On robust quickest detection procedures

Quickest detection procedures when underlying noise models are partially unknown are considered. We investigate robust quickest detectors of the maximin type, where the quantity to be optimized is an asymptotic performance measure relating the mean time between false alarms to the expected delay in detection. It is shown that the maximin asymptotic measure is equal to the Kullback-Leibler divergence. Consequently, the robust detector is obtained by maximizing the K-L divergence for the least favorable distribution in the allowable class. For the weak signal case, we show an equivalence between the performance measure, the classical efficacy, and Fisher´s information. The weak signal robust detector is obtained by finding the least favorable distribution for Fisher´s information. Performance curves are given to show the gains available when robustness is built into the detection procedure