Persymmetric Subspace Detectors With Multiple Observations in Homogeneous Environments

In this article, a target detection problem in homogeneous Gaussian noise with unknown covariance matrix is examined using multiple observations, which may be collected from multiple range cells, bands, and/or coherent processing intervals. In order to take into consideration mismatches of the target steering vector, we adopt a subspace model where the target steering vector is assumed to lie in a subspace spanned by the column vectors of a known matrix with unknown target coordinates. By exploiting persymmetric structures, we propose several adaptive detectors according to ad hoc modifications of generalized likelihood ratio test (GLRT), Rao test, and Wald test. It is found that the Rao test does not exist, whereas the two-step Wald test shares the same form as the two-step GLRT. Numerical examples show that the robustness of the proposed detectors is better than that of their counterparts in general. In particular, the proposed one-step GLRT is the most robust in most cases, and the proposed two-step GLRT and one-step Wald test can be more robust than the one-step GLRT in the case where the number of training data is small.