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

• We propose two detectors in the presence of spatial–temporal uncertainty.
• The proposed detectors have the CFAR property.
• They have better detection performance than the existing ones.

Azimuthal angles and Doppler frequencies of radar targets usually suffer from estimation uncertainty in practice, which poses a big challenge in target detection. In this work, we consider the problem of target detection in the presence of uncertainty in the azimuthal angle and Doppler frequency. This uncertainty is characterized by a subspace model. Precisely, the spatial and temporal steering vectors of the target are assumed to lie in certain known subspaces but with unknown coordinates. Two detectors are devised in the framework of generalized likelihood ratio test. Moreover, the properties of the proposed detectors are derived for the case of sufficiently large training data. It is shown by numerical examples that the detector derived according to the one-step design procedure has higher probability of detection than its counterparts in the absence of signal mismatch, while the detector devised according to the two-step design procedure is most robust to the signal mismatch.