Adaptive subspace detectors

In this paper, we use the theory of generalized likelihood ratio tests (GLR Ts) to adapt the matched subspace detectors (MSDs) of [1] and [2] to unknow n noise covariance matrices. In so doing, we produce adaptive MSDs that may be applied to signal detection for radar, sonar, and data communication. W e call the resulting detectors adaptive subspace detectors (ASDs), These in clude Kelly's GLRT and the adaptive cosine estimator (ACE) of [6] and [19] for scenarios in which the scaling of the test data may deviate from that o f the training data. We then present a unified analysis of the statistical behavior of the entire class of ASDs, obtaining statistically identical dec ompositions in which each ASD is simply decomposed into the nonadaptive mat ched filter, the nonadaptive cosine or t-statistic, and three other statist ically independent random variables that account for the performance-degrad ing effects of limited training data.