float test_quat2(void) {
struct FloatEulers eula2b;
EULERS_ASSIGN(eula2b, RadOfDeg(70.), RadOfDeg(0.), RadOfDeg(0.));
// DISPLAY_FLOAT_EULERS_DEG("eula2b", eula2b);
struct FloatQuat qa2b;
FLOAT_QUAT_OF_EULERS(qa2b, eula2b);
DISPLAY_FLOAT_QUAT("qa2b", qa2b);
struct DoubleEulers eula2b_d;
EULERS_ASSIGN(eula2b_d, RadOfDeg(70.), RadOfDeg(0.), RadOfDeg(0.));
struct DoubleQuat qa2b_d;
DOUBLE_QUAT_OF_EULERS(qa2b_d, eula2b_d);
DISPLAY_FLOAT_QUAT("qa2b_d", qa2b_d);
struct FloatVect3 u = { 1., 0., 0.};
float angle = RadOfDeg(70.);
struct FloatQuat q;
FLOAT_QUAT_OF_AXIS_ANGLE(q, u, angle);
DISPLAY_FLOAT_QUAT("q ", q);
struct FloatEulers eula2c;
EULERS_ASSIGN(eula2c, RadOfDeg(80.), RadOfDeg(0.), RadOfDeg(0.));
// DISPLAY_FLOAT_EULERS_DEG("eula2c", eula2c);
struct FloatQuat qa2c;
FLOAT_QUAT_OF_EULERS(qa2c, eula2c);
DISPLAY_FLOAT_QUAT("qa2c", qa2c);
struct FloatQuat qb2a;
FLOAT_QUAT_INVERT(qb2a, qa2b);
DISPLAY_FLOAT_QUAT("qb2a", qb2a);
struct FloatQuat qb2c1;
FLOAT_QUAT_COMP(qb2c1, qb2a, qa2c);
DISPLAY_FLOAT_QUAT("qb2c1", qb2c1);
struct FloatQuat qb2c2;
FLOAT_QUAT_INV_COMP(qb2c2, qa2b, qa2c);
DISPLAY_FLOAT_QUAT("qb2c2", qb2c2);
return 0.;
}
float test_quat2(void)
{
struct FloatEulers eula2b;
EULERS_ASSIGN(eula2b, RadOfDeg(70.), RadOfDeg(0.), RadOfDeg(0.));
// DISPLAY_FLOAT_EULERS_DEG("eula2b", eula2b);
struct FloatQuat qa2b;
float_quat_of_eulers(&qa2b, &eula2b);
DISPLAY_FLOAT_QUAT("qa2b", qa2b);
struct DoubleEulers eula2b_d;
EULERS_ASSIGN(eula2b_d, RadOfDeg(70.), RadOfDeg(0.), RadOfDeg(0.));
struct DoubleQuat qa2b_d;
double_quat_of_eulers(&qa2b_d, &eula2b_d);
DISPLAY_FLOAT_QUAT("qa2b_d", qa2b_d);
struct FloatVect3 u = { 1., 0., 0.};
float angle = RadOfDeg(70.);
struct FloatQuat q;
FLOAT_QUAT_OF_AXIS_ANGLE(q, u, angle);
DISPLAY_FLOAT_QUAT("q ", q);
struct FloatEulers eula2c;
EULERS_ASSIGN(eula2c, RadOfDeg(80.), RadOfDeg(0.), RadOfDeg(0.));
// DISPLAY_FLOAT_EULERS_DEG("eula2c", eula2c);
struct FloatQuat qa2c;
float_quat_of_eulers(&qa2c, &eula2c);
DISPLAY_FLOAT_QUAT("qa2c", qa2c);
struct FloatQuat qb2a;
FLOAT_QUAT_INVERT(qb2a, qa2b);
DISPLAY_FLOAT_QUAT("qb2a", qb2a);
struct FloatQuat qb2c1;
float_quat_comp(&qb2c1, &qb2a, &qa2c);
DISPLAY_FLOAT_QUAT("qb2c1", qb2c1);
struct FloatQuat qb2c2;
float_quat_inv_comp(&qb2c2, &qa2b, &qa2c);
DISPLAY_FLOAT_QUAT("qb2c2", qb2c2);
return 0.;
}
float test_quat(void) {
struct FloatVect3 u = { 1., 2., 3.};
FLOAT_VECT3_NORMALIZE(u);
float angle = RadOfDeg(30.);
struct FloatQuat q;
FLOAT_QUAT_OF_AXIS_ANGLE(q, u, angle);
DISPLAY_FLOAT_QUAT("q ", q);
struct FloatQuat iq;
FLOAT_QUAT_INVERT(iq, q);
DISPLAY_FLOAT_QUAT("iq", iq);
struct FloatQuat q1;
FLOAT_QUAT_COMP(q1, q, iq);
DISPLAY_FLOAT_QUAT("q1", q1);
