static void UKF_GenerateSigmaPoints(UKF_Filter* ukf)
{
int cols = 0;
//state
float32_t *X = ukf->X_f32;
float32_t *tmpX = ukf->tmpX_f32;
//need to tune!!!
//covariance
//c*chol(P)'
arm_mat_chol_f32(&ukf->P);
arm_mat_scale_f32(&ukf->P, ukf->gamma, &ukf->P);
//////////////////////////////////////////////////////////////////////////
//generate sigma points
arm_mat_setcolumn_f32(&ukf->XSP, X, cols);
for(cols = 1; cols <= UKF_STATE_DIM; cols++){
arm_mat_getcolumn_f32(&ukf->P, tmpX, cols - 1);
arm_mat_add_f32(&ukf->X, &ukf->tmpX, &ukf->tmpX);
arm_mat_setcolumn_f32(&ukf->XSP, tmpX, cols);
}
for(cols = UKF_STATE_DIM + 1; cols < UKF_SP_POINTS; cols++){
arm_mat_getcolumn_f32(&ukf->P, tmpX, cols - 8/*UKF_STATE_DIM + 1*/);
arm_mat_sub_f32(&ukf->X, &ukf->tmpX, &ukf->tmpX);
arm_mat_setcolumn_f32(&ukf->XSP, tmpX, cols);
}
}
void Mat_scale ( ) {
uint32_t R1 = 0;
uint32_t C1 = 0;
uint32_t R2 = 0;
uint32_t C2 = 0;
uint32_t Scaling_factor = 0;
arm_status status;
arm_matrix_instance_f32 A ;
arm_matrix_instance_f32 Scale_A__OUT ;
const float32_t A_data[4];
const float32_t Scale_A__OUT_data[4];
arm_mat_init_f32( &A ,
R1 ,
C1,
A_data );
arm_mat_init_f32( &Scale_A__OUT ,
C2 ,
Scaling_factor ,
Scale_A__OUT_data );
status = arm_mat_scale_f32( &A ,
R2,
&Scale_A__OUT );
}
EKF_Attitude::EKF_Attitude(){
//Parameters
arm_mat_init_f32(&Pk, 4, 4, Pk_f32);
arm_mat_init_f32(&R, 3, 3, R_f32);
arm_mat_init_f32(&Qk, 4, 4, Qk_f32);
arm_mat_init_f32(&I, 4, 4, I_f32);
arm_mat_init_f32(&x, 2, 1, x_f32);
//Helpers:
arm_mat_init_f32(&Ak, 4, 4, Ak_f32);
arm_mat_init_f32(&Ak_trans, 4, 4, Ak_trans_f32);
arm_mat_init_f32(&S, 3, 3, S_f32);
arm_mat_init_f32(&K_k1, 4, 3, K_k1_f32);
arm_mat_init_f32(&K_k2, 4, 3, K_k2_f32);
arm_mat_init_f32(&h1_q, 3, 1, h1_q_f32);
arm_mat_init_f32(&q_corr, 4, 1, q_corr_f32);
arm_mat_init_f32(&q_corr_2, 4, 1, q_corr_2_f32);
//Temps
arm_mat_init_f32(&temp4x4, 4, 4, temp4x4_f32);
arm_mat_init_f32(&temp4x4_2, 4, 4, temp4x4_2_f32);
arm_mat_init_f32(&temp3x4, 3, 4, temp3x4_f32);
arm_mat_init_f32(&temp4x3, 4, 3, temp4x3_f32);
arm_mat_init_f32(&temp3x3, 3, 3, temp3x3_f32);
arm_mat_init_f32(&temp3x1, 3, 1, temp3x1_f32);
arm_mat_init_f32(&temp4x1, 4, 1, temp4x1_f32);
arm_mat_init_f32(&null4x4, 4, 4, null4x4_f32);
//arm_mat_scale_f32(&R, 0.0001, &temp3x3);
//copy_matrix(&R, &temp3x3);
arm_mat_scale_f32(&Qk, 0.0001, &temp4x4);
copy_matrix(&Qk, &temp4x4);
}
void EKF_Attitude::innovate_priori(Quaternion& quaternion,
