Label Matching: It Is Complicated

This paper addresses the intractable track matching problem involved in multi-sensor multi-target tracking using the labeled multi-Bernoulli filters. Unlike the unlabeled density defined in the common state space, the labeled multi-target density is defined in the joint state and label space, where the label contains time-series/history information of the underlying track. To measure the similarity between labeled densities (individual tracks) that is required for inter-sensor track matching and fusion, one has to account for the divergences in both state and label spaces. The challenge, however, arises from the lack of a proper metric to measure the label difference. It requires considering the entire trajectory of the track, encompassing the whole-life information from the birth of the track to the present. In this paper, we provide a solution of comparing and matching labels based on the whole-life time-series state distributions of the labels/tracks, by extending the common divergences like the Cauchy-Schwarz and Kullback-Leibler from distributions at a single time-instant to those over time-series. Representative scenarios are considered for illustration.