GMTI Tracking via the Gaussian Mixture Cardinalized Probability Hypothesis Density Filter

The cardinalized probability hypothesis density (CPHD) filter is a recursive Bayesian algorithm for estimating multiple target states with a varying target number in clutter. In particular the Gaussian mixture variant (GMCPHD), which provides closed-form prediction and update equations for the filter in the case of linear Gaussian systems, is a candidate for real time multi-target tracking. The following three issues are addressed. First we show the equivalence between the GMCPHD filter and the standard multi hypothesis tracker (MHT) in the case of a single target. Second by using a Gaussian sum approach, we extend the GMCPHD filter to incorporate digital road maps for road constrained targets. The use of such external information leads to more precise tracks and faster and more reliable target number estimates. Third we model the effect of Doppler blindness by a target state-dependent detection probability, which leads to a more stable target-number estimation in the case of low-Doppler targets.