struct FloatQuat q2;
FLOAT_QUAT_COMP(q2, q, iq);
DISPLAY_FLOAT_QUAT("q2", q2);
struct FloatQuat qe;
QUAT_EXPLEMENTARY(qe, q);
DISPLAY_FLOAT_QUAT("qe", qe);
struct FloatVect3 a = { 2., 1., 3.};
DISPLAY_FLOAT_VECT3("a ", a);
struct FloatVect3 a1;
FLOAT_QUAT_VMULT(a1, q, a);
DISPLAY_FLOAT_VECT3("a1", a1);
struct FloatVect3 a2;
FLOAT_QUAT_VMULT(a2, qe, a);
DISPLAY_FLOAT_VECT3("a2", a2);
return 0.;
}
static void ahrs_do_update_mag(void) {
int i, j, k;
#ifdef BAFL_DEBUG2
printf("Mag update.\n");
#endif
MAGS_FLOAT_OF_BFP(bafl_mag, imu.mag);
/* P_prio = P */
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < BAFL_SSIZE; j++) {
bafl_Pprio[i][j] = bafl_P[i][j];
}
}
/*
* set up measurement matrix
*
* h = [236.; -2.; 396.];
* hx = [ h(2); -h(1); 0]; //only psi (phi and theta = 0)
* Hm = Cnb * hx;
* H = [ 0 0 0 0 0
* 0 0 Cnb*hx 0 0 0
* 0 0 0 0 0 ];
* */
/*bafl_H[0][2] = RMAT_ELMT(bafl_dcm, 0, 0) * bafl_h.y - RMAT_ELMT(bafl_dcm, 0, 1) * bafl_h.x;
bafl_H[1][2] = RMAT_ELMT(bafl_dcm, 1, 0) * bafl_h.y - RMAT_ELMT(bafl_dcm, 1, 1) * bafl_h.x;
bafl_H[2][2] = RMAT_ELMT(bafl_dcm, 2, 0) * bafl_h.y - RMAT_ELMT(bafl_dcm, 2, 1) * bafl_h.x;*/
bafl_H[0][2] = -RMAT_ELMT(bafl_dcm, 0, 1);
bafl_H[1][2] = -RMAT_ELMT(bafl_dcm, 1, 1);
bafl_H[2][2] = -RMAT_ELMT(bafl_dcm, 2, 1);
//rest is zero
/**********************************************
* compute Kalman gain K
*
* K = P_prio * H_T * inv(S)
* S = H * P_prio * HT + R
*
* K = P_prio * HT * inv(H * P_prio * HT + R)
*
**********************************************/
/* covariance residual S = H * P_prio * HT + R */
/* temp_S(3x6) = H(3x6) * P_prio(6x6)
*
* only third column of H is non-zero
*/
for (i = 0; i < 3; i++) {
for (j = 0; j < BAFL_SSIZE; j++) {
bafl_tempS[i][j] = bafl_H[i][2] * bafl_Pprio[2][j];
}
}
/* S(3x3) = temp_S(3x6) * HT(6x3) + R(3x3)
*
* only third row of HT is non-zero
*/
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
bafl_S[i][j] = bafl_tempS[i][2] * bafl_H[j][2]; /* H[j][2] = HT[2][j] */
}
bafl_S[i][i] += bafl_R_mag;
}
/* invert S
*/
FLOAT_MAT33_INVERT(bafl_invS, bafl_S);
/* temp_K(6x3) = P_prio(6x6) * HT(6x3)
*
* only third row of HT is non-zero
*/
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < 3; j++) {
/* not computing zero elements */
bafl_tempK[i][j] = bafl_Pprio[i][2] * bafl_H[j][2]; /* H[j][2] = HT[2][j] */
}
}
/* K(6x3) = temp_K(6x3) * invS(3x3)
*/
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < 3; j++) {
bafl_K[i][j] = bafl_tempK[i][0] * bafl_invS[0][j];
bafl_K[i][j] += bafl_tempK[i][1] * bafl_invS[1][j];
bafl_K[i][j] += bafl_tempK[i][2] * bafl_invS[2][j];
}
}
/**********************************************
* Update filter state.
