Optimal point estimates for multi-target states based on kernel distances

Almost all multi-target tracking systems have to generate point estimates for the targets, e.g., for displaying the tracks. The novel idea in this paper is to consider point estimates for multi-target states that are optimal according to a kernel distance measure. Because the kernel distance is a metric on point sets and ignores the target labels, shortcomings of Minimum Mean Squared Error (MMSE) estimates for multi-target states can be avoided. We show how the calculation of these point estimates can be casted as an optimization problem and it turns out that it corresponds to the problem of reducing the Probability Hypothesis Density (PHD) function to a Dirac mixture density. Finally, we discuss a generalization of the kernel distance called LCD distance, which does not require to choose a specific kernel width. The presented methods are evaluated in a Multiple-Hypotheses Tracker (MHT) setting with up to ten targets.