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In this paper we consider the problem of adaptive radar detection in Gaussian disturbance with unknown spectral properties. To this end we resort to a Bayesian approach based on a suitable model for the probability density function of the unknown disturbance covariance matrix. We devise two detectors based on the generalized likelihood ratio test (GLRT) criterion both one-step and two-step. The new decision rules achieve a better performance level than some conventional radar detectors in the presence of heterogeneous scenarios, where a small number of training data is available. Finally they ensure the same performance of the non Bayesian GLRT detectors when the size of the training set is sufficiently large.