  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.
