The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

TL;DR

This paper introduces a novel approach combining the Zig-Zag Sampler with the SMCMC framework to enhance high-dimensional state estimation accuracy in particle filtering, addressing weight degeneracy issues.

Contribution

It proposes discretizing the Zig-Zag Sampler and integrating it into the SMCMC framework with invertible particle flow, a novel combination for high-dimensional filtering.

Findings

Improved estimation accuracy in high-dimensional filtering tasks.

Higher acceptance ratios compared to existing methods.

Enhanced performance demonstrated through complex numerical experiments.

Abstract

Particle filtering methods are widely applied in sequential state estimation within nonlinear non-Gaussian state space model. However, the traditional particle filtering methods suffer the weight degeneracy in the high-dimensional state space model. Currently, there are many methods to improve the performance of particle filtering in high-dimensional state space model. Among these, the more advanced method is to construct the Sequential Makov chian Monte Carlo (SMCMC) framework by implementing the Composite Metropolis-Hasting (MH) Kernel. In this paper, we proposed to discrete the Zig-Zag Sampler and apply the Zig-Zag Sampler in the refinement stage of the Composite MH Kernel within the SMCMC framework which is implemented the invertible particle flow in the joint draw stage. We evaluate the performance of proposed method through numerical experiments of the challenging complex high-dimensional filtering examples. Nemurical experiments show that in high-dimensional state estimation examples, the proposed method improves estimation accuracy and increases the acceptance ratio compared with state-of-the-art filtering methods.