Riemannian median, geometry of covariance matrices and radar target detection

We develop a new geometric approach for radar target detection which is based on the notion of Riemannian median and the information geometry of covariance matrices. First of all, we give the definition of Riemannian median and a simple algorithm to compute it. After that, the explicit expressions of reflection coefficients parametrization of covariance matrices are obtained, with which the Riemannian metric on the manifold of covariance matrices has a very simple form. The explicit expressions of geodesics in the manifold are also obtained in order to facilitate the computation of the Riemannian median of covariance matrices. Finally, we give some simulation examples to illustrate the performance of this new method.