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Switch Kálmán filters to use Joseph form #1048

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Switch Kálmán filters to use Joseph form #1048

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13 changes: 11 additions & 2 deletions core/include/traccc/fitting/kalman_filter/gain_matrix_updater.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -121,7 +121,10 @@ struct gain_matrix_updater {
// Calculate the filtered track parameters
const matrix_type<6, 1> filtered_vec =
predicted_vec + K * (meas_local - H * predicted_vec);
const matrix_type<6, 6> filtered_cov = (I66 - K * H) * predicted_cov;
const matrix_type<6, 6> i_minus_kh = I66 - K * H;
const matrix_type<6, 6> filtered_cov =
i_minus_kh * predicted_cov * matrix::transpose(i_minus_kh) +
K * V * matrix::transpose(K);

// Return false if track is parallel to z-axis or phi is not finite
if (!std::isfinite(getter::element(filtered_vec, e_bound_theta, 0))) {
Expand All @@ -141,7 +144,13 @@ struct gain_matrix_updater {
const matrix_type<D, 1> residual = meas_local - H * filtered_vec;

// Calculate the chi square
const matrix_type<D, D> R = (I_m - H * K) * V;
const matrix_type<D, D> i_minus_hk = I_m - H * K;
// See
// https://indico.cern.ch/event/1564924/contributions/6629447/attachments/3113201/5519076/asami_250731_acts.pdf
const matrix_type<D, D> R =
i_minus_hk * V * matrix::transpose(i_minus_hk) +
H * i_minus_kh * predicted_cov * matrix::transpose(i_minus_kh) *
matrix::transpose(H);
const matrix_type<1, 1> chi2 =
algebra::matrix::transposed_product<true, false>(
residual, matrix::inverse(R)) *
Expand Down
15 changes: 12 additions & 3 deletions core/include/traccc/fitting/kalman_filter/two_filters_smoother.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -197,7 +197,10 @@ struct two_filters_smoother {
// Calculate the filtered track parameters
const matrix_type<6, 1> filtered_vec =
predicted_vec + K * (meas_local - H * predicted_vec);
const matrix_type<6, 6> filtered_cov = (I66 - K * H) * predicted_cov;
const matrix_type<6, 6> i_minus_kh = I66 - K * H;
const matrix_type<6, 6> filtered_cov =
i_minus_kh * predicted_cov * matrix::transpose(i_minus_kh) +
K * V * matrix::transpose(K);

// Update the bound track parameters
bound_params.set_vector(filtered_vec);
Expand All @@ -221,8 +224,14 @@ struct two_filters_smoother {
const matrix_type<D, 1> residual = meas_local - H * filtered_vec;

// Calculate backward chi2
const matrix_type<D, D> R = (I_m - H * K) * V;
// assert(matrix::determinant(R) != 0.f); // @TODO: This fails
const matrix_type<D, D> i_minus_hk = I_m - H * K;
// See
// https://indico.cern.ch/event/1564924/contributions/6629447/attachments/3113201/5519076/asami_250731_acts.pdf
const matrix_type<D, D> R =
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@niermann999 niermann999 Nov 7, 2025

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Should something like this also be done for R_smt? Or does that not make sense, since the smoothed covariance is calculated differently?

i_minus_hk * V * matrix::transpose(i_minus_hk) +
H * i_minus_kh * predicted_cov * matrix::transpose(i_minus_kh) *
matrix::transpose(H);
// assert(matrix::determinant(R) != 0.f);
assert(std::isfinite(matrix::determinant(R)));
const matrix_type<1, 1> chi2 =
algebra::matrix::transposed_product<true, false>(
Expand Down
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