On the generalized likelihood ratio test for a class of nonlinear detection problems

The authors examine 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 others. They show that the classical asymptotic analysis of the GLRT fails for this class, and demonstrate the existence of ill-behaved cases in this class. They then propose a modification of the GLRT. The main advantage of this modification is that its probability of false-alarm is easily computable, thus facilitating the choice of threshold according to the Neyman-Pearson criterion. Performance analysis of the modified GLRT is provided and supported by simulations