2025 Volume 33 Pages 231-244
Particle filtering methods are widely utilized for state estimation in nonlinear non-Gaussian state space models. However, traditional particle filtering methods often suffer from weight degeneracy issues in high-dimensional situations. To overcome this challenge, various particle filtering methods have been developed to enhance state estimation performance in high-dimensional situations. Among these, the Sequential Markov Chain Monte Carlo (SMCMC) methods, which utilize composite Metropolis-Hastings (MH) kernels, significantly improve state estimation performance. In SMCMC, different Markov Chain Monte Carlo (MCMC) samplers can be incorporated in composite MH kernels as the proposal distribution. Specifically, as a special type of MCMC samplers, the Piecewise Deterministic Markov Process (PDMP) samplers can construct more efficient proposal distributions by utilizing non-reversible Markov processes and have already been applied in the design of composite MH kernels within SMCMC. In this study, we propose a novel approach to further improve state estimation performance in high-dimensional situations. We integrated the Zig-Zag Sampler (ZZS) —a special PDMP sampler—into the SMCMC framework and employed it to construct proposal distributions for the composite MH kernels. This integration fully leverages the advantages of both the ZZS and SMCMC. We assess the efficacy of our proposal method through numerical experiments on challenging high-dimensional state estimation tasks. The results demonstrate that our method significantly improves estimation accuracy and computational efficiency compared to existing state-of-the-art filtering techniques in high-dimensional situations.
