Optimal decomposed particle filtering of two closely spaced Gaussian targets

For Bayesian filtering of two closely spaced linear Gaussian targets from Gaussian observations, the paper exploits a unique decomposition of the joint conditional density into a mixture of a permutation invariant density and a permutation strictly variant density. This leads to the development of a novel particle filter which performs optimal in the sense of either minimizing track swapping or minimizing track switching, and which includes estimation of the conditional track swap probability. Through Monte Carlo simulations, it is shown that minimizing track switching has a significant advantage over minimizing track swapping, and that the novel particle filter performs remarkably better than a standard particle filter.