/** * 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); }