Quickest detection in a system with correlated noise

This work considers the problem of quickest detection of signals in a system of 2 sensors coupled by a negatively correlated noise, which receive continuous sequential observations from the environment. It is assumed that the signals are time invariant and with equal strength, but that their onset times may differ from sensor to sensor. The objective is the optimal detection of the first time at which any sensor in the system receives a signal. The problem is formulated as a stochastic optimization problem in which an extended Lorden´s criterion is used as a measure of detection delay, with a constraint on the mean time to the first false alarm. The case in which the sensors employ their own cumulative sum (CUSUM) strategies is considered, and it is proved that the minimum of 2 CUSUMs is asymptotically optimal as the mean time to the first false alarm increases without bound. Implications of this asymptotic optimality result to the efficiency of the decentralized versus the centralized system of observations are further discussed.