Error Analysis of Approximated PCRLBs for Nonlinear Dynamics

In practical nonlinear filtering, the assessment of achievable filtering performance is important. In this paper, we focus on the problem of how to efficiently approximate the posterior Cramer-Rao lower bound (CRLB) using a recursive framework. 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 Taylorseries-expanded model using both of the state estimate and its 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 the CRLB, 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.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Ming Lei, Pierre Del Moral, Christophe Baehr
• Keywords: Achievable Filtering Performance, CORR 2010, Education, Practical Nonlinear Filtering, State Estimate