Beyond Prior Limits: Addressing Distribution Misalignment in Particle Filtering

2025-01-30

AI Summary

In particle filtering, the “prior boundary phenomenon”—estimation failure when target states exceed the limited support of the prior distribution—severely degrades robustness. Method: This paper proposes Diffusion-Enhanced Particle Filtering (DEPF), a novel framework introducing three core mechanisms: adaptive diffusion-based exploration, entropy-driven weight regularization, and dynamic kernel support expansion—enabling online, controllable adaptation of the prior support set. DEPF integrates diffusion process modeling, information-theoretic entropy constraints, kernel density perturbation, and Bayesian resampling to overcome prior boundary limitations while preserving computational efficiency. Contribution/Results: We provide theoretical convergence guarantees for DEPF. Empirical evaluation demonstrates substantial improvements in estimation success rate and accuracy under high-dimensional and non-convex dynamic scenarios; average estimation error decreases by over 40% compared to state-of-the-art baselines.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Particle Filtering
• Dynamic Systems
• State Estimation

Innovation

• Diffusion Enhanced Particle Filter
• Entropy Control
• Dynamic Kernel Extension