Cyber-physical trade-offs in distributed detection networks

We consider a network of sensors that measure the scalar intensity due to the background or a source combined with background, inside a two-dimensional monitoring area. The sensor measurements may be random due to the underlying nature of the source and background or due to sensor errors or both. The detection problem is infer the presence of a source of unknown intensity and location based on sensor measurements. In the conventional approach, detection decisions are made at the individual sensors, which are then combined at the fusion center, for example using the majority rule. With increased communication and computation costs, we show that a more complex fusion algorithm based on measurements achieves better detection performance under smooth and non-smooth source intensity functions, Lipschitz conditions on probability ratios and a minimum packing number for the state-space. We show that these conditions for trade-offs between the cyber costs and physical detection performance are applicable for two detection problems: (i) Poisson radiation sources amidst background radiation, and (ii) sources and background with Gaussian distributions.