Optimal Neyman-Pearson fusion in two-dimensional sensor networks with serial architecture and dependent observations

In this correspondence, we consider a sensor network with serial architecture. When solving a binary distributed detection problem where the sensor observations are dependent under each one of the two possible hypothesis, each fusion stage of the network applies a local decision rule. We assume that, based on the information available at each fusion stage, the decision rules provide a binary message regarding the presence or absence of an event of interest. Under this scenario and under a Neyman-Pearson formulation, we derive the optimal decision rules associated with each fusion stage. As it happens when the sensor observations are independent, we are able to show that, under the Neyman-Pearson criterion, the optimal fusion rules of a serial configuration with dependent observations also match optimal Neyman-Pearson tests.