Median matrices and their 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 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, the new devised estimators are applied to the problem of secondary data selection and their performances are compared with those obtained using geometric barycenters. The results show that data selectors exploiting geometric medians can outperform those based on geometric barycenters but the former requires a computational complexity higher than the latter.