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The authors consider the problem of knowledge-aided covariance matrix estimation and its application to adaptive radar detection. The authors assume that an a priori (knowledge-based) estimate of the disturbance covariance M, derived from a physical scattering model of the terrain and/or of the environment, is available. Hence, starting from a set of secondary data, the authors evaluate the maximum likelihood (ML) estimate of M assuming that it lies in a suitable neighbourhood of the a priori estimate and formulate this ML estimation in terms of a convex optimisation problem which falls within the class of MAXDET problems. Both the cases of unstructured and structured disturbance covariance are considered. At the analysis stage, the authors assess the performance of the new knowledge-aided covariance estimators both in terms of estimation error and detection probability achievable by a class of adaptive detectors. The results highlight that, if the a priori knowledge is reliable, satisfactory levels of performance can be achieved with considerably less training data than those exploited by conventional algorithms.