Asymptotically robust detection of a known signal in contaminated non-Gaussian noise
S.A. Kassam, John B. Thomas · IEEE Transactions on Information Theory · 1976
The Tukey-Huber contaminated noise model is used toobtain rain-max detectors in the asymptotic case for known signals inadditive noise. According to this model, the noise densityf(x)is defined byf(x) = (1 - \ )g(x) + \varepsilon h(x)for a given\varepsilonand densityg(x), withh(x)an arbitrary density from a large class. A general theorem is obtainedspecifying the most robust detector for additive contaminated noisewithg(x)satisfying certain regularity conditions. As an example,detector structures are derived by the application of the theorem for the case whereg(x)belongs to the class of generalized Gaussian densities(parameterized by their rates of exponential decay). The sign detector is shown to be the asymptotically most robust detector wheng(x)is a double-exponential density.