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Diffstat (limited to 'filter-kalman/kalman.cpp')
| -rw-r--r-- | filter-kalman/kalman.cpp | 338 |
1 files changed, 252 insertions, 86 deletions
diff --git a/filter-kalman/kalman.cpp b/filter-kalman/kalman.cpp index 1f23ed90..6ed5ca91 100644 --- a/filter-kalman/kalman.cpp +++ b/filter-kalman/kalman.cpp @@ -1,81 +1,220 @@ -/* Copyright (c) 2013 Stanislaw Halik <sthalik@misaki.pl> +/* Copyright (c) 2016 Michael Welter <mw.pub@welter-4d.de> * * Permission to use, copy, modify, and/or distribute this software for any * purpose with or without fee is hereby granted, provided that the above * copyright notice and this permission notice appear in all copies. */ -#include "ftnoir_filter_kalman.h" -#include "opentrack/plugin-api.hpp" +#include "kalman.h" #include <QDebug> #include <cmath> -constexpr double settings::mult_noise_stddev; +constexpr double settings::adaptivity_window_length; +constexpr double settings::deadzone_scale; +constexpr double settings::deadzone_exponent; +constexpr double settings::process_sigma_pos; +constexpr double settings::process_simga_rot; + +void KalmanFilter::init() +{ + // allocate and initialize matrices + measurement_noise_cov = MeasureMatrix::Zero(); + process_noise_cov = StateMatrix::Zero(); + state_cov = StateMatrix::Zero(); + state_cov_prior = StateMatrix::Zero(); + transition_matrix = StateMatrix::Zero(); + measurement_matrix = StateToMeasureMatrix::Zero(); + kalman_gain = MeasureToStateMatrix::Zero(); + // initialize state variables + state = StateVector::Zero(); + state_prior = StateVector::Zero(); + innovation = PoseVector::Zero(); +} + + +void KalmanFilter::time_update() +{ + state_prior = transition_matrix * state; + state_cov_prior = transition_matrix * state_cov * transition_matrix.transpose() + process_noise_cov; +} + + +void KalmanFilter::measurement_update(const PoseVector &measurement) +{ + MeasureMatrix tmp = measurement_matrix * state_cov_prior * measurement_matrix.transpose() + measurement_noise_cov; + MeasureMatrix tmp_inv = tmp.inverse(); + kalman_gain = state_cov_prior * measurement_matrix.transpose() * tmp_inv; + innovation = measurement - measurement_matrix * state_prior; + state = state_prior + kalman_gain * innovation; + state_cov = state_cov_prior - kalman_gain * measurement_matrix * state_cov_prior; +} + + + +void KalmanProcessNoiseScaler::init() +{ + base_cov = StateMatrix::Zero(NUM_STATE_DOF, NUM_STATE_DOF); + innovation_cov_estimate = MeasureMatrix::Zero(NUM_MEASUREMENT_DOF, NUM_MEASUREMENT_DOF); +} + + +/* Uses + innovation, measurement_matrix, measurement_noise_cov, and state_cov_prior + found in KalmanFilter. It sets + process_noise_cov +*/ +void KalmanProcessNoiseScaler::update(KalmanFilter &kf, double dt) +{ + MeasureMatrix ddT = kf.innovation * kf.innovation.transpose(); + double f = dt / (dt + settings::adaptivity_window_length); + innovation_cov_estimate = + f * ddT + (1. - f) * innovation_cov_estimate; + + double T1 = (innovation_cov_estimate - kf.measurement_noise_cov).trace(); + double T2 = (kf.measurement_matrix * kf.state_cov_prior * kf.measurement_matrix.transpose()).trace(); + double alpha = 0.001; + if (T2 > 0. && T1 > 0.) + { + alpha = T1 / T2; + alpha = std::sqrt(alpha); + alpha = std::min(1000., std::max(0.001, alpha)); + } + kf.process_noise_cov = alpha * base_cov; + //qDebug() << "alpha = " << alpha; +} + + +PoseVector