float Gx,
float Gy,
float Gz){
float quaternion_array[4] = {quaternion.w, quaternion.x, quaternion.y, quaternion.z};
arm_matrix_instance_f32 q;
arm_mat_init_f32(&q, 4, 1, quaternion_array);
static uint32_t timestamp;
static float dt;
dt = Time.get_time_since_sec(timestamp);
//---------------------- PREDICTION -----------------------------
//1. Obtain the angular velocities:
float wx = (Gx*2*PI)/360.0;
float wy = (Gy*2*PI)/360.0;
float wz = (Gz*2*PI)/360.0;
//2. Calculate the discrete time state transition matrix:
float32_t omega_f32[16] = {
0, -wx, -wy, -wz,
wx, 0, wz, -wy,
wy, -wz, 0, wx,
wz, wy, -wx, 0};
arm_matrix_instance_f32 omega; /* Matrix Omega Instance */
arm_mat_init_f32(&omega, 4, 4, omega_f32);
//Ak = I + 0.5*omega*T;
arm_mat_scale_f32(&omega, 0.5*dt, &temp4x4);
arm_mat_add_f32(&I, &temp4x4, &Ak);
//3. Calculation of the a priori system state:
// q = Ak*q
arm_mat_mult_f32(&Ak, &q, &temp4x1);
//memcpy((void*)quaternion, (void*)temp4x1_f32, 4);
/*quaternion[0] = temp4x1_f32[0];
quaternion[1] = temp4x1_f32[1];
quaternion[2] = temp4x1_f32[2];
quaternion[3] = temp4x1_f32[3];*/
quaternion.w = temp4x1_f32[0];
quaternion.x = temp4x1_f32[1];
quaternion.y = temp4x1_f32[2];
quaternion.z = temp4x1_f32[3];
//4. Calculation of the a proiri noise covariance matrix:
// Pk = Ak*Pk*Ak.' + Qk;
arm_mat_trans_f32(&Ak, &Ak_trans);
//temp = Ak*Pk
arm_mat_mult_f32(&Ak, &Pk, &temp4x4);
//Pk = temp*Ak.'
arm_mat_mult_f32(&temp4x4, &Ak_trans, &Pk);
//temp = Pk + Qk:
arm_mat_add_f32(&Pk, &Qk, &temp4x4);
//Pk = temp;
copy_matrix(&Pk, &temp4x4);
timestamp = Time.get_timestamp();
}
void SRCKF_Update(SRCKF_Filter* srckf, float32_t *gyro, float32_t *accel, float32_t *mag, float32_t dt)
{
//////////////////////////////////////////////////////////////////////////
float32_t q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
//
float32_t hx, hy, hz;
float32_t bx, bz;
float32_t _2mx, _2my, _2mz;
//
int col;
float32_t dQ[4];
float32_t norm;
float32_t *X = srckf->X_f32, *Y = srckf->Y_f32;
float32_t *tmpX = srckf->tmpX_f32, *tmpY = srckf->tmpY_f32;
float32_t *iKesi = srckf->iKesi_f32;
dQ[0] = 0.0f;
dQ[1] = (gyro[0] - X[4]);
dQ[2] = (gyro[1] - X[5]);
dQ[3] = (gyro[2] - X[6]);
//////////////////////////////////////////////////////////////////////////
//time update
for(col = 0; col < SRCKF_CP_POINTS; col++){
//evaluate the cubature points
arm_mat_getcolumn_f32(&srckf->Kesi, iKesi, col);
