A fundamental issue in knowledge-aided space-time adaptive processing (KA-STAP) is to determine the degree of accuracy of the a~priori knowledge and the optimal emphasis that should be placed on it. In KA-STAP, the a priori knowledge consists usually of an initial guess of the clutter covariance matrix. This can be obtained either by previous radar probings or by a map-based study. We consider a linear combination of the a~priori clutter covariance matrix with the sample covariance matrix obtained from secondary data, and derive an optimal weighting factor on the a priori knowledge by a maximum likelihood (ML) approach. The performance of the ML approach for KA-STAP is evaluated based on numerically simulated data.