Shooting two birds with two bullets: How to find Minimum Mean OSPA estimates

Abstract

Most area-defense formulations follow from the assumption that threats must first be identified and then neutralized. This is reasonable, but inherent to it is a process of labeling: threat A must be identified and then threat B, and then action must be taken. This manuscript begins from the assumption that such labeling (A & B) is irrelevant. The problem naturally devolves to one of Random Finite Set (RFS) estimation: we show that by eschewing any concern of target label we relax the estimation procedure, and it is perhaps not surprising that by such a removal of constraint (of labeling) performance (in terms of localization) is enhanced. A suitable measure for the estimation of unlabeled objects is the Mean OSPA (MOSPA). We derive a general algorithm which provided the optimal estimator which minimize the MOSPA. We call such an estimator a Minimum MOSPA (MMOSPA) estimator.

Track-before-detect labeled multi-bernoulli particle filter with label switching

“…Weight calculation for i = 1 to N do -Calculate the weight w i using (38). end for -Perform resampling to obtain even particle weights.…”

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

“…Note that these definitions are analogous to the Mean OSPA (MOSPA) [8] and Minimum Mean OSPA (MMOSPA) estimate [8]. For well-separated targets, the MMKD estimate coincides with the MMSE estimate.…”

“…As a consequence, the mean kernel distance to a point estimate (8) and its derivative can be calculated in closed form. We will show that it is no problem to extract point estimates for ten targets with respect to the kernel distance in Section IX.…”

“…RELATED WORK In [8], [9], [10], [11] it was suggested to employ Minimum Mean OSPA estimates, where OSPA denotes the Optimal Subpattern Assignment Metric [12]. In [4], [5], Maximum A Posteriori (MAP) estimates were used instead of the MMSE estimate.…”

“…2 compares the MMOSPA estimate with the MMKD estimate for kernel widths 0.5 and 1. The MMOSPA estimate [8], [9], [10] was computed using an exponent of 2 and no cut-off value. Note again that there are two MMOSPA and MMKD estimates as the target states can be switched.…”