Bayesian Rao and Wald test for radar adaptive detection

This paper deals with the adaptive detection of a signal of interest in the presence of Gaussian noise with unknown covariance matrix (CM). To this end, we resort to a Bayesian approach based on a suitable model for the probability density function (PDF) of unknown CM. Under this assumption, the maximum a-posteriori (MAP) estimation of CM is derived. The MAP estimate is in turn used to yield Bayesian version of Rao and Wald test. And the importance of the a priori knowledge can be tuned through scalar variable. Remarkably the devised detectors outperform Kelly´s GLRT and non Bayesian Rao and Wald test in the presence of strongly heterogeneous scenarios (where a very small number of training data is available). Meanwhile, the coincidence of Bayesian GLRT and Wald test is proved.