Asymptotically optimum tests for decentralized change detection

Assuming that sensors have full local memory, we introduce a novel test for the problem of decentralized change detection that is asymptotically optimum. According to our proposed scheme, sensors perform locally repeated SPRTs and communicate, asynchronously, their one-bit decisions to a fusion center. The fusion center in turn uses the sequentially acquired information to perform a CUSUM test in order to decide whether a change took place or not. We prove that the average detection delay of the proposed test differs from the optimum centralized CUSUM test only by a constant. This fact suggests order-2 asymptotic optimality as compared to existing schemes that are optimal of order-1.