diff --git a/src/algorithms/tracking/libs/CMakeLists.txt b/src/algorithms/tracking/libs/CMakeLists.txt index 3f772f149..fb816d0d8 100644 --- a/src/algorithms/tracking/libs/CMakeLists.txt +++ b/src/algorithms/tracking/libs/CMakeLists.txt @@ -33,6 +33,7 @@ set(TRACKING_LIB_SOURCES cpu_multicorrelator.cc cpu_multicorrelator_real_codes.cc cpu_multicorrelator_16sc.cc + cubature_filter.cc lock_detectors.cc tcp_communication.cc tcp_packet_data.cc @@ -50,6 +51,7 @@ set(TRACKING_LIB_HEADERS cpu_multicorrelator.h cpu_multicorrelator_real_codes.h cpu_multicorrelator_16sc.h + cubature_filter.h lock_detectors.h tcp_communication.h tcp_packet_data.h diff --git a/src/algorithms/tracking/libs/cubature_filter.cc b/src/algorithms/tracking/libs/cubature_filter.cc new file mode 100644 index 000000000..05b346a7c --- /dev/null +++ b/src/algorithms/tracking/libs/cubature_filter.cc @@ -0,0 +1,190 @@ +/*! + * \file cubature_filter.cc + * \brief Interface of a library with Bayesian noise statistic estimation + * + * Cubature_Filter implements the functionality of the Cubature Kalman + * Filter, which uses multidimensional cubature rules to estimate the + * time evolution of a nonlinear system. + * + * [1] I Arasaratnam and S Haykin. Cubature kalman filters. IEEE + * Transactions on Automatic Control, 54(6):1254–1269,2009. + * + * \authors + * ------------------------------------------------------------------------- + * + * Copyright (C) 2010-2019 (see AUTHORS file for a list of contributors) + * + * GNSS-SDR is a software defined Global Navigation + * Satellite Systems receiver + * + * This file is part of GNSS-SDR. + * + * GNSS-SDR is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * GNSS-SDR is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with GNSS-SDR. If not, see . + * + * ------------------------------------------------------------------------- + */ + +#include "cubature_filter.h" + + +Cubature_filter::Cubature_filter() +{ + int nx = 1; + x_pred_out = arma::zeros(nx, 1); + P_x_pred_out = arma::eye(nx, nx) * (nx + 1); + + x_est = x_pred_out; + P_x_est = P_x_pred_out; +} + +Cubature_filter::Cubature_filter(int nx) +{ + x_pred_out = arma::zeros(nx, 1); + P_x_pred_out = arma::eye(nx, nx) * (nx + 1); + + x_est = x_pred_out; + P_x_est = P_x_pred_out; +} + +Cubature_filter::Cubature_filter(const arma::vec& x_pred_0, const arma::mat& P_x_pred_0) +{ + x_pred_out = x_pred_0; + P_x_pred_out = P_x_pred_0; + + x_est = x_pred_out; + P_x_est = P_x_pred_out; +} + +Cubature_filter::~Cubature_filter() = default; + +void Cubature_filter::initialize(const arma::mat& x_pred_0, const arma::mat& P_x_pred_0) +{ + x_pred_out = x_pred_0; + P_x_pred_out = P_x_pred_0; + + x_est = x_pred_out; + P_x_est = P_x_pred_out; +} + + +/* + * Perform the prediction step of the cubature Kalman filter + */ +void Cubature_filter::predict_sequential(const arma::vec& x_post, const arma::mat& P_x_post, Model_Function* transition_fcn, const arma::mat& noise_covariance) +{ + // Compute number of cubature points + int nx = x_post.n_elem; + int np = 2 * nx; + + // Generator Matrix + arma::mat gen_one = arma::join_horiz(arma::eye(nx,nx),-1.0*arma::eye(nx,nx)); + + // Initialize predicted mean and covariance + arma::vec x_pred = arma::zeros(nx,1); + arma::mat P_x_pred = arma::zeros(nx,nx); + + // Factorize posterior covariance + arma::mat Sm_post = arma::chol(P_x_post, "lower"); + + // Propagate and evaluate cubature points + arma::vec Xi_post; + arma::vec Xi_pred; + + for (uint8_t i = 0; i < np; i++) + { + Xi_post = Sm_post * (std::sqrt(((float) np) / 2.0) * gen_one.col(i)) + x_post; + Xi_pred = (*transition_fcn)(Xi_post); + + x_pred = x_pred + Xi_pred; + P_x_pred = P_x_pred + Xi_pred*Xi_pred.t(); + } + + // Estimate