A Kushner-Stratonovich Monte Carlo Filter Applied to Nonlinear Dynamical System Identification

TL;DR

This paper introduces a novel Monte Carlo filter based on the Kushner-Stratonovich equation that improves convergence and accuracy in nonlinear system identification by using an additive update scheme instead of traditional weight-based methods.

Contribution

The paper presents a new particle filter with an additive update mechanism inspired by the KS equation, reducing weight collapse issues common in particle filters.

Findings

Demonstrates improved convergence over existing filters.

Shows enhanced accuracy in nonlinear dynamic system identification.

Provides error bounds for the proposed filtering scheme.

Abstract

A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation-prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight- based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter.