Decentralized CUSUM change detection

We consider the problem of decentralized change detection using the CUSUM test. More than one sensors acquire independent signals and send their quantized version to a fusion center that uses this information to detect a simultaneous change in all sensors. By introducing a recurrence relation that defines the optimum performance of the CUSUM lest for given quantization, we further optimize this measure with respect to the quantization scheme. We compare the resulting optimum test with a simple, asynchronous one shot strategy, where each sensor performs a local CUSUM test and communicates with the fusion center only once to signal its detection.