Extended target detection in interference whose covariance matrix is defined via uncertainty convex constraints

In this paper we deal with the problem of detecting extended targets embedded in Gaussian interference with structured covariance matrix. We model the target echo from each range bin as a deterministic signal with an unknown scaling factor that accounts for the target response. We also exploit some a-priori knowledge about the operating environment at the design stage. Specifically, we assume that inverse disturbance covariance matrix belongs to a set described through a family of unitary invariant convex functions. Hence, we derive a class of Generalized Likelihood Ratio Tests (GLRT´s) for the resulting hypothesis test. At the analysis stage, we assess the performance of some detectors, lying in the aforementioned class, in terms of Detection Probability (P_D). The results highlight that the better the covariance uncertainty characterization, the better the detection performance.