Particle Filtering Convergence Results for Radiation Source Detection

TL;DR

This paper proves the convergence of particle filtering methods for radiation source localization, demonstrating both theoretical guarantees and practical effectiveness with experimental and simulated data.

Contribution

It establishes extended convergence results for particle filters in radiation source detection and designs a specific SIR filter for this application.

Findings

The particle filter converges to the true source location distribution.

Experimental and simulated data validate the filter's effectiveness.

Theoretical proof confirms convergence to the true posterior.

Abstract

Recent research has shown a weak convergence - convergence in distribution - of particle filtering methods under certain assumptions. However, some applications of particle filtering methods, such as radiation source localization problems, can be shown to have an extended convergence in the following sense. Using the assumptions of statistically independent measurements and a measurement process that does not depend on the state space, we prove the convergence of the posterior and its approximation by the particle filtering algorithm to the true Dirac distribution characterizing the source location. We design a Sampling Importance Resampling (SIR) filter to detect and locate a radiation source using a network of sensors. To numerically assess the effectiveness of this particle filter we employ it to solve a source localization problem using both experimental open field data sets from Intelligent Radiation Sensor Systems (IRSS) tests and numerically simulated urban domain data using a ray-tracing model. We then prove the theoretical convergence of the estimate to the state posterior probability density function.