An efficient adaptive sequential procedure for detecting targets

Wald´s sequential probability ratio test (SPRT) is known to be optimal for simple hypotheses. However, the hypotheses in target detection applications are usually composite, because, as a rule, the models are only partially known. A major method traditionally used for testing composite hypotheses is based on a generalized likelihood ratio. However, the generalized SPRT suffers from a crucial drawback - it is very difficult to select thresholds in order to guarantee prescribed levels of false alarms and missed detections. We consider an adaptive approach that allows us to overcome this problem. At each stage, unknown parameters are replaced with an estimator which is based on previous observations, but not on the current observation. It is shown that the adaptive test is uniformly asymptotically optimal in the sense that it minimizes the average sample size for all parameter values when probabilities of errors are small. The general results are applied to the problem of detecting a target with unknown intensity in clutter with unknown variance.