Error Analysis of Approximated PCRLBs for Nonlinear Dynamics

TL;DR

This paper proposes and analyzes two Gaussian-based approximation methods for the posterior CRLB in nonlinear filtering, comparing their accuracy and providing insights into their differences and improvements.

Contribution

It introduces two recursive Gaussian approximation techniques for CRLB calculation and analytically compares their differences, enhancing understanding of filtering performance bounds.

Findings

Mean-covariance-based CRLB outperforms mean-based exact CRLB in simulations.

Theoretical difference between the two CRLBs can be reduced with improved filtering methods.

Simulation results validate the effectiveness of the proposed approximations.

Abstract

In practical nonlinear filtering, the assessment of achievable filtering performance is important. In this paper, we focus on the problem of efficiently approximate the posterior Cramer-Rao lower bound (CRLB) in a recursive manner. By using Gaussian assumptions, two types of approximations for calculating the CRLB are proposed: An exact model using the state estimate as well as a Taylor-series-expanded model using both of the state estimate and its error covariance, are derived. Moreover, the difference between the two approximated CRLBs is also formulated analytically. By employing the particle filter (PF) and the unscented Kalman filter (UKF) to compute, simulation results reveal that the approximated CRLB using mean-covariance-based model outperforms that using the mean-based exact model. It is also shown that the theoretical difference between the estimated CRLBs can be improved through an improved filtering method.