predicted state and error covariance + x_pred = x_pred / ((float) np); + P_x_pred = P_x_pred / ((float) np) - x_pred*x_pred.t() + noise_covariance; + + // Store predicted state and error covariance + x_pred_out = x_pred; + P_x_pred_out = P_x_pred; +} + +/* + * Perform the update step of the cubature Kalman filter + */ +void Cubature_filter::update_sequential(const arma::vec& z_upd, const arma::vec& x_pred, const arma::mat& P_x_pred, Model_Function* measurement_fcn, const arma::mat& noise_covariance) +{ + // Compute number of cubature points + int nx = x_pred.n_elem; + int nz = z_upd.n_elem; + int np = 2 * nx; + + // Generator Matrix + arma::mat gen_one = arma::join_horiz(arma::eye(nx,nx),-1.0*arma::eye(nx,nx)); + + // Evaluate predicted measurement and covariances + arma::mat z_pred = arma::zeros(nz,1); + arma::mat P_zz_pred = arma::zeros(nz,nz); + arma::mat P_xz_pred = arma::zeros(nx,nz); + + // Factorize predicted covariance + arma::mat Sm_pred = arma::chol(P_x_pred, "lower"); + + // Propagate and evaluate cubature points + arma::vec Xi_pred; + arma::vec Zi_pred; + for (uint8_t i = 0; i < np; i++) + { + Xi_pred = Sm_pred * (std::sqrt(((float) np) / 2.0) * gen_one.col(i)) + x_pred; + Zi_pred = (*measurement_fcn)(Xi_pred); + + z_pred = z_pred + Zi_pred; + P_zz_pred = P_zz_pred + Zi_pred*Zi_pred.t(); + P_xz_pred = P_xz_pred + Xi_pred*Zi_pred.t(); + } + + // Estimate measurement covariance and cross covariances + z_pred = z_pred / ((float) np); + P_zz_pred = P_zz_pred / ((float) np) - z_pred*z_pred.t() + noise_covariance; + P_xz_pred = P_xz_pred / ((float) np) - x_pred*z_pred.t(); + + // Estimate cubature Kalman gain + arma::mat W_k = P_xz_pred*arma::inv(P_zz_pred); + + // Estimate and store the updated state and error covariance + x_est = x_pred + W_k*(z_upd - z_pred); + P_x_est = P_x_pred - W_k*P_zz_pred*W_k.t(); +} + +arma::mat Cubature_filter::get_x_pred() const +{ + return x_pred_out; +} + +arma::mat Cubature_filter::get_P_x_pred() const +{ + return P_x_pred_out; +} + +arma::mat Cubature_filter::get_x_est() const +{ + return x_est; +} + +arma::mat Cubature_filter::get_P_x_est() const +{ + return P_x_est; +} diff --git a/src/algorithms/tracking/libs/cubature_filter.h b/src/algorithms/tracking/libs/cubature_filter.h new file mode 100644 index 000000000..6a0806e0e --- /dev/null +++ b/src/algorithms/tracking/libs/cubature_filter.h @@ -0,0 +1,84 @@ +/*! + * \file cubature_filter.h + * \brief Interface of a library with Bayesian noise statistic estimation + * + * Cubature_Filter implements the functionality of the Cubature Kalman + * Filter, which uses multidimensional cubature rules to estimate the + * time evolution of a nonlinear system. + * + * [1] I Arasaratnam and S Haykin. Cubature kalman filters. IEEE + * Transactions on Automatic Control, 54(6):1254–1269,2009. + * + * \authors + * ------------------------------------------------------------------------- + * + * Copyright (C) 2010-2019 (see AUTHORS file for a list of contributors) + * + * GNSS-SDR is a software defined Global Navigation + * Satellite Systems receiver + * + * This file is part of GNSS-SDR. + * + * GNSS-SDR is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * GNSS-SDR is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with GNSS-SDR. If not, see . + * + * ------------------------------------------------------------------------- + */ + +#ifndef GNSS_SDR_CUBATURE_FILTER_H_ +#define GNSS_SDR_CUBATURE_FILTER_H_ + +#include +#include + +// Abstract model function +class Model_Function{ + public: + Model_Function() {}; + virtual arma::vec operator() (arma::vec input) = 0; + virtual ~Model_Function() = default; +}; + +class Cubature_filter +{ +public: + // Constructors and destructors + Cubature_filter(); + Cubature_filter(int nx); + Cubature_filter(const arma::vec& x_pred_0, const arma::mat& P_x_pred_0); + ~Cubature_filter(); + + // Reinitialization function + void initialize(const arma::mat& x_pred_0, const arma::mat& P_x_pred_0); + + // Prediction and estimation + void predict_sequential(const arma::vec& x_post, const arma::mat& P_x_post, Model_Function* transition_fcn, const arma::mat& noise_covariance); + void update_sequential(const arma::vec& z_upd, const arma::vec& x_pred, const arma::mat& P_x_pred, Model_Function* measurement_fcn, const arma::mat& noise_covariance); + + // Getters + arma::mat get_x_pred() const; + arma::mat get_P_x_pred() const; + arma::mat get_x_est() const; + arma::mat get_P_x_est() const; + +private: + arma::vec x_pred_out; + arma::mat P_x_pred_out; + arma::vec x_est; + arma::mat P_x_est; +}; + +#endif diff --git a/src/tests/CMakeLists.txt b/src/tests/CMakeLists.txt index 266d33b9d..8eb57397e 100644 --- a/src/tests/CMakeLists.txt +++ b/src/tests/CMakeLists.txt @@ -799,6 +799,7 @@ if(NOT ENABLE_PACKAGING AND NOT ENABLE_FPGA) ${CMAKE_CURRENT_SOURCE_DIR}/unit-tests/signal-processing-blocks/tracking/tracking_loop_filter_test.cc ${CMAKE_CURRENT_SOURCE_DIR}/unit-tests/signal-processing-blocks/tracking/cpu_multicorrelator_real_codes_test.cc ${CMAKE_CURRENT_SOURCE_DIR}/unit-tests/signal-processing-blocks/tracking/bayesian_estimation_test.cc + ${CMAKE_CURRENT_SOURCE_DIR}/unit-tests/signal-processing-blocks/tracking/cubature_filter_test.cc ) if(${FILESYSTEM_FOUND}) target_compile_definitions(trk_test PRIVATE -DHAS_STD_FILESYSTEM=1) diff --git a/src/tests/test_main.cc b/src/tests/test_main.cc index 05df98d35..d22149fee 100644 --- a/src/tests/test_main.cc +++ b/src/tests/test_main.cc @@ -99,6 +99,7 @@ DECLARE_string(log_dir); #endif #include "unit-tests/signal-processing-blocks/tracking/bayesian_estimation_test.cc" +#include "unit-tests/signal-processing-blocks/tracking/cubature_filter_test.cc" #include "unit-tests/signal-processing-blocks/tracking/cpu_multicorrelator_real_codes_test.cc" #include "unit-tests/signal-processing-blocks/tracking/cpu_multicorrelator_test.cc" #include "unit-tests/signal-processing-blocks/tracking/galileo_e1_dll_pll_veml_tracking_test.cc" diff --git a/src/tests/unit-tests/signal-processing-blocks/tracking/bayesian_estimation_test.cc b/src/tests/unit-tests/signal-processing-blocks/tracking/bayesian_estimation_test.cc index dd7d0398b..6fa5f1da0 100644 --- a/src/tests/unit-tests/signal-processing-blocks/tracking/bayesian_estimation_test.cc +++ b/src/tests/unit-tests/signal-processing-blocks/tracking/bayesian_estimation_test.cc @@ -1,7 +1,7 @@ /*! - * \file bayesian_estimation_positivity_test.cc - * \brief This file implements timing tests for the Bayesian covariance estimator - * \author Gerald LaMountain, 20168. gerald(at)ece.neu.edu + * \file bayesian_estimation_test.cc + * \brief This file implements feasability test for the BCE library. + * \author Gerald LaMountain, 2018. gerald(at)ece.neu.edu * * * ------------------------------------------------------------------------- diff --git a/src/tests/unit-tests/signal-processing-blocks/tracking/cubature_filter_test.cc b/src/tests/unit-tests/signal-processing-blocks/tracking/cubature_filter_test.cc new file mode 100644 index 000000000..a86d5dd7c --- /dev/null +++ b/src/tests/unit-tests/signal-processing-blocks/tracking/cubature_filter_test.cc @@ -0,0 +1,156 @@ +/*! + * \file cubature_filter_test.cc + * \brief This file implements numerical accuracy test for the CKF library. + * \author Gerald LaMountain, 2019. gerald(at)ece.neu.edu + * + * ------------------------------------------------------------------------- + * + * Copyright (C) 2010-2019 (see AUTHORS file for a list of contributors) + * + * GNSS-SDR is a software defined Global Navigation + * Satellite Systems receiver + * + * This file is part of GNSS-SDR. + * + * GNSS-SDR is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * GNSS-SDR is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with GNSS-SDR. If not, see . + * + * ------------------------------------------------------------------------- + */ + +#include "cubature_filter.h" +#include +#include +#include + +#define CUBATURE_TEST_N_TRIALS 1000 + +class Transition_Model : public Model_Function { + public: + Transition_Model(arma::mat kf_F) {coeff_mat = kf_F;}; + virtual arma::vec operator() (arma::vec input) {return coeff_mat*input;}; + private: + arma::mat coeff_mat; +}; + +class Measurement_Model : public Model_Function { + public: + Measurement_Model(arma::mat kf_H) {coeff_mat = kf_H;}; + virtual arma::vec operator() (arma::vec input) {return coeff_mat*input;}; + private: + arma::mat coeff_mat; +}; + +TEST(CubatureFilterComputationTest, CubatureFilterTest) +{ + Cubature_filter kf_cubature; + + arma::vec kf_x; + arma::mat kf_P_x; + + arma::vec kf_x_pre; + arma::mat kf_P_x_pre; + + arma::vec ckf_x_pre; + arma::mat ckf_P_x_pre; + + arma::vec kf_x_post; + arma::mat kf_P_x_post; + + arma::vec ckf_x_post; + arma::mat ckf_P_x_post; + + arma::mat kf_F; + arma::mat kf_H; + + arma::mat kf_Q; + arma::mat kf_R; + + arma::vec eta; + arma::vec nu; + + arma::vec kf_y; + arma::mat kf_P_y; + arma::mat kf_K; + + Model_Function* transition_function; + Model_Function* measurement_function; + + //--- Perform initializations ------------------------------ + + std::random_device r; + std::default_random_engine e1(r()); + std::normal_distribution normal_dist(0, 5); + std::uniform_real_distribution uniform_dist(0.1, 5.0); + + uint8_t nx = 0; + uint8_t ny = 0; + + for (uint16_t k = 0; k < CUBATURE_TEST_N_TRIALS; k++) + { + nx = std::rand() % 5 + 1; + ny = std::rand() % 5 + 1; + + kf_x = arma::randn(nx,1); + + kf_P_x_post = 5.0 * arma::diagmat(arma::randu(nx,1)); + kf_x_post = arma::mvnrnd(kf_x, kf_P_x_post); + + kf_cubature.initialize(kf_x_post, kf_P_x_post); + + // Prediction Step + kf_F = arma::randu(nx,nx); + kf_Q = arma::diagmat(arma::randu(nx,1)); + + transition_function = new Transition_Model(kf_F); + arma::mat ttx = (*transition_function)(kf_x_post); + + kf_cubature.predict_sequential(kf_x_post,kf_P_x_post,transition_function,kf_Q); + + ckf_x_pre = kf_cubature.get_x_pred(); + ckf_P_x_pre = kf_cubature.get_P_x_pred(); + + kf_x_pre = kf_F * kf_x_post; + kf_P_x_pre = kf_F * kf_P_x_post * kf_F.t() + kf_Q; + + EXPECT_TRUE(arma::approx_equal(ckf_x_pre, kf_x_pre, "absdiff", 0.01)); + EXPECT_TRUE(arma::approx_equal(ckf_P_x_pre, kf_P_x_pre, "absdiff", 0.01)); + + // Update Step + kf_H = arma::randu(ny,nx); + kf_R = arma::diagmat(arma::randu(ny,1)); + + eta = arma::mvnrnd(arma::zeros(nx,1),kf_Q); + nu = arma::mvnrnd(arma::zeros(ny,1),kf_R); + + kf_y = kf_H*(kf_F*kf_x + eta) + nu; + + measurement_function = new Measurement_Model(kf_H); + kf_cubature.update_sequential(kf_y,kf_x_pre,kf_P_x_pre,measurement_function,kf_R); + + ckf_x_post = kf_cubature.get_x_est(); + ckf_P_x_post = kf_cubature.get_P_x_est(); + + kf_P_y = kf_H * kf_P_x_pre * kf_H.t() + kf_R; + kf_K = (kf_P_x_pre * kf_H.t()) * arma::inv(kf_P_y); + + kf_x_post = kf_x_pre + kf_K * (kf_y - kf_H * kf_x_pre); + kf_P_x_post = (arma::eye(nx,nx) - kf_K * kf_H) * kf_P_x_pre; + + EXPECT_TRUE(arma::approx_equal(ckf_x_post, kf_x_post, "absdiff", 0.01)); + EXPECT_TRUE(arma::approx_equal(ckf_P_x_post, kf_P_x_post, "absdiff", 0.01)); + + delete transition_function; + delete measurement_function; + } +}