Merge branch 'next' of https://github.com/gnss-sdr/gnss-sdr into next

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

src/algorithms/tracking/libs/cubature_filter.cc

@@ -0,0 +1,199 @@
+/*!
+ * \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 <ul>
+ *          <li> Gerald LaMountain, 2019. gerald(at)ece.neu.edu
+ *          <li> Jordi Vila-Valls 2019. jvila(at)cttc.es
+ *          </ul>
+ * -------------------------------------------------------------------------
+ *
+ * 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 <https://www.gnu.org/licenses/>.
+ *
+ * -------------------------------------------------------------------------
+ */
+
+#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(static_cast<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 / static_cast<float>(np);
+    P_x_pred = P_x_pred / static_cast<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(static_cast<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 / static_cast<float>(np);
+    P_zz_pred = P_zz_pred / static_cast<float>(np) - z_pred * z_pred.t() + noise_covariance;
+    P_xz_pred = P_xz_pred / static_cast<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;
+}

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 <ul>
+ *          <li> Gerald LaMountain, 2019. gerald(at)ece.neu.edu
+ *          <li> Jordi Vila-Valls 2019. jvila(at)cttc.es
+ *          </ul>
+ * -------------------------------------------------------------------------
+ *
+ * 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 <https://www.gnu.org/licenses/>.
+ *
+ * -------------------------------------------------------------------------
+ */
+
+#ifndef GNSS_SDR_CUBATURE_FILTER_H_
+#define GNSS_SDR_CUBATURE_FILTER_H_
+
+#include <armadillo>
+#include <gnuradio/gr_complex.h>
+
+// 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

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)

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"

src/tests/unit-tests/signal-processing-blocks/tracking/bayesian_estimation_test.cc

@@ -1,7 +1,7 @@
 /*!
- * \file bayesian_estimation_positivity_test.cc
+ * \file bayesian_estimation_test.cc
- * \brief  This file implements timing tests for the Bayesian covariance estimator
+ * \brief  This file implements feasability test for the BCE library.
- * \author Gerald LaMountain, 20168. gerald(at)ece.neu.edu
+ * \author Gerald LaMountain, 2018. gerald(at)ece.neu.edu
  *
  *
  * -------------------------------------------------------------------------

src/tests/unit-tests/signal-processing-blocks/tracking/cubature_filter_test.cc

@@ -0,0 +1,160 @@
+/*!
+ * \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 <https://www.gnu.org/licenses/>.
+ *
+ * -------------------------------------------------------------------------
+ */
+
+#include "cubature_filter.h"
+#include <armadillo>
+#include <gtest/gtest.h>
+#include <random>
+
+#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<float> normal_dist(0, 5);
+    std::uniform_real_distribution<float> 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<arma::vec>(nx, 1);
+
+            kf_P_x_post = 5.0 * arma::diagmat(arma::randu<arma::vec>(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<arma::mat>(nx, nx);
+            kf_Q = arma::diagmat(arma::randu<arma::vec>(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<arma::mat>(ny, nx);
+            kf_R = arma::diagmat(arma::randu<arma::vec>(ny, 1));
+
+            eta = arma::mvnrnd(arma::zeros<arma::vec>(nx, 1), kf_Q);
+            nu = arma::mvnrnd(arma::zeros<arma::vec>(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;
+        }
+}