DeadzoneFilter::filter(const PoseVector &input) +{ + PoseVector out; + for (int i = 0; i < input.rows(); ++i) + { + const double dz = dz_size[i]; + if (dz > 0.) + { + const double delta = input[i] - last_output[i]; + const double f = std::pow(std::fabs(delta) / dz, settings::deadzone_exponent); + const double response = f / (f + 1.) * delta; + out[i] = last_output[i] + response; + } + else + out[i] = input[i]; + last_output[i] = out[i]; + } + return out; +} + + +void FTNoIR_Filter::fill_transition_matrix(double dt) +{ + for (int i = 0; i < 6; ++i) + { + kf.transition_matrix(i, i + 6) = dt; + } +} + +void FTNoIR_Filter::fill_process_noise_cov_matrix(StateMatrix &target, double dt) const +{ + // This model is like movement at fixed velocity plus superimposed + // brownian motion. Unlike standard models for tracking of objects + // with a very well predictable trajectory (e.g. + // https://en.wikipedia.org/wiki/Kalman_filter#Example_application.2C_technical) + double sigma_pos = s.process_sigma_pos; + double sigma_angle = s.process_simga_rot; + double a_pos = sigma_pos * sigma_pos * dt; + double a_ang = sigma_angle * sigma_angle * dt; + static constexpr double b = 20; + static constexpr double c = 1.; + for (int i = 0; i < 3; ++i) + { + target(i, i) = a_pos; + target(i, i + 6) = a_pos * c; + target(i + 6, i) = a_pos * c; + target(i + 6, i + 6) = a_pos * b; + } + for (int i = 3; i < 6; ++i) + { + target(i, i) = a_ang; + target(i, i + 6) = a_ang * c; + target(i + 6, i) = a_ang * c; + target(i + 6, i + 6) = a_ang * b; + } +} + + +PoseVector FTNoIR_Filter::do_kalman_filter(const PoseVector &input, double dt, bool new_input) +{ + if (new_input) + { + dt = dt_since_last_input; + fill_transition_matrix(dt); + fill_process_noise_cov_matrix(kf_adaptive_process_noise_cov.base_cov, dt); + kf_adaptive_process_noise_cov.update(kf, dt); + kf.time_update(); + kf.measurement_update(input); + } + return kf.state.head(6); +} + + FTNoIR_Filter::FTNoIR_Filter() { reset(); - prev_slider_pos = s.noise_stddev_slider; } -// the following was written by Donovan Baarda <abo@minkirri.apana.org.au> +// The original code was written by Donovan Baarda <abo@minkirri.apana.org.au> // https://sourceforge.net/p/facetracknoir/discussion/1150909/thread/418615e1/?limit=25#af75/084b -void FTNoIR_Filter::reset() { - // Setup kalman with state (x) is the 6 tracker outputs then - // their 6 corresponding velocities, and the measurement (z) is - // the 6 tracker outputs. - kalman.init(12, 6, 0, CV_64F); - // Initialize the transitionMatrix and processNoiseCov for - // dt=0.1. This needs to be updated each frame for the real dt - // value, but this hows you what they should look like. See - // http://en.wikipedia.org/wiki/Kalman_filter#Example_application.2C_technical - double dt = 0.1; - kalman.transitionMatrix = (cv::Mat_<double>(12, 12) << - 1, 0, 0, 0, 0, 0, dt, 0, 0, 0, 0, 0, - 0, 1, 0, 0, 0, 0, 0, dt, 0, 0, 0, 0, - 0, 0, 1, 0, 0, 0, 0, 0, dt, 0, 0, 0, - 0, 0, 0, 1, 0, 0, 0, 0, 0, dt, 0, 0, - 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, dt, 0, - 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, dt, - 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1); - double accel_variance = accel_stddev * accel_stddev; - double a = dt * dt * accel_variance; // dt^2 * accel_variance. - double b = 0.5 * a * dt; // (dt^3)/2 * accel_variance. - double c = 0.5 * b * dt; // (dt^4)/4 * accel_variance. - kalman.processNoiseCov = (cv::Mat_<double>(12, 12) << - c, 0, 0, 0, 0, 0, b, 0, 0, 0, 0, 0, - 0, c, 0, 0, 0, 0, 0, b, 0, 0, 0, 0, - 0, 0, c, 0, 0, 0, 0, 0, b, 0, 0, 0, - 0, 0, 0, c, 0, 0, 0, 0, 0, b, 0, 0, - 0, 0, 0, 0, c, 0, 0, 0, 0, 0, b, 0, - 0, 0, 0, 0, 0, c, 0, 0, 0, 0, 0, b, - b, 0, 0, 0, 0, 0, a, 0, 0, 0, 0, 0, - 0, b, 0, 0, 0, 0, 0, a, 0, 0, 0, 0, - 0, 0, b, 0, 0, 0, 0, 0, a, 0, 0, 0, - 0, 0, 0, b, 0, 0, 0, 0, 0, a, 0, 0, - 0, 0, 0, 0, b, 0, 0, 0, 0, 0, a, 0, - 0, 0, 0, 0, 0, b, 0, 0, 0, 0, 0, a); - cv::setIdentity(kalman.measurementMatrix); - const double noise_stddev = (1+s.noise_stddev_slider) * s.mult_noise_stddev; - const double noise_variance = noise_stddev * noise_stddev; - cv::setIdentity(kalman.measurementNoiseCov, cv::Scalar::all(noise_variance)); - cv::setIdentity(kalman.errorCovPost, cv::Scalar::all(accel_variance * 1e4)); +void FTNoIR_Filter::reset() +{ + kf.init(); + kf_adaptive_process_noise_cov.init(); + for (int i = 0; i < 6; ++i) + { + // initialize part of the transition matrix that do not change. + kf.transition_matrix(i, i) = 1.; + kf.transition_matrix(i + 6, i + 6) = 1.; + // "extract" positions, i.e. the first 6 state dof. + kf.measurement_matrix(i, i) = 1.; + } + + double noise_variance_position = settings::map_slider_value(s.noise_pos_slider_value); + double noise_variance_angle = settings::map_slider_value(s.noise_rot_slider_value); + for (int i = 0; i < 3; ++i) + { + kf.measurement_noise_cov(i , i ) = noise_variance_position; + kf.measurement_noise_cov(i + 3, i + 3) = noise_variance_angle; + } + + fill_transition_matrix(0.03); + fill_process_noise_cov_matrix(kf_adaptive_process_noise_cov.base_cov, 0.03); + + kf.process_noise_cov = kf_adaptive_process_noise_cov.base_cov; + kf.state_cov = kf.process_noise_cov; + for (int i = 0; i < 6; i++) { last_input[i] = 0; } first_run = true; + dt_since_last_input = 0; + + prev_slider_pos[0] = static_cast<slider_value>(s.noise_pos_slider_value); + prev_slider_pos[1] = static_cast<slider_value>(s.noise_rot_slider_value); + + dz_filter.reset(); } -void FTNoIR_Filter::filter(const double* input, double *output) + +void FTNoIR_Filter::filter(const double* input_, double *output_) { - if (prev_slider_pos != s.noise_stddev_slider) + // almost non-existent cost, so might as well ... + Eigen::Map<const PoseVector> input(input_, PoseVector::RowsAtCompileTime, 1); + Eigen::Map<PoseVector> output(output_, PoseVector::RowsAtCompileTime, 1); + + if (!(prev_slider_pos[0] == s.noise_pos_slider_value && + prev_slider_pos[1] == s.noise_rot_slider_value)) { reset(); - prev_slider_pos = s.noise_stddev_slider; } + // Start the timer on first filter evaluation. if (first_run) { @@ -84,54 +223,81 @@ void FTNoIR_Filter::filter(const double* input, double *output) return; } + // Note this is a terrible way to detect when there is a new + // frame of tracker input, but it is the best we have. + bool new_input = input.cwiseNotEqual(last_input).any(); + // Get the time in seconds since last run and restart the timer. const double dt = timer.elapsed_seconds(); + dt_since_last_input += dt; timer.start(); - // Note this is a terrible way to detect when there is a new - // frame of tracker input, but it is the best we have. - bool new_input = false; - for (int i = 0; i < 6 && !new_input; i++) - new_input = (input[i] != last_input[i]); - - // Update the transitionMatrix and processNoiseCov for dt. - double accel_variance = accel_stddev * accel_stddev; - double a = dt * dt * accel_variance; // dt^2 * accel_variance. - double b = 0.5 * a * dt; // (dt^3)/2 * accel_variance. - double c = 0.5 * b * dt; // (dt^4)/4 * accel_variance. - for (int i = 0; i < 6; i++) { - kalman.transitionMatrix.at<double>(i,i+6) = dt; - kalman.processNoiseCov.at<double>(i,i) = c; - kalman.processNoiseCov.at<double>(i+6,i+6) = a; - kalman.processNoiseCov.at<double>(i,i+6) = b; - kalman.processNoiseCov.at<double>(i+6,i) = b; - } - // Get the updated predicted position. - cv::Mat next_output = kalman.predict(); - // If we have new tracker input, get the corrected position. - if (new_input) { - cv::Mat measurement(6, 1, CV_64F); - for (int i = 0; i < 6; i++) { - measurement.at<double>(i) = input[i]; - // Save last_input for detecting new tracker input. - last_input[i] = input[i]; - } - next_output = kalman.correct(measurement); + output = do_kalman_filter(input, dt, new_input); + + { + // Compute deadzone size base on estimated state variance. + // Given a constant input plus measurement noise, KF should converge to the true input. + // This works well. That is the output pose becomes very still afte some time. + // The QScaling adaptive filter makes the state cov vary depending on the estimated noise + // and the measured noise of the innovation sequence. After a sudden movement it peaks + // and then decays asymptotically to some constant value taken in stationary state. + // We can use this to calculate the size of the deadzone, so that in the stationary state the + // deadzone size is small. Thus the tracking error due to the dz-filter becomes also small. + PoseVector variance = kf.state_cov.diagonal().head(6); + dz_filter.dz_size = variance.cwiseSqrt() * s.deadzone_scale; } - // Set output to the next_output. - for (int i = 0; i < 6; i++) { - output[i] = next_output.at<double>(i); + output = dz_filter.filter(output); + + if (new_input) + { + dt_since_last_input = 0; + last_input = input; } } + + +FilterControls::FilterControls() + : filter(nullptr) +{ + ui.setupUi(this); + connect(ui.buttonBox, SIGNAL(accepted()), this, SLOT(doOK())); + connect(ui.buttonBox, SIGNAL(rejected()), this, SLOT(doCancel())); + + tie_setting(s.noise_rot_slider_value, ui.noiseRotSlider); + tie_setting(s.noise_pos_slider_value, ui.noisePosSlider); + + connect(&s.noise_rot_slider_value, SIGNAL(valueChanged(const slider_value&)), this, SLOT(updateLabels(const slider_value&))); + connect(&s.noise_pos_slider_value, SIGNAL(valueChanged(const slider_value&)), this, SLOT(updateLabels(const slider_value&))); + + updateLabels(slider_value()); +} + + +void FilterControls::updateLabels(const slider_value&) +{ + // M$ hates unicode! (M$ autoconverts source code of one kind of utf-8 format, + // the one without BOM, to another kind that QT does not like) + // Previous attempt to use c++11 utf8 strings like u8" °" now failed for unkown + // reasons where it worked before. Hence fallback to QChar(0x00b0). + this->ui.noiseRotLabel->setText( + QString::number(settings::map_slider_value(s.noise_rot_slider_value), 'f', 3) + " " + QChar(0x00b0)); + + this->ui.noisePosLabel->setText( + QString::number(settings::map_slider_value(s.noise_pos_slider_value), 'f', 3) + " cm"); +} + + void FilterControls::doOK() { s.b->save(); close(); } + void FilterControls::doCancel() { close(); } + OPENTRACK_DECLARE_FILTER(FTNoIR_Filter, FilterControls, FTNoIR_FilterDll) |