ON THE GENERALIZED LIKELIHOOD RATIO TEST FOR A CLASS OF NONLINEAR DETECTION PROBLEMS

This note examines the generalized likelihood ratio test (GLRT) for a certain class of detection problems. This class is characterized by a model which is linear in some parameters and nonlinear in other. We sh ow that the classical asymptotic analysis of the GLRT fails for this c lass, and demonstrate the existence of ill-behaved cases in this class . We then propose a modification of the GLRT. The main advantage of th is modification is in that its probability of false-alarm is easily co mputable, thus facilitating the choice of threshold according to Neyma n-Pearson criterion. Performance analysis of the modified GLRT is prov ided and supported by some simulations.