Robust adaptive threshold for control of false alarms

The thresholding of univariate test statistics for signal detection is considered for the case in which the pertinent probability distributions are not known but some training data is available. A distribution-free method for setting the threshold is derived. This threshold value maintains the average probability of false alarm (Pfa) at a fixed level and can be applied to noise/clutter data from any underlying probability distribution. Detection and false alarm performance are evaluated for the case in which the true, underlying univariate probability density is exponential for both noise and signal-plus-noise data. Performance is compared to the best adaptive detector, which is invariant to the exponential parameter governing the noise distribution, as well as the bounding case in which the exponential parameter is completely known. For this case, it is shown that the cost for a robust design is a small loss in the average probability of detection for a fixed average probability of false alarm. The study is of particular interest to radar and sonar.