Extreme-value analysis for ML-PMHT, Part 1: threshold determination

The Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT) can be used as a powerful multisensor, low-observable, multitarget active sonar tracker. It is a non-Bayesian algorithm that uses a generalized likelihood ratio test to differentiate between clutter and targets. Prior to this paper, the detection threshold used for target discrimination was determined either through trial and error or with lengthy Monte Carlo simulations.We present a new method for determining this threshold by assuming that clutter is uniformly distributed in the search space (which is one of the basic assumptions of the ML-PMHT algorithm) and then treating the log-likelihood ratio (LLR) as a random variable transformation. In this manner we can obtain an expression for the value of any random point on the likelihood surface caused by clutter. We then use extreme value theory to obtain an expression for the probability density function (PDF) of the peak point of the LLR surface due to clutter. From this peak PDF, we can then calculate a threshold based on some desired (small) false track acceptance probability.