*
* The a priori filter state is zero since the errors are corrected after each update.
*
* X = X_prio + K (y - H * X_prio)
* X = K * y
**********************************************/
/* innovation
* y = Cnb * [hx; hy; hz] - mag
*/
FLOAT_RMAT_VECT3_MUL(bafl_ym, bafl_dcm, bafl_h); //can be optimized
FLOAT_VECT3_SUB(bafl_ym, bafl_mag);
/* X(6) = K(6x3) * y(3)
*/
for (i = 0; i < BAFL_SSIZE; i++) {
bafl_X[i] = bafl_K[i][0] * bafl_ym.x;
bafl_X[i] += bafl_K[i][1] * bafl_ym.y;
bafl_X[i] += bafl_K[i][2] * bafl_ym.z;
}
/**********************************************
* Update the filter covariance.
*
* P = P_prio - K * H * P_prio
* P = ( I - K * H ) * P_prio
*
**********************************************/
/* temp(6x6) = I(6x6) - K(6x3)*H(3x6)
*
* last 3 columns of H are zero
*/
for (i = 0; i < 6; i++) {
for (j = 0; j < 6; j++) {
if (i == j) {
bafl_tempP[i][j] = 1.;
} else {
bafl_tempP[i][j] = 0.;
}
if (j == 2) { /* omit the parts where H is zero */
for (k = 0; k < 3; k++) {
bafl_tempP[i][j] -= bafl_K[i][k] * bafl_H[k][j];
}
}
}
}
/* P(6x6) = temp(6x6) * P_prio(6x6)
*/
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < BAFL_SSIZE; j++) {
bafl_P[i][j] = bafl_tempP[i][0] * bafl_Pprio[0][j];
for (k = 1; k < BAFL_SSIZE; k++) {
bafl_P[i][j] += bafl_tempP[i][k] * bafl_Pprio[k][j];
}
}
}
#ifdef LKF_PRINT_P
printf("Pum=");
for (i = 0; i < 6; i++) {
printf("[");
for (j = 0; j < 6; j++) {
printf("%f\t", bafl_P[i][j]);
}
printf("]\n ");
}
printf("\n");
#endif
/**********************************************
* Correct errors.
*
*
**********************************************/
/* Error quaternion.
*/
QUAT_ASSIGN(bafl_q_m_err, 1.0, bafl_X[0]/2, bafl_X[1]/2, bafl_X[2]/2);
FLOAT_QUAT_INVERT(bafl_q_m_err, bafl_q_m_err);
/* normalize */
float q_sq;
q_sq = bafl_q_m_err.qx * bafl_q_m_err.qx + bafl_q_m_err.qy * bafl_q_m_err.qy + bafl_q_m_err.qz * bafl_q_m_err.qz;
if (q_sq > 1) { /* this should actually never happen */
FLOAT_QUAT_SMUL(bafl_q_m_err, bafl_q_m_err, 1 / sqrtf(1 + q_sq));
printf("mag error quaternion q_sq > 1!!\n");
} else {
bafl_q_m_err.qi = sqrtf(1 - q_sq);
}
/* correct attitude
*/
FLOAT_QUAT_COMP(bafl_qtemp, bafl_q_m_err, bafl_quat);
FLOAT_QUAT_COPY(bafl_quat, bafl_qtemp);
/* correct gyro bias
*/
RATES_ASSIGN(bafl_b_m_err, bafl_X[3], bafl_X[4], bafl_X[5]);
RATES_SUB(bafl_bias, bafl_b_m_err);
/*
* compute all representations
*/
/* maintain rotation matrix representation */
FLOAT_RMAT_OF_QUAT(bafl_dcm, bafl_quat);
/* maintain euler representation */
