Path Integral Particle Filtering for Hybrid Systems via Saltation Matrices

2026-03-01

AI Summary

This work addresses the challenge of state estimation in hybrid systems subject to intermittent contact, where non-Gaussian noise and abrupt dynamic shifts degrade performance. To this end, we propose a novel path integral filtering method that integrates a jump matrix to explicitly model the discontinuous dynamics and uncertainty propagation induced by contact events. By reformulating the state smoothing problem as an optimal control problem, our approach embeds the jump matrix into the path integral framework for the first time, yielding a new particle filtering algorithm tailored for stochastic hybrid systems. This integration significantly enhances robustness against outliers and non-Gaussian disturbances. Experimental results demonstrate that the proposed method consistently outperforms strong existing baselines across multiple scenarios, achieving efficient and reliable state estimation.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We present an optimal-control-based particle filtering method for state estimation in hybrid systems that undergo intermittent contact with their environments. We follow the path integral filtering framework that exploits the duality between the smoothing problem and optimal control. We leverage saltation matrices to map out the uncertainty propagation during contact events for hybrid systems. The resulting path integral optimal control problem allows for a state estimation algorithm robust to outlier effects, flexible to non-Gaussian noise distributions, that also handles the challenging contact dynamics in hybrid systems. This work offers a computationally efficient and reliable estimation algorithm for hybrid systems with stochastic dynamics. We also present extensive experimental results demonstrating that our approach consistently outperforms strong baselines across multiple settings.

Problem

• hybrid systems
• state estimation
• contact dynamics
• non-Gaussian noise
• outlier robustness

Innovation

• Path Integral Filtering
• Saltation Matrices
• Hybrid Systems
• Particle Filtering
• Optimal Control