Space-time CUSUM for distributed quickest detection using randomly spaced sensors along a path

This work investigates the distributed quickest detection problem, where a set of sensors receive independent observations and send messages to a fusion center, which makes a final decision. We are interested in detecting an event as soon as possible even though the set of affected sensors is unknown. We consider a scenario where the sensors are randomly spaced along a path, and then the affected sensors are assumed to be consecutive. Based on the assumption that the affected sensors are consecutive, we propose a solution based on the detection of a transient change in the spatial domain (i.e. from different sensors). This is done by applying a double CUSUM to detect both the appearance and disappearance of the change in the space samples. Numerical results are presented showing the superior performance of our proposed solution, for different scenarios, with respect to other methods in the literature.