Can this target be tracked?

In the field of target tracking, it is often assumed that as long as a target is present and detectable, it should be “trackable.” Any failure to track a target that is generating detectable measurements is assumed to be due to a sub-optimal tracking algorithm or perhaps an algorithm that is not properly “tuned.” There seems to exist the idea that “if this knob is turned slightly, or this parameter is adjusted a little, our tracker should be able to follow the target … ” This work shows that, as should really be expected, there are times when, even though there is a target present that is producing measurements, the output statistical distribution produced by these measurements cannot be differentiated from the output statistical distribution of the too-numerous clutter-generated measurements, and the target simply cannot be tracked. This degree of “trackability” is demonstrated by employing the Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT), which is a powerful non-Bayesian algorithm that uses a generalized likelihood ratio test (GLRT) to check for a target in the presence of clutter. For various combinations of measurement dimensionality, amplitude features, and classification features, we treat the ML-PMHT log-likelihood ratio (LLR) as a random variable (RV) transformation and then use extreme-value theory to calculate the probability density function (PDF) for the peak point in the LLR due to clutter as well as the PDF of the peak point in the LLR due to a target. In doing so, the tracking problem is reduced to a simple detection problem, making it possible to answer the question, “Can this target be tracked?”