Robust GLRT approaches to signal detection in the presence of spatial–temporal uncertainty

GLRT-based generalized direction detector in partially homogeneous environment

“…Dear editor, Target detection is a basic function for any radar system [1]. For the problem of generalized direction detection, two adaptive detectors were proposed in [2], according to the generalized likelihood ratio test (GLRT). For the above problem, under the signal-presence hypothesis, the rows and columns of a rank-one matrix-valued signal belong to known subspaces; however, the corresponding coordinates are unknown.…”

“…It is worth pointing out that the problem of generalized direction detection in [2] was solved under the assumption of homogeneous environment. Precisely, the noise in the training data and test data is all subject to mean-zero complex Gaussian distribution, sharing the identical covariance matrix.…”

“…Problem formulation. The problem of generalized direction detection is formulated as the following binary hypothesis test [2]:…”

“…Different from the homogeneous environment assumed in [2], we focus the case of PHE such that R t = σ 2 R, with σ 2 and R are both unknown. The N × J signal matrix A and M × K signal matrix C are known in advance, whereas the J × 1 coordinate vector θ and M × 1 coordinate vector α are unknown.…”

“…where X 1 = X − Aθα H C, det(•) denotes the determinant, and tr(•) denotes the trace. There exists an ambiguity regarding the maximum likelihood estimates (MLEs) of θ and α [2]. To eliminate the ambiguity, it is assumed that θ satisfies the following constraint:…”