An Alternative Derivation of Generalized Likelihood Tests for Track-to-Track Correlation

In this paper, an alternative derivation for a generalized likelihood ratio test (GLRT) for pairwise track-to-track correlation is provided to be complementary to methods previously published. Hypothesis likelihoods for the case of a single target and the case for two targets are derived, and the generalized likelihood ratio is formed with the maximum likelihood estimates for the unknown parameter(s) under each hypothesis. A threshold is defined for a given probability of false alarms (i.e., miss-correlations). For more than two targets, each hypothesis has a varying number of true targets, and the generalized likelihoods are penalized using model selection criteria, such as minimum descriptor length (MDL) and Akaike information criteria (AIC) to determine the optimal number of targets (i.e., parameters) given the reported tracks to be correlated. Simulation results compare the generalized likelihood ratio to an extant procedure and the unrealistic clairvoyant detector for pairwise track-to-track correlation. For multi-sensor multi-target hypotheses, simulation results show the probability of correct correlation for the AIC and MDL methods for a varying number of targets and for various target separation.