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We present a new method to estimate the clutter-plus-noise covariance matrix used to compute an adaptive filter in space-time adaptive processing (STAP). The method computes a ML estimate of the clutter scattering coefficients using a Bayesian framework and knowledge on the structure of the covariance matrix. A priori information on the clutter statistics is used to regularize the estimation method. Other estimation methods based on the computation of the power spectrum using for instance the periodogram are compared to our method. The result in terms of SINR loss shows that the proposed method outperforms the other ones.