FLOAT_EULERS_OF_RMAT(bafl_eulers, bafl_dcm);
AHRS_TO_BFP();
AHRS_LTP_TO_BODY();
}
static void ahrs_do_update_accel(void) {
int i, j, k;
#ifdef BAFL_DEBUG2
printf("Accel update.\n");
#endif
/* P_prio = P */
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < BAFL_SSIZE; j++) {
bafl_Pprio[i][j] = bafl_P[i][j];
}
}
/*
* set up measurement matrix
*
* g = 9.81
* gx = [ 0 -g 0
* g 0 0
* 0 0 0 ]
* H = [ 0 0 0 ]
* [ -Cnb*gx 0 0 0 ]
* [ 0 0 0 ]
*
* */
bafl_H[0][0] = -RMAT_ELMT(bafl_dcm, 0, 1) * BAFL_g;
bafl_H[0][1] = RMAT_ELMT(bafl_dcm, 0, 0) * BAFL_g;
bafl_H[1][0] = -RMAT_ELMT(bafl_dcm, 1, 1) * BAFL_g;
bafl_H[1][1] = RMAT_ELMT(bafl_dcm, 1, 0) * BAFL_g;
bafl_H[2][0] = -RMAT_ELMT(bafl_dcm, 2, 1) * BAFL_g;
bafl_H[2][1] = RMAT_ELMT(bafl_dcm, 2, 0) * BAFL_g;
/* rest is zero
bafl_H[0][2] = 0.;
bafl_H[1][2] = 0.;
bafl_H[2][2] = 0.;*/
/**********************************************
* compute Kalman gain K
*
* K = P_prio * H_T * inv(S)
* S = H * P_prio * HT + R
*
* K = P_prio * HT * inv(H * P_prio * HT + R)
*
**********************************************/
/* covariance residual S = H * P_prio * HT + R */
/* temp_S(3x6) = H(3x6) * P_prio(6x6)
* last 4 columns of H are zero
*/
for (i = 0; i < 3; i++) {
for (j = 0; j < BAFL_SSIZE; j++) {
bafl_tempS[i][j] = bafl_H[i][0] * bafl_Pprio[0][j];
bafl_tempS[i][j] += bafl_H[i][1] * bafl_Pprio[1][j];
}
}
/* S(3x3) = temp_S(3x6) * HT(6x3) + R(3x3)
*
* bottom 4 rows of HT are zero
*/
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
bafl_S[i][j] = bafl_tempS[i][0] * bafl_H[j][0]; /* H[j][0] = HT[0][j] */
bafl_S[i][j] += bafl_tempS[i][1] * bafl_H[j][1]; /* H[j][0] = HT[0][j] */
}
bafl_S[i][i] += bafl_R_accel;
}
/* invert S
*/
FLOAT_MAT33_INVERT(bafl_invS, bafl_S);
/* temp_K(6x3) = P_prio(6x6) * HT(6x3)
*
* bottom 4 rows of HT are zero
*/
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < 3; j++) {
/* not computing zero elements */
bafl_tempK[i][j] = bafl_Pprio[i][0] * bafl_H[j][0]; /* H[j][0] = HT[0][j] */
bafl_tempK[i][j] += bafl_Pprio[i][1] * bafl_H[j][1]; /* H[j][1] = HT[1][j] */
}
}
/* K(6x3) = temp_K(6x3) * invS(3x3)
*/
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < 3; j++) {
bafl_K[i][j] = bafl_tempK[i][0] * bafl_invS[0][j];
bafl_K[i][j] += bafl_tempK[i][1] * bafl_invS[1][j];
bafl_K[i][j] += bafl_tempK[i][2] * bafl_invS[2][j];
}
}
/**********************************************
* Update filter state.
*
* The a priori filter state is zero since the errors are corrected after each update.
