Classical target detection schemes are usually obtained deriving thelikelihood ratio under Gaussian hypothesis and replacing the unknown backgroundparameters by their estimates. In most applications, interference signals areassumed to be Gaussian with zero mean or with a known mean vector that can beremoved and with unknown covariance matrix. When mean vector is unknown, it hasto be jointly estimated with the covariance matrix, as it is the case forinstance in hyperspectral imaging. In this paper, the adaptive versions of theclassical Matched Filter and the Normalized Matched Filter, as well as twoversions of the Kelly detector are first derived and then are analyzed for thecase when the mean vector of the background is unknown. More precisely,theoretical closed-form expressions for false-alarm regulation are derived andthe Constant False Alarm Rate property is pursued to allow the detector to beindependent of nuisance parameters. Finally, the theoretical contribution isvalidated through simulations and on real hyperspectral scenes.
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