Detection of a distributed target with direction uncertainty

In this study, the authors deal with the problem of detecting a distributed target in coloured noise with unknown covariance matrix. The target echoes are all assumed to come from the same direction. However, the exact direction is unknown a priori. Precisely, the signal steering vector lies in a certain known subspace, but with unknown coordinate. They derive the Wald test and two-step Wald test and also show that there is no meaningful Rao test or its two-step variation. Moreover, it is found that the two-step Wald test is equivalent to an existing direction detector. Additionally, it is shown that the Wald test possesses the constant false alarm rate property. Some numerical examples are given to compare the detection performance of the novel direction detector with its counterparts, both in the cases of matched and mismatched signals.