Local and nonlocal robustness measures with application to distributed sensor systems

We investigate the robustness of distributed sensor systems by considering the case where the system consists of N sensors which make independent decisions, whereupon the fusion center implements a Neyman-Pearson (NP) test. Applying geometric techniques, we obtain robustness measures which allow the computation of the approximate change in overall false alarm probability and overall detection probability as the corresponding sensor probabilities are perturbed from these nominal values. We consider both the situation where all sensors experience perturbation and the situation where only one sensor is perturbed. Our analysis is based on local (linearized) methods which are valid for only small perturbations, but we also extend these methods to the more practical nonlocal case where larger perturbations are admitted.