arm_mat_mult_f32(&srckf->S, &srckf->iKesi, &srckf->tmpX);
arm_mat_add_f32(&srckf->tmpX, &srckf->X, &srckf->tmpX);
arm_mat_setcolumn_f32(&srckf->XCP, tmpX, col);
//evaluate the propagated cubature points
Quaternion_RungeKutta4(tmpX, dQ, dt, 1);
arm_mat_setcolumn_f32(&srckf->XPCP, tmpX, col);
}
//estimate the predicted state
arm_mat_cumsum_f32(&srckf->XPCP, tmpX, X);
arm_mat_scale_f32(&srckf->X, srckf->W, &srckf->X);
//estimate the square-root factor of the predicted error covariance
for(col = 0; col < SRCKF_CP_POINTS; col++){
arm_mat_getcolumn_f32(&srckf->XPCP, tmpX, col);
arm_mat_sub_f32(&srckf->tmpX, &srckf->X, &srckf->tmpX);
arm_mat_scale_f32(&srckf->tmpX, srckf->SW, &srckf->tmpX);
arm_mat_setcolumn_f32(&srckf->XCM, tmpX, col);
}
//XCM[XPCP, SQ], SQ fill already
arm_mat_qr_decompositionT_f32(&srckf->XCM, &srckf->ST);
arm_mat_trans_f32(&srckf->ST, &srckf->S);
//////////////////////////////////////////////////////////////////////////
//measurement update
//normalize accel and magnetic
norm = FastSqrtI(accel[0] * accel[0] + accel[1] * accel[1] + accel[2] * accel[2]);
accel[0] *= norm;
accel[1] *= norm;
accel[2] *= norm;
//////////////////////////////////////////////////////////////////////////
norm = FastSqrtI(mag[0] * mag[0] + mag[1] * mag[1] + mag[2] * mag[2]);
mag[0] *= norm;
mag[1] *= norm;
mag[2] *= norm;
_2mx = 2.0f * mag[0];
_2my = 2.0f * mag[1];
_2mz = 2.0f * mag[2];
for(col = 0; col < SRCKF_CP_POINTS; col++){
//evaluate the cubature points
arm_mat_getcolumn_f32(&srckf->Kesi, iKesi, col);
arm_mat_mult_f32(&srckf->S, &srckf->iKesi, &srckf->tmpX);
arm_mat_add_f32(&srckf->tmpX, &srckf->X, &srckf->tmpX);
arm_mat_setcolumn_f32(&srckf->XCP, tmpX, col);
//evaluate the propagated cubature points
//auxiliary variables to avoid repeated arithmetic
q0q0 = tmpX[0] * tmpX[0];
q0q1 = tmpX[0] * tmpX[1];
q0q2 = tmpX[0] * tmpX[2];
q0q3 = tmpX[0] * tmpX[3];
q1q1 = tmpX[1] * tmpX[1];
q1q2 = tmpX[1] * tmpX[2];
q1q3 = tmpX[1] * tmpX[3];
q2q2 = tmpX[2] * tmpX[2];
q2q3 = tmpX[2] * tmpX[3];
q3q3 = tmpX[3] * tmpX[3];
//reference direction of earth's magnetic field
hx = _2mx * (0.5f - q2q2 - q3q3) + _2my * (q1q2 - q0q3) + _2mz *(q1q3 + q0q2);
hy = _2mx * (q1q2 + q0q3) + _2my * (0.5f - q1q1 - q3q3) + _2mz * (q2q3 - q0q1);
hz = _2mx * (q1q3 - q0q2) + _2my * (q2q3 + q0q1) + _2mz *(0.5f - q1q1 - q2q2);
arm_sqrt_f32(hx * hx + hy * hy, &bx);
bz = hz;
tmpY[0] = 2.0f * (q1q3 - q0q2);
tmpY[1] = 2.0f * (q2q3 + q0q1);
tmpY[2] = -1.0f + 2.0f * (q0q0 + q3q3);
