Adaptive detection of point-like targets based on a reduced-dimensional data model

Abstract

Abstract This paper approaches the problem of detecting a point-like target in Gaussian background. The useful signal lies in an one-dimensional subspace spanned by a known steering vector. The Gaussian disturbance fills the whole observation space. Since the disturbance outside the signal subspace is unrelated to the decision result, it is eliminated by pre-multiplying the recorded data by the conjugate transpose of the steering vector in this paper. This preprocessing is not applied in the classical detectors, such as the generalized likelihood ratio test (GLRT), the adaptive matched filter (AMF), etc. This preprocessing results in a new scalar data model where the useful signal and disturbance lie in the same space. Based on this scalar data model, two new detectors are designed through the one-step and two-step GLRT, respectively. Their probabilities of false alarms and detections are derived analytically. The one- (two-) step GLRT-based detector has the (approximately) constant false alarm rate feature in the Gaussian background. Simulation results show that the proposed detectors outperform those classical ones when finite training data is available. The one-step GLRT-based detector is more robust to mismatched signals than those classical detectors.