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

Avishy Carmi (1) , Lyudmila Mihaylova (2) , François Septier (3, 4)

1 Department of Mechanical Engineering [Beer-Sheva]
2 University of Sheffield [Sheffield]
3 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
4 Institut TELECOM/TELECOM Lille1

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 (l1 constrained) algorithm. The results show high estimation accuracy.

Keywords: Markov chain Monte Carlo methods; High dimensional systems; Compressed sensing; L1 optimisation; Filtering

Domains: Signal and Image processing; Applications [stat.AP]; Computation [stat.CO]; Methodology [stat.ME]

Avishy Carmi, Lyudmila Mihaylova, François Septier. Subgradient-based Markov Chain Monte Carlo particle methods for discrete-time nonlinear filtering. Signal Processing, 2016, 120, pp.532-536. ⟨10.1016/j.sigpro.2015.10.015⟩. ⟨hal-01238925⟩