ROBUST MULTIPLE CLASSIFICATION OF KNOWN SIGNALS IN ADDITIVE NOISE - AN ASYMPTOTIC WEAK SIGNAL APPROACH

The problem of extracting one out of a finite number of possible signa ls of known form given observations in an additive noise model is cons idered. Two approaches are studied: either the signal with shortest di stance to the observed data or the signal having maximal correlation w ith some transformation of the observed data is chosen. With a weak si gnal approach, the limiting error probability is a monotone function o f the Pitman efficacy and it is the same for both the distance-based a nd correlation-based detectors. Using the minimax theory of Huber, it is possible to derive robust choices of distance/correlation when the limiting error probability is used as performance criterion. This gene ralizes previous work in the area, from two signals to an arbitrary nu mber of signals. We consider M-type and R-type distances and also one- dimensional as well as two-dimensional signals. Finally, some Monte Ca rlo simulations are performed to compare the finite sample size error probabilities with the asymptotic error probabilities.