/**
* Incorporate one 3D vector measurement
*/
static inline void update_state(const struct FloatVect3 *i_expected, struct FloatVect3* b_measured, struct FloatVect3* noise) {
/* converted expected measurement from inertial to body frame */
struct FloatVect3 b_expected;
FLOAT_QUAT_VMULT(b_expected, ahrs_impl.ltp_to_imu_quat, *i_expected);
// S = HPH' + JRJ
float H[3][6] = {{ 0., -b_expected.z, b_expected.y, 0., 0., 0.},
{ b_expected.z, 0., -b_expected.x, 0., 0., 0.},
{-b_expected.y, b_expected.x, 0., 0., 0., 0.}};
float tmp[3][6];
MAT_MUL(3,6,6, tmp, H, ahrs_impl.P);
float S[3][3];
MAT_MUL_T(3,6,3, S, tmp, H);
/* add the measurement noise */
S[0][0] += noise->x;
S[1][1] += noise->y;
S[2][2] += noise->z;
float invS[3][3];
MAT_INV33(invS, S);
// K = PH'invS
float tmp2[6][3];
MAT_MUL_T(6,6,3, tmp2, ahrs_impl.P, H);
float K[6][3];
MAT_MUL(6,3,3, K, tmp2, invS);
// P = (I-KH)P
float tmp3[6][6];
MAT_MUL(6,3,6, tmp3, K, H);
float I6[6][6] = {{ 1., 0., 0., 0., 0., 0. },
{ 0., 1., 0., 0., 0., 0. },
{ 0., 0., 1., 0., 0., 0. },
{ 0., 0., 0., 1., 0., 0. },
{ 0., 0., 0., 0., 1., 0. },
{ 0., 0., 0., 0., 0., 1. }};
float tmp4[6][6];
MAT_SUB(6,6, tmp4, I6, tmp3);
float tmp5[6][6];
MAT_MUL(6,6,6, tmp5, tmp4, ahrs_impl.P);
memcpy(ahrs_impl.P, tmp5, sizeof(ahrs_impl.P));
// X = X + Ke
struct FloatVect3 e;
VECT3_DIFF(e, *b_measured, b_expected);
ahrs_impl.gibbs_cor.qx += K[0][0]*e.x + K[0][1]*e.y + K[0][2]*e.z;
ahrs_impl.gibbs_cor.qy += K[1][0]*e.x + K[1][1]*e.y + K[1][2]*e.z;
ahrs_impl.gibbs_cor.qz += K[2][0]*e.x + K[2][1]*e.y + K[2][2]*e.z;
ahrs_impl.gyro_bias.p += K[3][0]*e.x + K[3][1]*e.y + K[3][2]*e.z;
ahrs_impl.gyro_bias.q += K[4][0]*e.x + K[4][1]*e.y + K[4][2]*e.z;
ahrs_impl.gyro_bias.r += K[5][0]*e.x + K[5][1]*e.y + K[5][2]*e.z;
}
/**
* Fit a linear model from samples to target values.
* Effectively a wrapper for the pprz_svd_float and pprz_svd_solve_float functions.
*
* @param[in] targets The target values
* @param[in] samples The samples / feature vectors
* @param[in] D The dimensionality of the samples
* @param[in] count The number of samples
* @param[in] use_bias Whether to use the bias. Please note that params should always be of size D+1, but in case of no bias, the bias value is set to 0.
* @param[out] parameters* Parameters of the linear fit
* @param[out] fit_error* Total error of the fit
*/
void fit_linear_model(float *targets, int D, float (*samples)[D], uint16_t count, bool use_bias, float *params,
float *fit_error)
{
// We will solve systems of the form A x = b,
// where A = [nx(D+1)] matrix with entries [s1, ..., sD, 1] for each sample (1 is the bias)
// and b = [nx1] vector with the target values.
// x in the system are the parameters for the linear regression function.
// local vars for iterating, random numbers:
int sam, d;
uint16_t n_samples = count;
uint8_t D_1 = D + 1;
// ensure that n_samples is high enough to ensure a result for a single fit:
n_samples = (n_samples < D_1) ? D_1 : n_samples;
// n_samples should not be higher than count:
n_samples = (n_samples < count) ? n_samples : count;
// initialize matrices and vectors for the full point set problem:
// this is used for determining inliers
float _AA[count][D_1];
MAKE_MATRIX_PTR(AA, _AA, count);
float _targets_all[count][1];
MAKE_MATRIX_PTR(targets_all, _targets_all, count);
for (sam = 0; sam < count; sam++) {
for (d = 0; d < D; d++) {
AA[sam][d] = samples[sam][d];
}
if (use_bias) {
AA[sam][D] = 1.0f;
} else {
AA[sam][D] = 0.0f;
}
targets_all[sam][0] = targets[sam];
}
// decompose A in u, w, v with singular value decomposition A = u * w * vT.
