Max-Entropy Moment Filtering for Stochastic Hybrid Systems

TL;DR

This paper introduces a new filtering method for stochastic hybrid systems that efficiently propagates moments and reconstructs probability distributions using maximum-entropy principles, accounting for boundary effects.

Contribution

It extends the Max-Entropy Moment Kalman Filter to hybrid systems, enabling tractable moment propagation and belief reconstruction without solving complex PDEs.

Findings

Successfully captures reset-induced non-Gaussianity in simulations

Provides a boundary-flux correction for accurate moment dynamics

Avoids solving hybrid Fokker-Planck equations

Abstract

Stochastic hybrid systems combine continuous-time stochastic dynamics with discrete reset events, producing intrinsically non-Gaussian and often multimodal uncertainty. A consistent propagation law must also account for boundary-induced probability flux across guard sets, making direct density propagation through hybrid Fokker-Planck equations expensive. We develop a hybrid extension of the Max-Entropy Moment Kalman Filter (MEM-KF) that performs filtering from partial statistical information by propagating a finite collection of moments through stochastic hybrid dynamics and reconstructing beliefs using moment-constrained maximum-entropy distributions. The key step is a moment propagation rule derived from Dynkin's formula with a jump-sum, in which reset effects appear as a boundary-flux correction over the guard set. This yields tractable moment dynamics without solving the underlying hybrid PDE. In a stochastic bouncing-ball example, the proposed method captures reset-induced non-Gaussianity through corrected moment equations while retaining the MEM-KF's optimization-based maximum-entropy representation.