Offline and Real-Time Methods for ML-PDA Track Validation

We present two procedures for validating track estimates obtained using the maximum-likelihood probabilistic data association (ML-PDA) algorithm. The ML-PDA, developed for very low observable (VLO) target tracking, always provides a track estimate that must then be tested for target existence by comparing the value of the log likelihood ratio (LLR) at the track estimate to a threshold. Using extreme value theory, we show that in the absence of a target the LLR at the track estimate obeys approximately a Gumbel distribution rather than the Gaussian distribution previously ascribed to it in the literature. The offline track validation procedure relies on extensive offline simulations to obtain a set of track validation thresholds that are then used by the tracking system. The real-time procedure uses the data set that produced the track estimate to also determine the track validation threshold. The performance of these two procedures is investigated through simulation of two active sonar tracking scenarios by comparing the false and true track acceptance probabilities. These techniques have potential for use in a broader class of maximum likelihood estimation problems with similar structure