Decision-Making Accuracy for Sensor Networks with Inhomogeneous Poisson Observations

The paper considers a network of sensors which observes a time-inhomogeneous Poisson signal and has to decide, within a fixed time interval, between two hypotheses concerning the intensity of the observed signal. The focus is on the impact of information sharing among individual sensors on the accuracy of a decision. Each sensor computes locally a likelihood ratio based on its own observations, and, at the end of the decision interval, shares this information with its neighbors according to a communication graph, transforming each sensor to a decision-making unit. Using analytically derived upper bounds on the decision error probabilities, the capacity of each sensor as a decision maker is evaluated, and consequences of ranking are explored. Example communication topologies are studied to highlight the interplay between a sensor's location in the underlying communication graph (quantity of information) and the strength of the signal it observes (quality of information). The results are illustrated through application to the problem of deciding whether or not a moving target carries a radioactive source.