Robust detection of small stochastic signals

We consider the problem of detecting a stochastic signal in white not-necessarily-Gaussian noise, using vector valued observations. The locally optimal detector is presented and its performance evaluated. The least-favorable signal spectrum and noise density (over specified classes) are found, and it is shown that the detector using these least-favorable assumptions is minimax robust. The class of spectra is that of any stochastic signal of specified power whose spectrum can be bounded from above and from below by two given positive functions. The class of densities is the /spl epsi/-contamination model. We present examples of the performance achievable with the robust detector in one of these the spectral uncertainty class corresponds to the unknown Doppler shift of a radar return signal. It is demonstrated that the standard matched-filter's performance degradation with increasing Doppler shift can be avoided almost entirely through use of the robust processor.