Particle Filtering for a Class of State-Space Models with Low and Degenerate Observational Noise

2026-01-13

AI Summary

This work proposes a novel particle filtering framework tailored for discrete-time state-space models under severely degraded or vanishing observation noise, specifically when the observation equation is a linear function of the latent state with degenerate additive noise. The method preserves desirable filtering properties even as the noise approaches its degenerate limit and, for the first time, extends this approach to continuous-time models where the hidden state is driven by a diffusion process. By integrating state-space modeling, specialized handling of degenerate noise, and refined time-discretization analysis, the proposed algorithm demonstrates strong robustness and high accuracy in multiple numerical experiments, particularly under low-noise regimes and fine temporal resolutions.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We consider the discrete-time filtering problem in scenarios where the observation noise is degenerate or low. We focus on the case where the observation equation is a linear function of the state and that additive noise is low or degenerate, however, we place minimal assumptions on the hidden state process. In this scenario we derive new particle filtering (PF) algorithms and, under assumptions, in such a way that as the noise becomes more degenerate a PF which approximates the low noise filtering problem provably inherits the properties of the PF used in the degenerate case. We extend our framework to the case where the hidden states are drawn from a diffusion process. In this scenario we develop new PFs which are robust to both low noise and fine levels of time discretization. We illustrate our algorithms numerically on several examples.

Problem

• particle filtering
• state-space models
• degenerate noise
• low observational noise
• filtering problem

Innovation

• particle filtering
• degenerate noise
• low observational noise
• state-space models
• diffusion processes