Add unscented filter to nonlinear_filtering library and add associated unit test

src/algorithms/tracking/libs/nonlinear_tracking.cc

@@ -1,10 +1,12 @@
 /*!
  * \file cubature_filter.cc
- * \brief Interface of a library with Bayesian noise statistic estimation
+ * \brief Interface of a library for nonlinear tracking algorithms
  *
  * Cubature_Filter implements the functionality of the Cubature Kalman
  * Filter, which uses multidimensional cubature rules to estimate the
- * time evolution of a nonlinear system.
+ * time evolution of a nonlinear system. Unscented_filter implements
+ * an Unscented Kalman Filter which uses Unscented Transform rules to
+ * perform a similar estimation.
  *
  * [1] I Arasaratnam and S Haykin. Cubature kalman filters. IEEE 
  * Transactions on Automatic Control, 54(6):1254–1269,2009.
@@ -38,8 +40,9 @@
  * -------------------------------------------------------------------------
  */
 
-#include "cubature_filter.h"
+#include "nonlinear_tracking.h"
 
+/***************** CUBATURE KALMAN FILTER *****************/
 
 Cubature_filter::Cubature_filter()
 {
@@ -113,11 +116,11 @@ void Cubature_filter::predict_sequential(const arma::vec& x_post, const arma::ma
         P_x_pred = P_x_pred + Xi_pred*Xi_pred.t();
     }
     
-    // Estimate predicted state and error covariance
+    // Compute predicted mean 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
+    // Store predicted mean and error covariance
     x_pred_out = x_pred;
     P_x_pred_out = P_x_pred;
 }
@@ -135,7 +138,7 @@ void Cubature_filter::update_sequential(const arma::vec& z_upd, const arma::vec&
     // Generator Matrix
     arma::mat gen_one = arma::join_horiz(arma::eye(nx,nx),-1.0*arma::eye(nx,nx));
 
-    // Evaluate predicted measurement and covariances
+    // Initialize estimated 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);
@@ -156,15 +159,15 @@ void Cubature_filter::update_sequential(const arma::vec& z_upd, const arma::vec&
         P_xz_pred = P_xz_pred + Xi_pred*Zi_pred.t();
     }
 
-    // Estimate measurement covariance and cross covariances
+    // Compute measurement mean, covariance and cross covariance
     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
+    // Compute cubature Kalman gain
     arma::mat W_k = P_xz_pred*arma::inv(P_zz_pred);
 
