Monte Carlo Set-Membership Filtering for Nonlinear Dynamic Systems

TL;DR

This paper introduces a Monte Carlo set-membership filtering method for nonlinear dynamic systems with unknown noise distributions, combining convex optimization and boundary sampling to improve estimation accuracy over particle filters.

Contribution

It proposes a novel filtering approach that integrates set-membership theory with Monte Carlo boundary sampling for nonlinear systems with bounded noise.

Findings

Outperforms particle filters when noise PDFs are unknown

Efficiently solves semi-infinite optimization problems in nonlinear filtering

Provides better estimation accuracy in target tracking scenarios

Abstract

When underlying probability density functions of nonlinear dynamic systems are unknown, the filtering problem is known to be a challenging problem. This paper attempts to make progress on this problem by proposing a new class of filtering methods in bounded noise setting via set-membership theory and Monte Carlo (boundary) sampling technique, called Monte Carlo set-membership filter. The set-membership prediction and measurement update are derived by recent convex optimization methods based on S-procedure and Schur complement. To guarantee the on-line usage, the nonlinear dynamics are linearized about the current estimate and the remainder terms are then bounded by an optimization ellipsoid, which can be described as a semi-infinite optimization problem. In general, it is an analytically intractable problem when dynamic systems are nonlinear. However, for a typical nonlinear dynamic system in target tracking, we can analytically derive some regular properties for the remainder. Moreover, based on the remainder properties and the inverse function theorem, the semi-infinite optimization problem can be efficiently solved by Monte Carlo boundary sampling technique. Compared with the particle filter, numerical examples show that when the probability density functions of noises are unknown, the performance of the Monte Carlo set-membership filter is better than that of the particle filter.