Geometric target detection based on total Bregman divergence

This paper develops a geometric detection approach based upon the total Bregman divergence on the Riemannian manifold of Hermitian Positive-Definite (HPD) matrices to realize target detection in a clutter. First of all, the radar received clutter data in each range cell in one coherent processing interval is modeled and mapped into an HPD matrix space, which can be described as a complex Riemannian manifold. Each point of this manifold is an HPD matrix. Then, a class of total Bregman divergences are presented to measure the closeness between HPD matrices. Based on these divergences, the medians for a finite collection of HPD matrices are derived. Furthermore, the three divergences, namely the total square loss, the total log-determinant divergence, and the total von Neumann divergence are deduced, and their corresponding geometric detection methods are designed. The principle of detection is that if a location has enough dissimilarity from the median estimated by its neighboring locations, targets are supposed to appear at this location. Numerical experiments and real clutter data are given to demonstrate the effectiveness of the proposed geometric detection methods.