Deployment of an unreliable robotic sensor network for spatial estimation

This paper studies an optimal deployment problem for a network of robotic sensors moving in the real line. Consider the scenario where each sensor is to take a measurement of a spatial process of interest and send it back to a data fusion center. Assume only a specific fraction of the messages containing the measurements will arrive at the center. We show that, for several fraction values, the optimal deployment configurations have the following features: agents are grouped into clusters, the clusters are deployed optimally as if at least a message from each cluster was guaranteed to reach the center, and for each fraction value, there is a specific optimal cluster size. The technical approach combines convex analysis, nonsmooth analysis, and combinatorics.