-    // Estimate and store the updated state and error covariance
+    // Compute and store the updated mean 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();
 }
@@ -188,3 +191,180 @@ arma::mat Cubature_filter::get_P_x_est() const
 {
     return P_x_est;
 }
+/***************** END CUBATURE KALMAN FILTER *****************/
+
+/***************** UNSCENTED KALMAN FILTER *****************/
+
+Unscented_filter::Unscented_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;
+}
+
+Unscented_filter::Unscented_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;
+}
+
+Unscented_filter::Unscented_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;
+}
+
+Unscented_filter::~Unscented_filter() = default;
+
+void Unscented_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 Unscented Kalman filter
+ */
+void Unscented_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 sigma points
+    int nx = x_post.n_elem;
+    int np = 2 * nx + 1;
+
+    float alpha = 0.001;
+    float kappa = 0.0;
+    float beta = 2.0;
+
+    float lambda = std::pow(alpha,2.0)*(((float) nx) + kappa) - ((float) nx);
+
+    // Compute UT Weights
+    float W0_m = lambda / (((float) nx) + lambda);
+    float W0_c = lambda / (((float) nx) + lambda) + (1 - std::pow(alpha,2.0) + beta);
+    float Wi_m = 1.0 / (2.0 * (((float) nx) + lambda));
+
+    // Propagate and evaluate sigma points
+    arma::mat Xi_fact = arma::zeros(nx,nx);
+    arma::mat Xi_post = arma::zeros(nx,np);
+    arma::mat Xi_pred = arma::zeros(nx,np);
+
+
+    Xi_post.col(0) = x_post;
+    Xi_pred.col(0) = (*transition_fcn)(Xi_post.col(0));
+    for (uint8_t i = 1; i <= nx; i++)
+    {
+        Xi_fact = std::sqrt(((float) nx) + lambda) * arma::sqrtmat_sympd(P_x_post);
+        Xi_post.col(i) = x_post + Xi_fact.col(i-1);
+        Xi_post.col(i+nx) = x_post - Xi_fact.col(i-1);
+
+        Xi_pred.col(i) = (*transition_fcn)(Xi_post.col(i)); 
+        Xi_pred.col(i+nx) = (*transition_fcn)(Xi_post.col(i+nx)); 
+    }
+
+    // Compute predicted mean
+    arma::vec x_pred = W0_m*Xi_pred.col(0) + Wi_m*arma::sum(Xi_pred.cols(1,np-1),1);
+
+    // Compute predicted error covariance
+    arma::mat P_x_pred = W0_c*((Xi_pred.col(0)-x_pred) * (Xi_pred.col(0).t()-x_pred.t()));
+    for (uint8_t i = 1; i < np; i++)
+    {
+        P_x_pred = P_x_pred + Wi_m*((Xi_pred.col(i)-x_pred) * (Xi_pred.col(i).t()-x_pred.t()));
+    }
+    P_x_pred = P_x_pred + noise_covariance;
+
+    // Store predicted mean and error covariance
+    x_pred_out = x_pred;
+    P_x_pred_out = P_x_pred;
+}
+
+/*
+ * Perform the update step of the Unscented Kalman filter
+ */
+void Unscented_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 sigma points
+    int nx = x_pred.n_elem;
+    int nz = z_upd.n_elem;
+    int np = 2 * nx + 1;
+
+    float alpha = 0.001;
+    float kappa = 0.0;
+    float beta = 2.0;
+
+    float lambda = std::pow(alpha,2.0)*(((float) nx) + kappa) - ((float) nx);
+
+    // Compute UT Weights
+    float W0_m = lambda / (((float) nx) + lambda);
+    float W0_c = lambda / (((float) nx) + lambda) + (1 - std::pow(alpha,2.0) + beta);
+    float Wi_m = 1.0 / (2.0 * (((float) nx) + lambda));
+
+    // Propagate and evaluate sigma points
+    arma::mat Xi_fact = arma::zeros(nx,nx);
+    arma::mat Xi_pred = arma::zeros(nx,np);
+    arma::mat Zi_pred = arma::zeros(nz,np);
+
+    Xi_pred.col(0) = x_pred;
+    Zi_pred.col(0) = (*measurement_fcn)(Xi_pred.col(0));
+    for (uint8_t i = 1; i <= nx; i++)
+    {
+        Xi_fact = std::sqrt(((float) nx) + lambda) * arma::sqrtmat_sympd(P_x_pred);
+        Xi_pred.col(i) = x_pred + Xi_fact.col(i-1);
+        Xi_pred.col(i+nx) = x_pred - Xi_fact.col(i-1);
+
+        Zi_pred.col(i) = (*measurement_fcn)(Xi_pred.col(i)); 
+        Zi_pred.col(i+nx) = (*measurement_fcn)(Xi_pred.col(i+nx)); 
+    }
+
+    // Compute measurement mean
+    arma::mat z_pred = W0_m*Zi_pred.col(0) + Wi_m*arma::sum(Zi_pred.cols(1,np-1),1);
+
+    // Compute measurement covariance and cross covariance
+    arma::mat P_zz_pred = W0_c * ((Zi_pred.col(0) - z_pred) * (Zi_pred.col(0).t() - z_pred.t()));
+    arma::mat P_xz_pred = W0_c * ((Xi_pred.col(0) - x_pred) * (Zi_pred.col(0).t() - z_pred.t()));
+    for (uint8_t i = 0; i < np; i++)
+    {
+        P_zz_pred = P_zz_pred + Wi_m * ((Zi_pred.col(i) - z_pred) * (Zi_pred.col(i).t() - z_pred.t()));
+        P_xz_pred = P_xz_pred + Wi_m * ((Xi_pred.col(i) - x_pred) * (Zi_pred.col(i).t() - z_pred.t()));
+    }
+    P_zz_pred = P_zz_pred + noise_covariance;
+
+    // Estimate cubature Kalman gain
+    arma::mat W_k = P_xz_pred*arma::inv(P_zz_pred);
+
+    // Estimate and store the updated mean 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 Unscented_filter::get_x_pred() const
+{
+    return x_pred_out;
+}
+
+arma::mat Unscented_filter::get_P_x_pred() const
+{
+    return P_x_pred_out;
+}
+
+arma::mat Unscented_filter::get_x_est() const
+{
+    return x_est;
+}
+
+arma::mat Unscented_filter::get_P_x_est() const
+{
+    return P_x_est;
+}
+/***************** END UNSCENTED KALMAN FILTER *****************/

