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

Abstract

Abstract-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 multitarget 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.

Hypothesis structure in enhanced multiple-hypothesis tracking

“…The third measure is cardinality error (CE), which quantifies the discrepancy between the number of targets and tracks. The fourth measure is the integrated squared distance (ISD), for which analytical expressions for sums of Gaussians are known [6,9]. The multi-target ground truth distribution is a sum of Dirac delta functions, so we increase target and track covariances by 2 / 2 .…”

Counting targets with MHT and CPHD

“…This phenomenon is particularly relevant in low I detection-probability settings, or in multi-sensor settings with disparate detection probabilities and revisit intervals. Our use of the MISD is motivated by related work [4][5].…”