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This paper considers the problem of knowledge-aided space-time adaptive processing (STAP) in nonhomogeneous environments, where the covariance matrices of the training and test signals are assumed random and different from each other. A Bayesian detector is proposed by incorporating some a priori knowledge of the disturbance covariance matrices, and exploring their inherent block-Toeplitz structure. Specifically, the block-Toeplitz structure of the covariance matrix allows us to model the training signals as a multichannel auto-regressive (AR) process. The resulting detector is referred to as the Bayesian parametric adaptive matched filter (B-PAMF) which, compared with nonparametric Bayesian detectors, entails a lower training requirement and alleviates the computational complexity. Numerical results show that the proposed B-PAMF detector outperforms the standard PAMF test in nonhomogeneous environments.