Knowledge-Aided Covariance Matrix Estimation: a MAXDET Approach

In this paper, we consider the problem of knowledge-aided covariance matrix estimation and its application to adaptive radar detection. We 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, we evaluate the Maximum Likelihood (ML) estimate of M assuming that it lies in a suitable neighborhood of the a-priori estimate. We formulate this ML estimation in terms of a convex optimization problem which falls within the class of MAXDET problems. Both the cases of unstructured and structured disturbance covariance are considered. At the analysis stage, we assess the performance of the new knowledge-aided covariance estimators in terms of 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.