ML-PDA Track Validation Thresholds

Abstract

The maximum likelihood probabilistic data association (ML-PDA) algorithm, developed for very low observable (VLO) target tracking, will always provide a candidate track that must then be either validated or rejected. By comparing the value of the log likelihood ratio (LLR) at the parameter estimate to a threshold value, track validation is accomplished. Using extreme value theory, we show that in the absence of a target the LLR global maximum obeys approximately a Gumbel distribution and not the Gaussian distribution previously ascribed to it in the literature. It is shown that the Gaussian approximation yields inaccurate false track acceptance probabilities. Using a Gumbel distribution, the probability of false track rejection can be obtained for a given threshold value. The probability of true track detection is obtained assuming the LLR global maximum obeys approximately a Gaussian distribution in the presence of a target. A system operating characteristic (SOC) is developed that unifies the detection processing and track algorithm performance into a single performance metric. The performance of this test is demonstrated through simulations.