Analysis of a GLRT for the detection of an extended target

For a high-resolution radar, an extended target is characterized by a few main scatterers spread over several range gates not necessarily consecutive. The joint detections and localizations of these scatterers are of particular interest in order to estimate the range profile and identify the target. In this paper, we study a detector based on the Generalized Likelihood Ratio Test considering the unknown locations of the scatterers. Given the number of scatterers and using order statistics results, we derive approximations of the probability of false alarm and the probability of detection and localization which can be a relevant measure of performance in this context. Finally, a comparative study is carried out with other existing detectors.