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Recent research has shown a weak convergence - convergence in distribution -of particle filtering methods under certain assumptions. However, someapplications of particle filtering methods, such as radiation sourcelocalization problems, can be shown to have an extended convergence in thefollowing sense. Using the assumptions of statistically independentmeasurements and a measurement process that does not depend on the state space,we prove the convergence of the posterior and its approximation by the particlefiltering algorithm to the true Dirac distribution characterizing the sourcelocation. We design a Sampling Importance Resampling (SIR) filter to detect andlocate a radiation source using a network of sensors. To numerically assess theeffectiveness of this particle filter we employ it to solve a sourcelocalization problem using both experimental open field data sets fromIntelligent Radiation Sensor Systems (IRSS) tests and numerically simulatedurban domain data using a ray-tracing model. We then prove the theoreticalconvergence of the estimate to the state posterior probability densityfunction.

Particle Filtering Convergence Results for Radiation Source Detection