Covariance matrix estimation via geometric barycenters and its application to radar training data selection

This study deals with the problem of covariance matrix estimation for radar signal processing applications. The authors propose and analyse a class of estimators that 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 geometric barycenter of some basic covariance matrix estimates obtained from the available secondary data set. Then, the authors introduce an adaptive detection structure, exploiting the new covariance matrix estimators, based on two stages. The former consists of a data selector screening among the training data, whereas the latter is a conventional adaptive matched filter taking the final decision about the target presence. At the analysis stage, the authors assess the performance of the proposed two-stage scheme in terms of probability of correct outliers excision, constant false alarm rate behaviour and detection probability. The analysis is conducted both on simulated data and on the challenging KASSPER datacube.