Posterior Cramer-Rao Bounds for Discrete-Time Nonlinear Filtering with Finitely Correlated Noise

TL;DR

This paper derives a recursive lower bound for mean-square error in discrete-time nonlinear filtering with correlated noises, improving accuracy over traditional bounds that ignore noise correlation, and demonstrates its impact on sensor selection.

Contribution

It introduces a unified recursive formula for the Cramer-Rao lower bound considering multi-step correlated noises in nonlinear filtering.

Findings

The new bound significantly differs from traditional bounds ignoring noise correlation.

Applying the bound affects sensor selection decisions in target tracking.

The bound is validated through two target tracking examples.

Abstract

In this paper, an approximation recursive formula of the mean-square error lower bound for the discrete-time nonlinear filtering problem when noises of dynamic systems are temporally correlated is derived based on the Van Trees (posterior) version of the Cramer-Rao inequality. The formula is unified in the sense that it can be applied to the multi-step correlated process noise, multi-step correlated measurement noise and multi-step cross-correlated process and measurement noise simultaneously. The lower bound is evaluated by two typical target tracking examples respectively. Both of them show that the new lower bound is significantly different from that of the method which ignores correlation of noises. Thus, when they are applied to sensor selection problems, number of selected sensors becomes very different to obtain a desired estimation performance.