A scoring procedure for the multiple target correlation and tracking problem

This paper develops scoring procedures for those multiple target correlator-trackers, which, in effect, can be considered to be of the 'hard-decision' type- i.e., those correlator-trackers which form a partitioning Q of the accumulated data Z from multiple sensor sources into disjoint target track sets and a possible false alarm set. The accumulated data may involve missed detections, false alarms, and measured target positions, velocities, or various target attributes such as hull lengths, emitted frequencies, or identifications. One such score J for a given correlator-tracker is defined to be J(Q,Z) = -2 log pr(Q|Z), a form related to the posterior distribution of data partitionings. Choice of J is justified from both information theory and statistical decision theory viewpoints: In general, the smaller numerically J is, or its expectation with respect to (Z|Q) is, the better Q is as an estimator of the unknown true partitioning Q'. A closely related score J'(Q|Z) = -2 log pr(Z|Q) has similar theoretical properties to J, and is computationally more convenient. Emphasis in this paper is on J'. Following some simplifying assumptions, including linear Gauss-Markov target motion and measurement models, J' is shown to decompose into a sum of three terms. The first term involves geolocation goodness-of-fit and utilizes quadratic forms in innovations from the Kalman filters of the track sets as well as constant error dispersion matrices. The second term similarly describes the plausibility of the perceived false alarm set. The last term determines the good - ness-of-fit of the target attributes at hand to the perceived targets. (J'|Q) is shown to be distributed as the statistical independent sum of a constant, a chi-square random variable, and a discrete random variable. By making additional Gaussian approximations in the modelling of the target attribute data, the distribution of (J'|Q) simplifies to that of a constant plus a chi-square random variable. However, it is also shown that type I and type II decision errors in choosing the best Q through use of J' are difficult to compute, since the distribution of (J'(Q,Z) - J'(Q',Z)|Q) cannot be obtained in closed form. Use of J' in a real-world setting is outlined.