Persymmetric Subspace Rao and Wald Tests for Distributed Target in Partially Homogeneous Environment

We consider the problem of distributed target detection in partially homogeneous Gaussian clutter with unknown covariance matrix. The target is assumed to lie in a multi-rank subspace with unknown coordinates. By incorporating the persymmetric structure of the covariance matrix into the detector design, we devise a persymmetric subspace Rao detector (Per-Rao) and a persymmetric subspace Wald detector (Per-Wald). It is remarkable that the Per-Rao coincide with the Per-Wald in the partially homogeneous environment, and both detectors are shown to ensure constant false alarm rate (CFAR) with respect to the covariance matrix. Numerical examples verify the superiority of the proposed methods in training-restricted situations.