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In space-time adaptive processing (STAP), the clutter covariance matrix is routinely estimated from secondary ldquotarget-freerdquo data. Because this type of data is, more often than not, rather scarce, the so-obtained estimates of the clutter covariance matrix are typically rather poor. In knowledge-aided (KA) STAP, an a priori guess of the clutter covariance matrix (e.g., derived from knowledge of the terrain probed by the radar) is available. In this note, we describe a computationally simple and fully automatic method for combining this prior guess with secondary data to obtain a theoretically optimal (in the mean-squared error sense) estimate of the clutter covariance matrix. The authors apply the proposed method to the KASSPER data set to illustrate the type of achievable performance.