Beyond Prior Limits: Addressing Distribution Misalignment in Particle Filtering

TL;DR

This paper introduces a novel diffusion-enhanced particle filtering framework that overcomes prior distribution limits, improving robustness and accuracy in dynamic state estimation for out-of-boundary targets.

Contribution

The paper proposes a new framework with adaptive diffusion, entropy regularisation, and kernel perturbations to address the prior boundary phenomenon in particle filtering.

Findings

Significant improvement in success rates for out-of-boundary targets

Enhanced estimation accuracy in high-dimensional scenarios

Framework validated through theoretical analysis and extensive experiments

Abstract

Particle filtering is a Bayesian inference method and a fundamental tool in state estimation for dynamic systems, but its effectiveness is often limited by the constraints of the initial prior distribution, a phenomenon we define as the Prior Boundary Phenomenon. This challenge arises when target states lie outside the prior's support, rendering traditional particle filtering methods inadequate for accurate estimation. Although techniques like unbounded priors and larger particle sets have been proposed, they remain computationally prohibitive and lack adaptability in dynamic scenarios. To systematically overcome these limitations, we propose the Diffusion-Enhanced Particle Filtering Framework, which introduces three key innovations: adaptive diffusion through exploratory particles, entropy-driven regularisation to prevent weight collapse, and kernel-based perturbations for dynamic support expansion. These mechanisms collectively enable particle filtering to explore beyond prior boundaries, ensuring robust state estimation for out-of-boundary targets. Theoretical analysis and extensive experiments validate framework's effectiveness, indicating significant improvements in success rates and estimation accuracy across high-dimensional and non-convex scenarios.