ML-PMHT threshold determination for false track probability using extreme-value analysis

The Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT) can be used as a powerful multisensor, low-observable, multitarget tracker. It is a non-Bayesian algorithm that uses a generalized likelihood ratio (LR) test to differentiate between clutter and target tracks. Prior to this work, the detection threshold used for target track acceptance 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 the clutter is uniformly distributed in the search space, and then treating the log-likelihood ratio (LLR) as a random variable transformation. In this manner, we can obtain an expression for the PDF of the likelihood function caused by clutter. We then use extreme value theory to obtain an expression for the 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.