Bayesian Conditional Monte Carlo Algorithms for Sequential Single and Multi-Object filtering

TL;DR

This paper introduces Bayesian Conditional Monte Carlo algorithms that leverage the recursive structure of Sequential Monte Carlo methods to improve estimation accuracy in single and multi-object filtering tasks.

Contribution

It develops Bayesian CMC estimators that outperform standard Monte Carlo methods and can be efficiently computed in various hidden Markov models and multitarget filtering scenarios.

Findings

Bayesian CMC estimators outperform crude Monte Carlo estimators.

Exact or efficient approximation of CMC estimators in HMC, JMSS, and multitarget filtering.

Validated through simulation experiments.

Abstract

Bayesian filtering aims at tracking sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density function (pdf) of the hidden process given the available observations. On the other hand, Conditional Monte Carlo (CMC) is a variance reduction technique which replaces the estimator of a moment of interest by its conditional expectation given another variable. In this paper we show that up to some adaptations, one can make use of the time recursive nature of SMC algorithms in order to propose natural temporal CMC estimators of some point estimates of the hidden process, which outperform the associated crude Monte Carlo (MC) estimator whatever the number of samples. We next show that our Bayesian CMC estimators can be computed exactly, or approximated efficiently, in some hidden Markov chain (HMC) models; in some jump Markov state-space systems (JMSS); as well as in multitarget filtering. Finally our algorithms are validated via simulations.