Subgradient-based Markov Chain Monte Carlo particle methods for discrete-time nonlinear filtering

This work shows how a carefully designed instrumental distribution can improve the performance of a Markov chain Monte Carlo (MCMC) filter for systems with a high state dimension. We propose a special subgradient-based kernel from which candidate Moves are drawn. This facilitates the implementation of the filtering algorithm in high dimensional settings using a remarkably small number of particles. We demonstrate our approach in solving a nonlinear non-Gaussian high-dimensional problem in comparison with a recently developed block particle filter and over a dynamic compressed sensing (l(1) constrained) algorithm. The results show high estimation accuracy. (C) 2015 Elsevier B.V. All rights reserved.