Passive multi-target tracking with the marginalized Kalman GM-PHD filter

A marginalized Kalman Gaussian mixture Probability Hypothesis Density (GM-PHD) is proposed for jointly estimating the time-varying number of targets and their states from a sequence of observation sets in the presence of nonlinear state and observation model, detection uncertainty, noise and false alarms. The marginalized transformation (MT) is applied to calculate the prediction and update distribution of target states for the nonlinear models, and then the analytical expression of the target state and its covariance can be got. The measurement driven birth intensity is applied in the filter to ensure the target birth intensity could cover the entire state space. Finally, the resulting marginalized Kalman GM-PHD (MK-PHD) is compared to the EK-PHD, UK-PHD and CK-PHD in aspects of estimation of target number, OSPA distance and computation time. The evaluations show the effectivity of the theoretical analysis and the advantages of the proposed filter.