Invertible Particle Flow-based Sequential MCMC with extension to Gaussian Mixture noise models

TL;DR

This paper introduces a novel approach combining invertible particle flow with sequential MCMC, enhanced by Gaussian mixture models, to improve high-dimensional non-linear state estimation accuracy and efficiency.

Contribution

It proposes a new composite MH kernel within SMCMC using invertible particle flow and extends it with GMM-based particle flow for multi-modal distributions, addressing high-dimensional filtering challenges.

Findings

Significantly increased acceptance rates in high-dimensional scenarios

Improved estimation accuracy over existing algorithms

Minimal additional computational overhead

Abstract

Sequential state estimation in non-linear and non-Gaussian state spaces has a wide range of applications in statistics and signal processing. One of the most effective non-linear filtering approaches, particle filtering, suffers from weight degeneracy in high-dimensional filtering scenarios. Several avenues have been pursued to address high-dimensionality. Among these, particle flow particle filters construct effective proposal distributions by using invertible flow to migrate particles continuously from the prior distribution to the posterior, and sequential Markov chain Monte Carlo (SMCMC) methods use a Metropolis-Hastings (MH) accept-reject approach to improve filtering performance. In this paper, we propose to combine the strengths of invertible particle flow and SMCMC by constructing a composite Metropolis-Hastings (MH) kernel within the SMCMC framework using invertible particle flow. In addition, we propose a Gaussian mixture model (GMM)-based particle flow algorithm to construct effective MH kernels for multi-modal distributions. Simulation results show that for high-dimensional state estimation example problems the proposed kernels significantly increase the acceptance rate with minimal additional computational overhead and improve estimation accuracy compared with state-of-the-art filtering algorithms.