Radar covariance matrix estimation through geometric barycenters

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 geometric barycenter of some basic covariance matrix estimates obtained from the available secondary data set. Then, we 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 (AMF) taking the final decision about the target presence. At the analysis stage, we assess the performance of the proposed two-stage scheme in terms of probability of correct outliers excision and target detection. The analysis is conducted both on simulated data and on the challenging KASSPER datacube.