Bayesian Metropolis methods for source localization in an urban environment

Abstract

We apply Bayesian techniques to determine the location and intensity of a gamma radiation source in an urban environment using count rates taken from a distributed detector network. A simplified model of the radiation transport process is used to construct a statistical model for the detector count rates in the presence of a randomly varying background. Markov Chain Monte Carlo is used to generate samples from the Bayesian posterior density, which can be used to inform search and interdiction efforts. We also present a modification of the traditional Metropolis sampling algorithm that allows us to incorporate fixed parameter uncertainties in building macroscopic cross sections and account for their effects on the posterior distribution. This method is then applied to a test problem based on a real urban geometry with different levels of uncertainty in the building cross sections. The results show that the uncertainty in the estimated source location is modest, even with a large degree of uncertainty in the building cross sections.