arXiv:2501.18501stat.MLcs.AI2025-01

突破粒子滤波的先验限制,让系统能准确追踪超出初始假设范围的目标。

Beyond Prior Limits: Addressing Distribution Misalignment in Particle Filtering

  • 用可探索的粒子自适应扩散,动态扩展搜索范围。
  • 在高维非凸场景中,成功率和估计精度显著提升。
  • 适合需要精准追踪异常或未知状态的复杂系统应用。

粒子滤波是动态系统状态估计中的贝叶斯推断方法,但其性能常受限于初始先验分布的约束,这种现象称为先验边界效应。当目标状态位于先验支撑集之外时,传统粒子滤波难以实现准确估计。尽管已有无界先验和增大粒子数等方法,但计算成本高且难以适应动态环境。为此,我们提出扩散增强粒子滤波框架,包含三项创新:通过探索性粒子实现自适应扩散、基于熵的正则化防止权重坍塌、基于核函数的扰动实现动态支持扩展。这些机制共同使粒子滤波能够突破先验边界,确保对边界外目标的鲁棒状态估计。理论分析与大量实验验证了该框架的有效性,在高维与非凸场景中均显著提升成功率与估计精度。

原文摘要 · Abstract (English)

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.

粒子滤波状态估计贝叶斯推断动态系统

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