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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 GLRT criterion both one-step and two-step. The suggested decision rules ensure the same performance of the non Bayesian GLRT detectors when the size of the training set is sufficiently large. However they significantly outperform the counterparts in the presence of heterogeneous scenarios, where a small number of homogeneous training data is available. The analysis is also supported by results on high fidelity radar data from the KASSPER program.