A Multiple-Detection Probability Hypothesis Density Filter

Most conventional target tracking algorithms assume that one target can generate at most one detection per scan. However, in many practical target tracking applications, one target may generate multiple detections in one scan, because of multipath propagation, or high sensor resolution or some other reason. If the multiple detections from the same target can be effectively utilized, the performance of the multitarget tracking system can be improved. However, the challenge is that the uncertainty in the number of targets and the measurement set-to-target association will increase the complexity of tracking algorithms. To solve this problem, the random finite set (RFS) modeling and the random finite set statistics (FISST) are used in this paper. Without any extra approximation beyond those made in the standard probability hypothesis density (PHD) filter, a general multi-detection PHD (MD-PHD) update formulation is derived. It is also established in this paper that, with certain reasonable assumptions, the proposed MD-PHD recursion can function as a generalized extended target PHD or multisensor PHD filter. Furthermore, a Gaussian Mixture (GM) implementation of the proposed MD-PHD formulation, called the MD-GM-PHD filter, is presented. The proposed MD-GM-PHD filter is demonstrated on a simulated over-the-horizon radar (OTHR) scenario.