Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces

TL;DR

This paper introduces Langevin and Hamiltonian based Sequential MCMC methods that significantly improve Bayesian filtering efficiency in high-dimensional state-space models, addressing limitations of traditional particle filtering.

Contribution

The paper develops novel SMCMC algorithms utilizing Langevin diffusion and Hamiltonian dynamics, enhancing performance in high-dimensional Bayesian filtering tasks.

Findings

Proposed algorithms outperform existing methods in high-dimensional settings.

Langevin and Hamiltonian strategies improve sampling efficiency.

Simulation results demonstrate significant performance gains.

Abstract

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems. In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion and Hamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms.