Distributed sampling of random fields with unknown covariance

This paper considers robotic sensor networks performing spatial estimation tasks. We model a physical process of interest as a spatiotemporal random field with mean unknown and covariance known up to a scaling parameter. We design a distributed coordination algorithm for an heterogeneous network composed of mobile agents that take point measurements of the field and static nodes that fuse the information received from the agents and compute directions of maximum descent of the estimation uncertainty. The technical approach builds on a novel reformulation of Bayesian sequential field estimation, and combines tools from distributed linear iterations, nonlinear programming, and spatial statistics.