The CFAR adaptive subspace detector is a scale-invariant GLRT

• Published in: IEEE transactions on signal processing Vol. 47; no. 9; pp. 2538 - 2541
• Main Authors: Kraut, S., Scharf, L.L.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.1999; Institute of Electrical and Electronics Engineers
• Subjects: Adaptive signal detection; Adaptive structures; Applied sciences; Covariance; Covariance matrix; Detectors; Exact sciences and technology; Noise; Noise level; Noise levels; Noise measurement; Radiolocalization and radionavigation; Signal detection; Signal to noise ratio; Subspaces; Target detection; Telecommunications; Telecommunications and information theory; Testing; Training; Training data; Variable speed drives; Matched filter; Radar target; Signal processing; Adaptive filter; Covariance matrix; Maximum likelihood; Multidimensional system; Target detection; Signal detection; False alarm rate
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.782198

The constant false alarm rate (CFAR) matched subspace detector (CFAR MSD) is the uniformly most-powerful-invariant test and the generalized likelihood ratio test (GLRT) for detecting a target signal in noise whose covariance structure is known but whose level is unknown. Previously, the CFAR adaptive subspace detector (CFAR ASD), or adaptive coherence estimator (ACE), was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data. We show here that the CFAR ASD is GLRT when the test measurement is not constrained to have the same noise level as the training data, As a consequence, this GLRT is invariant to a more general scaling condition on the test and training data than the well-known GLRT of Kelly (1986).