Decomposed particle filtering and track swap estimation in tracking two closely spaced targets

In a preceding paper at Fusion 2009, the existence and characterization of a unique decomposition of the joint conditional density of the states of two targets has been proven. This decomposition consists of a weighted sum of a permutation invariant density and a permutation strictly variant density. In the current paper we exploit this unique decomposition for the development of a novel particle filter for tracking two closely spaced linear Gaussian targets. Thanks to the unique decomposition this novel particle filter is able to provide a conditional estimate of the track swap probability. The remarkable working of this novel particle filter is demonstrated through running Monte Carlo simulations for an example in tracking two closely spaced targets.