*
* X = X_prio + K (y - H * X_prio)
* X = K * y
**********************************************/
/*printf("R = ");
for (i = 0; i < 3; i++) {
printf("[");
for (j = 0; j < 3; j++) {
printf("%f\t", RMAT_ELMT(bafl_dcm, i, j));
}
printf("]\n ");
}
printf("\n");*/
/* innovation
* y = Cnb * -[0; 0; g] - accel
*/
bafl_ya.x = -RMAT_ELMT(bafl_dcm, 0, 2) * BAFL_g - bafl_accel_measure.x;
bafl_ya.y = -RMAT_ELMT(bafl_dcm, 1, 2) * BAFL_g - bafl_accel_measure.y;
bafl_ya.z = -RMAT_ELMT(bafl_dcm, 2, 2) * BAFL_g - bafl_accel_measure.z;
/* X(6) = K(6x3) * y(3)
*/
for (i = 0; i < BAFL_SSIZE; i++) {
bafl_X[i] = bafl_K[i][0] * bafl_ya.x;
bafl_X[i] += bafl_K[i][1] * bafl_ya.y;
bafl_X[i] += bafl_K[i][2] * bafl_ya.z;
}
/**********************************************
* Update the filter covariance.
*
* P = P_prio - K * H * P_prio
* P = ( I - K * H ) * P_prio
*
**********************************************/
/* temp(6x6) = I(6x6) - K(6x3)*H(3x6)
*
* last 4 columns of H are zero
*/
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < BAFL_SSIZE; j++) {
if (i == j) {
bafl_tempP[i][j] = 1.;
} else {
bafl_tempP[i][j] = 0.;
}
if (j < 2) { /* omit the parts where H is zero */
for (k = 0; k < 3; k++) {
bafl_tempP[i][j] -= bafl_K[i][k] * bafl_H[k][j];
}
}
}
}
/* P(6x6) = temp(6x6) * P_prio(6x6)
*/
for (i = 0; i < BAFL_SSIZE; i++) {
for (j = 0; j < BAFL_SSIZE; j++) {
bafl_P[i][j] = bafl_tempP[i][0] * bafl_Pprio[0][j];
for (k = 1; k < BAFL_SSIZE; k++) {
bafl_P[i][j] += bafl_tempP[i][k] * bafl_Pprio[k][j];
}
}
}
#ifdef LKF_PRINT_P
printf("Pua=");
for (i = 0; i < 6; i++) {
printf("[");
for (j = 0; j < 6; j++) {
printf("%f\t", bafl_P[i][j]);
}
printf("]\n ");
}
printf("\n");
#endif
/**********************************************
* Correct errors.
*
*
**********************************************/
/* Error quaternion.
*/
QUAT_ASSIGN(bafl_q_a_err, 1.0, bafl_X[0]/2, bafl_X[1]/2, bafl_X[2]/2);
FLOAT_QUAT_INVERT(bafl_q_a_err, bafl_q_a_err);
/* normalize
* Is this needed? Or is the approximation good enough?*/
float q_sq;
q_sq = bafl_q_a_err.qx * bafl_q_a_err.qx + bafl_q_a_err.qy * bafl_q_a_err.qy + bafl_q_a_err.qz * bafl_q_a_err.qz;
if (q_sq > 1) { /* this should actually never happen */
FLOAT_QUAT_SMUL(bafl_q_a_err, bafl_q_a_err, 1 / sqrtf(1 + q_sq));
printf("Accel error quaternion q_sq > 1!!\n");
} else {
bafl_q_a_err.qi = sqrtf(1 - q_sq);
}
/* correct attitude
*/
FLOAT_QUAT_COMP(bafl_qtemp, bafl_q_a_err, bafl_quat);
FLOAT_QUAT_COPY(bafl_quat, bafl_qtemp);
/* correct gyro bias
*/
RATES_ASSIGN(bafl_b_a_err, bafl_X[3], bafl_X[4], bafl_X[5]);
RATES_SUB(bafl_bias, bafl_b_a_err);
/*
* compute all representations
*/
/* maintain rotation matrix representation */
FLOAT_RMAT_OF_QUAT(bafl_dcm, bafl_quat);
/* maintain euler representation */
FLOAT_EULERS_OF_RMAT(bafl_eulers, bafl_dcm);
AHRS_TO_BFP();
AHRS_LTP_TO_BODY();
}
