Multitarget tracking algorithm - Joint IPDA and Gaussian mixture PHD filter

Random finite set approach is a mathematically rigorous framework for multi-target tracking. It provides a Bayesian recursion of multi-target distribution through finite set calculus. But practical implementation of multi-target posterior recursion is difficult because of its combinatorial nature. Probability hypothesis density (PHD) filter is an alternative to this problem where only the first order moment of the complete multi-target posterior is propagated in time. One of the suitable implementations of probability density filter is Gaussian mixture PHD filter. Parallel to this approach, several multi-target tracking algorithms are devised based on corresponding single target tracking algorithms. Joint integrated probabilistic data association is one of the most successful of such algorithms. This article shows that PHD filter recursion reduces to joint IPDA formalism under linear Gaussian assumptions.