Performance assessment, diagnosis, and optimal selection of non-linear state filters

Abstract

Non-linear state filters of different approximations and capabilities allow for real-time estimation of unmeasured states in non-linear stochastic processes. It is well known that the performance of non-linear filters depends on the underlying numerical and statistical approximations used in their design. Despite the theoretical and practical interest in evaluating the performance of non-linear filtering methods, it remains one of the most complex problems in the area of state estimation. We propose the use of posterior Cramér–Rao lower bound (PCRLB) or mean square error (MSE) inequality as a filtering performance benchmark. Using the PCRLB inequality, we develop assessment and diagnosis tools for monitoring and evaluating the performance of non-linear filters. Using the PCRLB inequality-based performance assessment tool, an optimal non-linear filter switching strategy is proposed for state estimation in general non-linear systems. The non-linear filter switching strategy is an optimal performance strategy, which maintains high filtering performance under all operating conditions. The complex, high dimensional integrals involved in the computation of the PCRLB inequality-based non-linear filter assessment and diagnosis tools are approximated using sequential Monte-Carlo (SMC) methods. The utility and efficacy of the developed tools are illustrated through a numerical example.