Abstract
The posterior Cramér-Rao bound (PCRB) is a fundamental tool to assess the accuracy limit of the Bayesian estimation problem. In this article, we propose a novel framework to compute the PCRB for the general nonlinear filtering problem with additive white Gaussian noise. It uses the Gaussian mixture model to represent and propagate the uncertainty contained in the state vector and uses the Gauss-Hermite quadrature rule to compute mathematical expectations of vector-valued nonlinear functions of the state variable. The detailed pseudocodes for both the small and large component covariance cases are also presented. Three numerical experiments are conducted. All of the results show that the proposed method has high accuracy and it is more efficient than the plain Monte Carlo integration approach in the small component covariance case.
Highlights
N ONLINEAR state estimation or filtering is ubiquitous in engineering fields such as target tracking, space vehicle navigation, and robotics
Finding the optimal nonlinear state estimator is usually intractable under limited computational resources, many effective suboptimal filtering algorithms have been proposed, including the extended Kalman filter (EKF) [3], unscented Kalman filter (UKF) [4], [5], and particle filter (PF) [6]
A novel Gaussian mixture model (GMM)based approach to accurately compute the posterior Cramer-Rao bound (PCRB) for general nonlinear filtering problems with the additive white Gaussian noise (AWGN) is proposed. This method uses the GMM to represent and propagate the uncertainty contained in the state vector and uses the Gauss-Hermite quadrature rule to compute the mathematical expectation of a vector-valued nonlinear function of the state variable
Summary
N ONLINEAR state estimation or filtering is ubiquitous in engineering fields such as target tracking, space vehicle navigation, and robotics. The authors first computed the expectations with respect to the measurement-conditioned state PDF by using the SMC approach and with respect to the measurement PDF by the standard Monte Carlo method This method is suitable for general nonlinear, non-Gaussian filtering problems. A novel Gaussian mixture model (GMM)based approach to accurately compute the PCRB for general nonlinear filtering problems with the AWGN is proposed. This method uses the GMM to represent and propagate the uncertainty contained in the state vector and uses the Gauss-Hermite quadrature rule to compute the mathematical expectation of a vector-valued nonlinear function of the state variable.
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