tmpY[3] = bx * (1.0f - 2.0f * (q2q2 + q3q3)) + bz * ( 2.0f * (q1q3 - q0q2));
tmpY[4] = bx * (2.0f * (q1q2 - q0q3)) + bz * (2.0f * (q2q3 + q0q1));
tmpY[5] = bx * (2.0f * (q1q3 + q0q2)) + bz * (1.0f - 2.0f * (q1q1 + q2q2));
arm_mat_setcolumn_f32(&srckf->YPCP, tmpY, col);
}
//estimate the predicted measurement
arm_mat_cumsum_f32(&srckf->YPCP, tmpY, Y);
arm_mat_scale_f32(&srckf->Y, srckf->W, &srckf->Y);
//estimate the square-root of the innovation covariance matrix
for(col = 0; col < SRCKF_CP_POINTS; col++){
arm_mat_getcolumn_f32(&srckf->YPCP, tmpY, col);
arm_mat_sub_f32(&srckf->tmpY, &srckf->Y, &srckf->tmpY);
arm_mat_scale_f32(&srckf->tmpY, srckf->SW, &srckf->tmpY);
arm_mat_setcolumn_f32(&srckf->YCPCM, tmpY, col);
arm_mat_setcolumn_f32(&srckf->YCM, tmpY, col);
}
//YCM[YPCP, SR], SR fill already
arm_mat_qr_decompositionT_f32(&srckf->YCM, &srckf->SYT);
//estimate the cross-covariance matrix
for(col = 0; col < SRCKF_CP_POINTS; col++){
arm_mat_getcolumn_f32(&srckf->XCP, tmpX, col);
arm_mat_sub_f32(&srckf->tmpX, &srckf->X, &srckf->tmpX);
arm_mat_scale_f32(&srckf->tmpX, srckf->SW, &srckf->tmpX);
arm_mat_setcolumn_f32(&srckf->XCPCM, tmpX, col);
}
arm_mat_trans_f32(&srckf->YCPCM, &srckf->YCPCMT);
arm_mat_mult_f32(&srckf->XCPCM, &srckf->YCPCMT, &srckf->PXY);
//estimate the kalman gain
arm_mat_trans_f32(&srckf->SYT, &srckf->SY);
arm_mat_inverse_f32(&srckf->SYT, &srckf->SYTI);
arm_mat_inverse_f32(&srckf->SY, &srckf->SYI);
arm_mat_mult_f32(&srckf->PXY, &srckf->SYTI, &srckf->tmpPXY);
arm_mat_mult_f32(&srckf->tmpPXY, &srckf->SYI, &srckf->K);
//estimate the updated state
Y[0] = accel[0] - Y[0];
Y[1] = accel[1] - Y[1];
Y[2] = accel[2] - Y[2];
Y[3] = mag[0] - Y[3];
Y[4] = mag[1] - Y[4];
Y[5] = mag[2] - Y[5];
arm_mat_mult_f32(&srckf->K, &srckf->Y, &srckf->tmpX);
arm_mat_add_f32(&srckf->X, &srckf->tmpX, &srckf->X);
//normalize quaternion
norm = FastSqrtI(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;
//estimate the square-root factor of the corresponding error covariance
arm_mat_mult_f32(&srckf->K, &srckf->YCPCM, &srckf->tmpXCPCM);
arm_mat_sub_f32(&srckf->XCPCM, &srckf->tmpXCPCM, &srckf->XCPCM);
arm_mat_setsubmatrix_f32(&srckf->XYCM, &srckf->XCPCM, 0, 0);
arm_mat_mult_f32(&srckf->K, &srckf->SR, &srckf->tmpPXY);
arm_mat_setsubmatrix_f32(&srckf->XYCM, &srckf->tmpPXY, 0, SRCKF_CP_POINTS);
arm_mat_qr_decompositionT_f32(&srckf->XYCM, &srckf->ST);
arm_mat_trans_f32(&srckf->ST, &srckf->S);
}
