Add cubature filter library to tracking and associated unit test to tests

src/algorithms/tracking/libs/cubature_filter.cc

@@ -6,7 +6,8 @@
  * Filter, which uses multidimensional cubature rules to estimate the
  * time evolution of a nonlinear system.
  *
- * [1] TODO: Refs
+ * [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
@@ -14,7 +15,7 @@
  *          </ul>
  * -------------------------------------------------------------------------
  *
- * Copyright (C) 2010-2018  (see AUTHORS file for a list of contributors)
+ * Copyright (C) 2010-2019  (see AUTHORS file for a list of contributors)
  *
  * GNSS-SDR is a software defined Global Navigation
  *          Satellite Systems receiver
@@ -70,7 +71,7 @@ Cubature_filter::Cubature_filter(const arma::vec& x_pred_0, const arma::mat& P_x
 
 Cubature_filter::~Cubature_filter() = default;
 
-void Cubature_filter::init(const arma::mat& x_pred_0, const arma::mat& P_x_pred_0)
+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;
@@ -83,29 +84,33 @@ void Cubature_filter::init(const arma::mat& x_pred_0, const arma::mat& P_x_pred_
 /*
  * 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, arma::vec (*transition_fcn)(const arma::mat&), const arma::mat& noise_covariance)
+void Cubature_filter::predict_sequential(const arma::vec& x_post, const arma::mat& P_x_post, ModelFunction* 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);
+    arma::mat Sm_post = arma::chol(P_x_post, "lower");
     
     // Propagate and evaluate cubature points
     arma::vec Xi_post;
     arma::vec Xi_pred;
-    for (int32_t i = 0; i < np; i++)
+
+    for (uint8_t i = 0; i < np; i++)
     {
-        Xi_post = Sm_post*std::sqrt(((float) np) / 2.0)*arma::ones(nx,1) + x_post;
+        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_post + Xi_pred;
-        P_x_pred = P_x_post + Xi_pred*Xi_pred.t();
+       
+        x_pred = x_pred + Xi_pred;
+        P_x_pred = P_x_pred + Xi_pred*Xi_pred.t();
     }
     
     // Estimate predicted state and error covariance
@@ -120,34 +125,37 @@ void Cubature_filter::predict_sequential(const arma::vec& x_post, const arma::ma
 /*
  * 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, arma::vec (*measurement_fcn)(const arma::mat&), const arma::mat& noise_covariance)
+void Cubature_filter::update_sequential(const arma::vec& z_upd, const arma::vec& x_pred, const arma::mat& P_x_pred, ModelFunction* 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(nx,1);
+    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);
+    arma::mat Sm_pred = arma::chol(P_x_pred, "lower");
 
     // Propagate and evaluate cubature points
     arma::vec Xi_pred;
     arma::vec Zi_pred;
-    for (int32_t i = 0; i < np; i++)
+    for (uint8_t i = 0; i < np; i++)
     {
-        Xi_pred = Sm_pred*std::sqrt(((float) np) / 2.0)*arma::ones(nx,1) + x_pred;
+        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;
@@ -180,3 +188,8 @@ arma::mat Cubature_filter::get_P_x_est() const
 {
     return P_x_est;
 }
+
+double Cubature_filter::func_number(double number, TestModel* func)
+{
+    return (*func)(number);
+}

src/algorithms/tracking/libs/cubature_filter.h

@@ -6,7 +6,8 @@
  * Filter, which uses multidimensional cubature rules to estimate the
  * time evolution of a nonlinear system.
  *
- * [1] TODO: Refs
+ * [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
@@ -14,7 +15,7 @@
  *          </ul>
  * -------------------------------------------------------------------------
  *
- * Copyright (C) 2010-2018  (see AUTHORS file for a list of contributors)
+ * Copyright (C) 2010-2019  (see AUTHORS file for a list of contributors)
  *
  * GNSS-SDR is a software defined Global Navigation
  *          Satellite Systems receiver
@@ -43,6 +44,22 @@
 #include <armadillo>
 #include <gnuradio/gr_complex.h>
 
+// Abstract model function
+class ModelFunction{
+    public:
+        ModelFunction() {};
+        virtual arma::vec operator() (arma::vec input) = 0;
+        virtual ~ModelFunction() = default;
+};
+
+class TestModel{
+    public:
+        TestModel() {};
+        //virtual arma::vec operator() (arma::vec input) = 0;
+        virtual double operator() (double input) = 0;
+        virtual ~TestModel() = default;
+};
+
 class Cubature_filter
 {
 public:
@@ -53,17 +70,21 @@ public:
     ~Cubature_filter();
 
     // Reinitialization function
-    void init(const arma::mat& x_pred_0, const arma::mat& P_x_pred_0);
+    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, arma::vec (*transition_fcn)(const arma::mat&), const arma::mat& noise_covariance);
-    void update_sequential(const arma::vec& z_upd, const arma::vec& x_pred, const arma::mat& P_x_pred, arma::vec (*measurement_fcn)(const arma::mat&), const arma::mat& noise_covariance);
+    void predict_sequential(const arma::vec& x_post, const arma::mat& P_x_post, ModelFunction* 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, ModelFunction* 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;
+
+    //Test-dev
+    double func_number(double number, TestModel* func);
+
 private:
     arma::vec x_pred_out;
     arma::mat P_x_pred_out;

src/tests/CMakeLists.txt

@@ -755,6 +755,7 @@ 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
     )
 
     target_link_libraries(trk_test

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
- * \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
  *
  *
  * -------------------------------------------------------------------------

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 <https://www.gnu.org/licenses/>.
+ *
+ * -------------------------------------------------------------------------
+ */
+
+#include "cubature_filter.h"
+#include <armadillo>
+#include <gtest/gtest.h>
+#include <random>
+
+#define CUBATURE_TEST_N_TRIALS 1000
+
+class TransitionModel : public ModelFunction {
+    public:
+        TransitionModel(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 MeasurementModel : public ModelFunction {
+    public:
+        MeasurementModel(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;
+
+    ModelFunction* transition_function;
+    ModelFunction* 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 TransitionModel(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 MeasurementModel(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;
+        }
+}