float dt) {
q0 = x(0);
q1 = x(1);
q2 = x(2);
q3 = x(3);
//Normalise accelerometer triad
norm = sqrt(calibratedData->x*calibratedData->x + calibratedData->y*calibratedData->y + calibratedData->z*calibratedData->z);
z(0) = calibratedData->x / norm;
z(1) = calibratedData->y / norm;
z(2) = -calibratedData->z / norm;
//Map measurements to states
h(0) = 2*q0*q2 - 2*q1*q3;
h(1) = -2*q0*q1 - 2*q2*q3;
h(2) = -q0*q0 + q1*q1 + q2*q2 - q3*q3;
//Measurement residual
y = z - h;
//Populate h jacobian
H(0,0) = 2*q2;
H(0,1) = -2*q3;
H(0,2) = 2*q0;
H(0,3) = -2*q1;
H(0,4) = 0;
H(0,5) = 0;
H(0,6) = 0;
H(1,0) = -2*q1;
H(1,1) = -2*q0;
H(1,2) = -2*q3;
H(1,3) = -2*q2;
H(1,4) = 0;
H(1,5) = 0;
H(1,6) = 0;
H(2,0) = -2*q0;
H(2,1) = 2*q1;
H(2,2) = 2*q2;
H(2,3) = -2*q3;
H(2,4) = 0;
H(2,5) = 0;
H(2,6) = 0;
//Measurement covariance update + Kalman gain calculation + corrected prediction
//S = H*P*H' + R
S = H*P*H.transpose() + R; //H*P*H' is evaluating to 0 for some reason
//K = P*H'/S
K = P*H.transpose()*S.inverse();
//Correct state estimate
x = x + K*y;
//Normalise to unit quaternion
norm = sqrt(x(0)*x(0) + x(1)*x(1) + x(2)*x(2) + x(3)*x(3));
x(0) /= norm;
x(1) /= norm;
x(2) /= norm;
x(3) /= norm;
//Update state covariance
P = (I - K*H)*P;
QuaternionClass q;
q.w = x(0);
q.x = x(1);
q.y = x(2);
q.z = x(3);
return q;
}