On a class of constrained particle filters for continuous-discrete state space models

2026-04-23

AI Summary

This work addresses Bayesian filtering for continuous-discrete state-space models where the hidden state evolves according to an Itô stochastic differential equation and observations arrive at discrete time instances. The authors propose a novel constrained particle filter that enforces hard support constraints on the state at each observation time via barrier functions, directly restricting the system dynamics rather than truncating the likelihood, thereby enhancing numerical stability. A unified theoretical analysis establishes convergence and time-uniform error bounds that explicitly account for numerical integration errors arising from the SDE solver. Experimental results on the stochastic Lorenz-96 system demonstrate that the proposed method effectively confines the state exploration range while maintaining high accuracy, significantly outperforming conventional particle filters.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Privacy-enhancing technologies
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search

Abstract

Particle filters (PFs) are recursive Monte Carlo algorithms for Bayesian tracking and prediction in state space models. This paper addresses continuous-discrete filtering problems, where the hidden state evolves as an Itô stochastic differential equation (SDE) and observations arrive at discrete times. We propose a novel class of constrained PFs that enforce compact support on the state at each observation instant, thereby limiting exploration to plausible regions of the state space. Unlike earlier approaches that truncate the likelihood, the proposed method constrains the dynamics directly, yielding improved numerical stability. Under standard regularity assumptions, we prove convergence of the constrained filter, derive uniform-in-time error estimates, and extend the analysis to account for discretisation errors arising from numerical SDE solvers. A numerical study on a stochastic Lorenz-96 system demonstrates the practical application of the methodology when the constraint is implemented via barrier functions.

Problem

• continuous-discrete filtering
• state space models
• particle filters
• stochastic differential equations
• Bayesian tracking

Innovation

• constrained particle filter
• continuous-discrete state space models
• stochastic differential equations
• compact support
• numerical stability