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Add unscented filter to nonlinear_filtering library and add associated unit test

This commit is contained in:
Gerald LaMountain 2019-06-13 15:42:52 -04:00
parent 49a8f9a22a
commit 0e68befe7c
5 changed files with 384 additions and 14 deletions

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@ -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):12541269,2009.
@ -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 *****************/

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@ -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):12541269,2009.
@ -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

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@ -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)

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@ -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"

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@ -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;
}
}