On Distributed Sampling for Detection of Poisson Sources

In this paper, we study the detection of Poisson point sources when the central detector observes the remote source via a restricted number of samples from distributed sensors. More specifically, we consider the scenario in which a Poisson source is observed, in noise, at two remote observers or samplers. At each sampler, the noisy observations are sampled as part of a distributed strategy designed by the central detector by accounting for a communication constraint between the sensor and the detector. Such limited sampling/estimation/communication scenarios are fundamental to modern cyberphysical systems. In such systems, discrete events such as signals for detection, control, and feedback propagate through a common communication and sensing infrastructure. For this scenario, we study the problem of optimally selecting the distributed sampling strategy employed at all remote samplers under the constraint that samples can be acquired for a given fraction of time across both samplers. We focus on point processes in this work and derive an optimal sampling strategy for the case of a homogeneous Poisson source which may be corrupted by another independent, additive and homogeneous Poisson noise source with known intensity. We show that any optimal solution combines either or both of these two distributed sampling strategies: (i) a time-sharing strategy -samplers communicate samples corresponding to non-overlapping time intervals, and (ii) a noise rejection strategy -samplers communicate samples during an identical time interval of activity, thus allowing for identification and subsequent rejection of the spurious additive noise realizations at either sampler. We argue that these two strategies play a crucial role in more general scenarios, encompassing a more general class of sources and noise realizations.