Beyond Prior Limits: Addressing Distribution Misalignment in Particle Filtering
Yiwei Shi, Jingyu Hu, Yu Zhang, Mengyue Yang, Weinan Zhang, Cunjia Liu, Weiru Liu
TL;DR
This paper identifies a fundamental limitation in particle filtering, termed the Prior Boundary Phenomenon, where the posterior exploration is confined to the initial prior support. To address this, it introduces the Diffusion-Enhanced Particle Filtering Framework (DEPF), which combines exploratory particles, entropy-driven diffusion regularisation, and kernel-based perturbations to expand the effective support beyond $\mathcal{S}_{\text{prior}}$. Theoretical results formalise the recursive confinement and provide proofs that, with the proposed diffusion mechanisms, the support range can be expanded to cover previously unreachable regions, enabling robust estimation of out-of-boundary targets. Extensive experiments across 1D–7D, with diverse priors including non-convex shapes, demonstrate DEPF’s superior accuracy, resilience to prior misalignment, and improved success rates compared to traditional PF. The work thus broadens the applicability of sequential Bayesian estimation in high-dimensional and complex environments, with implications for target tracking, robotics, and environmental sensing.
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.