LDA-MIG Detectors for Maritime Targets in Nonhomogeneous Sea Clutter

This article deals with the problem of detecting maritime targets embedded in nonhomogeneous sea clutter, where the limited number of secondary data is available due to the heterogeneity of sea clutter. A class of linear discriminant analysis (LDA)-based matrix information geometry (MIG) detectors is proposed in the supervised scenario. As customary, Hermitian positive-definite (HPD) matrices are used to model the observational sample data, and the clutter covariance matrix of the received dataset is estimated as the geometric mean of the secondary HPD matrices. Given a set of training HPD matrices with class labels, which are elements of a higher dimensional HPD matrix manifold, the LDA manifold projection learns a mapping from the higher dimensional HPD matrix manifold to a lower dimensional one subject to maximum discrimination. In this study, the LDA manifold projection, with the cost function maximizing between-class distance while minimizing within-class distance, is formulated as an optimization problem in the Stiefel manifold. Four robust LDA-MIG detectors corresponding to different geometric measures are proposed. Numerical results based on both simulated radar clutter with interferences and real IPIX radar data show the advantage of the proposed LDA-MIG detectors against their counterparts without using LDA and the state-of-the-art maritime target detection methods in nonhomogeneous sea clutter.