Application of maximal invariance to the ACE detection problem
Three simple adaptive detection statistics frequently appearing in the radar detection literature, which employ a sample covariance estimate for clutter suppression, are Kelly's GLRT, the adaptive matched filter (AMF), and the adaptive cosine estimator (ACE), which is also a GLRT, for the problem where the test-data power level is unconstrained relative to the training data. Bose and Steinhardt found a two-dimensional maximal invariant statistic for the adaptive detection problem for which Kelly's statistic is a GLRT, a one-to-one function of the Kelly GLRT and the AMF. We extend this maximal-invariant framework to the adaptive detection problem for which ACE is a GLRT, showing that ACE is a one-dimensional maximal invariant.
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