Geometric barycenters for covariance estimation in compound-Gaussian clutter

The authors consider the problem of covariance matrix estimation in heterogeneous environments for radar signal processing applications, where the secondary data exhibit heterogeneity in local power and share the same covariance structure. Without resorting to the complete statistical characterisation of the sample support, a class of estimators, each of them defined as the geometric barycenter of a set of basic covariances estimates (obtained from the available secondary data) with a specific distance employed, is proposed. The basic estimates are obtained by exploiting the characteristics of positive-definite matrix space and a condition number upper bound constraint. Finally, they evaluate the detection capabilities of an adaptive normalised matched filter with the proposed estimators in the presence of compound-Gaussian disturbance comparing it with existing alternatives.