Estimation of posterior distributions with population Monte Carlo sampling and graphical modeling

An important step in applying graphical models to signal processing is the implementation of belief propagation. Belief propagation represents an efficient way of solving inference problems based on passing local messages. When we deal with continuous hidden variables, belief propagation requires solving integrals which usually do not have analytical solutions. In this paper we show how this can be accomplished on factor graphs using population Monte Carlo (PMC) sampling. We propose a scheme that enforces the same set of particles to be used by the different factors, which allows for easy fusion of messages while forming the belief of each variable. We present the proposed scheme with an application to target localization with signal strength measurements.