// u replaces A as output:
float _parameters[D_1][1];
MAKE_MATRIX_PTR(parameters, _parameters, D_1);
float w[n_samples], _v[D_1][D_1];
MAKE_MATRIX_PTR(v, _v, D_1);
// solve the system:
pprz_svd_float(AA, w, v, count, D_1);
pprz_svd_solve_float(parameters, AA, w, v, targets_all, count, D_1, 1);
// used to determine the error of a set of parameters on the whole set:
float _bb[count][1];
MAKE_MATRIX_PTR(bb, _bb, count);
float _C[count][1];
MAKE_MATRIX_PTR(C, _C, count);
// error is determined on the entire set
// bb = AA * parameters:
MAT_MUL(count, D_1, 1, bb, AA, parameters);
// subtract bu_all: C = 0 in case of perfect fit:
MAT_SUB(count, 1, C, bb, targets_all);
*fit_error = 0;
for (sam = 0; sam < count; sam++) {
*fit_error += fabsf(C[sam][0]);
}
*fit_error /= count;
for (d = 0; d < D_1; d++) {
params[d] = parameters[d][0];
}
}
/**
* Analyze a linear flow field, retrieving information such as divergence, surface roughness, focus of expansion, etc.
* @param[in] vectors The optical flow vectors
* @param[in] count The number of optical flow vectors
* @param[in] error_threshold Error used to determine inliers / outliers.
* @param[in] n_iterations Number of RANSAC iterations.
* @param[in] n_samples Number of samples used for a single fit (min. 3).
* @param[out] parameters_u* Parameters of the horizontal flow field
* @param[out] parameters_v* Parameters of the vertical flow field
* @param[out] fit_error* Total error of the finally selected fit
* @param[out] min_error_u* Error fit horizontal flow field
* @param[out] min_error_v* Error fit vertical flow field
* @param[out] n_inliers_u* Number of inliers in the horizontal flow fit.
* @param[out] n_inliers_v* Number of inliers in the vertical flow fit.
*/
void fit_linear_flow_field(struct flow_t *vectors, int count, float error_threshold, int n_iterations, int n_samples, float *parameters_u, float *parameters_v, float *fit_error, float *min_error_u, float *min_error_v, int *n_inliers_u, int *n_inliers_v)
{
// We will solve systems of the form A x = b,
// where A = [nx3] matrix with entries [x, y, 1] for each optic flow location
// and b = [nx1] vector with either the horizontal (bu) or vertical (bv) flow.
// x in the system are the parameters for the horizontal (pu) or vertical (pv) flow field.
// local vars for iterating, random numbers:
int sam, p, i_rand, si, add_si;
// ensure that n_samples is high enough to ensure a result for a single fit:
n_samples = (n_samples < MIN_SAMPLES_FIT) ? MIN_SAMPLES_FIT : n_samples;
// n_samples should not be higher than count:
n_samples = (n_samples < count) ? n_samples : count;
// initialize matrices and vectors for the full point set problem:
// this is used for determining inliers
float _AA[count][3];
MAKE_MATRIX_PTR(AA, _AA, count);
float _bu_all[count][1];
MAKE_MATRIX_PTR(bu_all, _bu_all, count);
float _bv_all[count][1];
MAKE_MATRIX_PTR(bv_all, _bv_all, count);
for (sam = 0; sam < count; sam++) {
AA[sam][0] = (float) vectors[sam].pos.x;
AA[sam][1] = (float) vectors[sam].pos.y;
AA[sam][2] = 1.0f;
bu_all[sam][0] = (float) vectors[sam].flow_x;
bv_all[sam][0] = (float) vectors[sam].flow_y;
}
// later used to determine the error of a set of parameters on the whole set:
float _bb[count][1];
MAKE_MATRIX_PTR(bb, _bb, count);
float _C[count][1];
MAKE_MATRIX_PTR(C, _C, count);
// ***************
// perform RANSAC:
// ***************
// set up variables for small linear system solved repeatedly inside RANSAC:
float _A[n_samples][3];
MAKE_MATRIX_PTR(A, _A, n_samples);
float _bu[n_samples][1];
MAKE_MATRIX_PTR(bu, _bu, n_samples);
float _bv[n_samples][1];
MAKE_MATRIX_PTR(bv, _bv, n_samples);
float w[n_samples], _v[3][3];
MAKE_MATRIX_PTR(v, _v, 3);
float _pu[3][1];
MAKE_MATRIX_PTR(pu, _pu, 3);
float _pv[3][1];
MAKE_MATRIX_PTR(pv, _pv, 3);
// iterate and store parameters, errors, inliers per fit:
float PU[n_iterations * 3];
float PV[n_iterations * 3];
float errors_pu[n_iterations];
errors_pu[0] = 0.0;
float errors_pv[n_iterations];
errors_pv[0] = 0.0;
int n_inliers_pu[n_iterations];
int n_inliers_pv[n_iterations];
int it, ii;
for (it = 0; it < n_iterations; it++) {
// select a random sample of n_sample points:
int sample_indices[n_samples];
i_rand = 0;
// sampling without replacement:
while (i_rand < n_samples) {
si = rand() % count;
add_si = 1;
for (ii = 0; ii < i_rand; ii++) {
if (sample_indices[ii] == si) { add_si = 0; }
}
if (add_si) {
sample_indices[i_rand] = si;
i_rand ++;
}
}
// Setup the system:
for (sam = 0; sam < n_samples; sam++) {
A[sam][0] = (float) vectors[sample_indices[sam]].pos.x;
A[sam][1] = (float) vectors[sample_indices[sam]].pos.y;
A[sam][2] = 1.0f;
bu[sam][0] = (float) vectors[sample_indices[sam]].flow_x;
bv[sam][0] = (float) vectors[sample_indices[sam]].flow_y;
//printf("%d,%d,%d,%d,%d\n",A[sam][0],A[sam][1],A[sam][2],bu[sam][0],bv[sam][0]);
}
// Solve the small system:
// for horizontal flow:
// decompose A in u, w, v with singular value decomposition A = u * w * vT.
// u replaces A as output:
pprz_svd_float(A, w, v, n_samples, 3);
pprz_svd_solve_float(pu, A, w, v, bu, n_samples, 3, 1);
PU[it * 3] = pu[0][0];
PU[it * 3 + 1] = pu[1][0];
PU[it * 3 + 2] = pu[2][0];
// for vertical flow:
pprz_svd_solve_float(pv, A, w, v, bv, n_samples, 3, 1);
PV[it * 3] = pv[0][0];
PV[it * 3 + 1] = pv[1][0];
PV[it * 3 + 2] = pv[2][0];
// count inliers and determine their error on all points:
errors_pu[it] = 0;
errors_pv[it] = 0;
n_inliers_pu[it] = 0;
n_inliers_pv[it] = 0;
// for horizontal flow:
// bb = AA * pu:
MAT_MUL(count, 3, 1, bb, AA, pu);
// subtract bu_all: C = 0 in case of perfect fit:
MAT_SUB(count, 1, C, bb, bu_all);
for (p = 0; p < count; p++) {
C[p][0] = abs(C[p][0]);
if (C[p][0] < error_threshold) {
errors_pu[it] += C[p][0];
n_inliers_pu[it]++;
} else {
errors_pu[it] += error_threshold;
}
}
// for vertical flow:
// bb = AA * pv:
MAT_MUL(count, 3, 1, bb, AA, pv);
// subtract bv_all: C = 0 in case of perfect fit:
MAT_SUB(count, 1, C, bb, bv_all);
for (p = 0; p < count; p++) {
C[p][0] = abs(C[p][0]);
if (C[p][0] < error_threshold) {
errors_pv[it] += C[p][0];
n_inliers_pv[it]++;
} else {
errors_pv[it] += error_threshold;
}
}
}
// After all iterations:
// select the parameters with lowest error:
// for horizontal flow:
int param;
int min_ind = 0;
*min_error_u = (float)errors_pu[0];
for (it = 1; it < n_iterations; it++) {
if (errors_pu[it] < *min_error_u) {
*min_error_u = (float)errors_pu[it];
min_ind = it;
}
}
for (param = 0; param < 3; param++) {
parameters_u[param] = PU[min_ind * 3 + param];
}
*n_inliers_u = n_inliers_pu[min_ind];
// for vertical flow:
min_ind = 0;
*min_error_v = (float)errors_pv[0];
for (it = 0; it < n_iterations; it++) {
if (errors_pv[it] < *min_error_v) {
*min_error_v = (float)errors_pv[it];
min_ind = it;
}
}
for (param = 0; param < 3; param++) {
parameters_v[param] = PV[min_ind * 3 + param];
}
*n_inliers_v = n_inliers_pv[min_ind];
// error has to be determined on the entire set without threshold:
// bb = AA * pu:
MAT_MUL(count, 3, 1, bb, AA, pu);
// subtract bu_all: C = 0 in case of perfect fit:
MAT_SUB(count, 1, C, bb, bu_all);
*min_error_u = 0;
for (p = 0; p < count; p++) {
*min_error_u += abs(C[p][0]);
}
// bb = AA * pv:
MAT_MUL(count, 3, 1, bb, AA, pv);
// subtract bv_all: C = 0 in case of perfect fit:
MAT_SUB(count, 1, C, bb, bv_all);
*min_error_v = 0;
for (p = 0; p < count; p++) {
*min_error_v += abs(C[p][0]);
}
*fit_error = (*min_error_u + *min_error_v) / (2 * count);
}
