Regularization synthesis of stable detectors of signals in the presence of normal noise

Detection of known signals containing an unknown parameter and of normal random signals is discussed in the presence of normal noise, when the mean values and the correlation functions of signals and noise are specified with an error. The signal-to-noise ratio prior to the threshold device is selected as the quality criterion of the detectors. It is shown that Tikhonov's regularization method can be used to synthesize detectors which are stable with respect to small perturbations of the hypotheses being tested. Algorithms of detector synthesis are given.