Median matrices and geometric barycenters for training data selection

This paper deals with the problem of covariance matrix estimation for radar signal processing applications. We propose and analyze a class of estimators which do not require any knowledge about the probability distribution of the sample support and exploit the characteristics of the positive definite matrix space. Any estimator of the class is associated with a suitable distance in the considered space and is defined as the median matrix of some basic covariance matrix estimates obtained from the available secondary data set. Then, we apply the new devised estimators to the problem of secondary data selection and compare their performances with those obtained using geometric barycenters.