src/algorithms/tracking/libs/nonlinear_tracking.h

@@ -1,10 +1,12 @@
 /*!
- * \file cubature_filter.h
- * \brief Interface of a library with Bayesian noise statistic estimation
+ * \file nonlinear_tracking.h
+ * \brief Interface of a library for nonlinear tracking algorithms
  *
  * Cubature_Filter implements the functionality of the Cubature Kalman
  * Filter, which uses multidimensional cubature rules to estimate the
- * time evolution of a nonlinear system.
+ * time evolution of a nonlinear system. Unscented_filter implements
+ * an Unscented Kalman Filter which uses Unscented Transform rules to
+ * perform a similar estimation.
  *
  * [1] I Arasaratnam and S Haykin. Cubature kalman filters. IEEE 
  * Transactions on Automatic Control, 54(6):1254–1269,2009.
@@ -38,8 +40,8 @@
  * -------------------------------------------------------------------------
  */
 
-#ifndef GNSS_SDR_CUBATURE_FILTER_H_
-#define GNSS_SDR_CUBATURE_FILTER_H_
+#ifndef GNSS_SDR_NONLINEAR_TRACKING_H_
+#define GNSS_SDR_NONLINEAR_TRACKING_H_
 
 #include <armadillo>
 #include <gnuradio/gr_complex.h>
@@ -81,4 +83,33 @@ private:
     arma::mat P_x_est;
 };
 
+class Unscented_filter
+{
+public:
+    // Constructors and destructors
+    Unscented_filter();
+    Unscented_filter(int nx);
+    Unscented_filter(const arma::vec& x_pred_0, const arma::mat& P_x_pred_0);
+    ~Unscented_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

@@ -782,6 +782,7 @@ if(NOT ENABLE_PACKAGING AND NOT ENABLE_FPGA)
         ${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
+        ${CMAKE_CURRENT_SOURCE_DIR}/unit-tests/signal-processing-blocks/tracking/unscented_filter_test.cc
     )
     if(${FILESYSTEM_FOUND})
         target_compile_definitions(trk_test PRIVATE -DHAS_STD_FILESYSTEM=1)

src/tests/test_main.cc

@@ -100,6 +100,7 @@ DECLARE_string(log_dir);
 
 #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/unscented_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/unscented_filter_test.cc

@@ -0,0 +1,157 @@
+/*!
+ * \file unscented_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 "nonlinear_tracking.h"
+#include <armadillo>
+#include <gtest/gtest.h>
+#include <random>
+
+#define UNSCENTED_TEST_N_TRIALS 10
+#define UNSCENTED_TEST_TOLERANCE 10
+
+class Transition_Model_UKF : public Model_Function {
+    public:
+        Transition_Model_UKF(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_UKF : public Model_Function {
+    public:
+        Measurement_Model_UKF(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(UnscentedFilterComputationTest, UnscentedFilterTest)
+{
+    Unscented_filter kf_unscented;
+
+    arma::vec kf_x;
+    arma::mat kf_P_x;
+
+    arma::vec kf_x_pre;
+    arma::mat kf_P_x_pre;
+
+    arma::vec ukf_x_pre;
+    arma::mat ukf_P_x_pre;
+
+    arma::vec kf_x_post;
+    arma::mat kf_P_x_post;
+
+    arma::vec ukf_x_post;
+    arma::mat ukf_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 < UNSCENTED_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_unscented.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_UKF(kf_F);
+            arma::mat ttx = (*transition_function)(kf_x_post);
+
+            kf_unscented.predict_sequential(kf_x_post,kf_P_x_post,transition_function,kf_Q);
+
+            ukf_x_pre = kf_unscented.get_x_pred();
+            ukf_P_x_pre = kf_unscented.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(ukf_x_pre, kf_x_pre, "absdiff", UNSCENTED_TEST_TOLERANCE));
+            EXPECT_TRUE(arma::approx_equal(ukf_P_x_pre, kf_P_x_pre, "absdiff", UNSCENTED_TEST_TOLERANCE));
+
+            // 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_UKF(kf_H);
+            kf_unscented.update_sequential(kf_y,kf_x_pre,kf_P_x_pre,measurement_function,kf_R);
+
+            ukf_x_post = kf_unscented.get_x_est();
+            ukf_P_x_post = kf_unscented.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(ukf_x_post, kf_x_post, "absdiff", UNSCENTED_TEST_TOLERANCE));
+            EXPECT_TRUE(arma::approx_equal(ukf_P_x_post, kf_P_x_post, "absdiff", UNSCENTED_TEST_TOLERANCE));
+
+            delete transition_function;
+            delete measurement_function;
+        }
+}