Extreme-value analysis for mlML-PMHT, Part 2: target trackability

The Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT) can be used as a powerful multisensor, low-observable, multitarget active tracker. It is a non-Bayesian algorithm that uses a generalized likelihood ratio test (GLRT) to differentiate between clutter and targets. We use a new method, initially developed to obtain the probability density function (pdf) of the maximum point in the ML-PMHT log-likelihood ratio (LLR) due to clutter, to now develop a pdf for the maximum value of the ML-PMHT LLR caused by a target. With expressions for the pdfs of the maximum points caused by both clutter (developed in a companion article) and a target, we can, for a given set of tracking parameters (signal-to-noise ratio, search volume, target measurement probability of detection, etc.), develop ML-PMHT "tracker operating characteristic" curves, similar to receiver operating characteristic curves for a detector. Since ML-PMHT can be thought of as an optimal algorithm in the sense that, as long as the target and the environment match the algorithm's assumptions, all the information from all the available measurements can be used, and no approximations are necessary to get the algorithm to function, the analysis presented in this paper offers for the first time part of the answer to the fundamental question: Can a particular target be tracked?