B. Porat et B. Friedlander, ON THE GENERALIZED LIKELIHOOD RATIO TEST FOR A CLASS OF NONLINEAR DETECTION PROBLEMS, IEEE transactions on signal processing, 41(11), 1993, pp. 3186-3190
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.