Interacting Multiple Model-Feedback Particle Filter for Stochastic Hybrid Systems

TL;DR

This paper introduces the IMM-FPF, a feedback particle filter for stochastic hybrid systems that generalizes the Kalman filter-based IMM algorithm to nonlinear problems, maintaining feedback structure and demonstrating effectiveness in target tracking.

Contribution

The paper presents a novel IMM-FPF algorithm that extends feedback particle filtering to nonlinear hybrid systems, combining multiple models with mode probability updates.

Findings

Retains feedback structure for nonlinear filtering

Handles mode interaction via control-based merging

Demonstrates effectiveness in target tracking simulation

Abstract

In this paper, a novel feedback control-based particle filter algorithm for the continuous-time stochastic hybrid system estimation problem is presented. This particle filter is referred to as the interacting multiple model-feedback particle filter (IMM-FPF), and is based on the recently developed feedback particle filter. The IMM-FPF is comprised of a series of parallel FPFs, one for each discrete mode, and an exact filter recursion for the mode association probability. The proposed IMM-FPF represents a generalization of the Kalmanfilter based IMM algorithm to the general nonlinear filtering problem. The remarkable conclusion of this paper is that the IMM-FPF algorithm retains the innovation error-based feedback structure even for the nonlinear problem. The interaction/merging process is also handled via a control-based approach. The theoretical results are illustrated with the aid of a numerical example problem for a maneuvering target tracking application.