Cooperative adaptive sampling via approximate entropy maximization

This work deals with a group of mobile sensors sampling a spatiotemporal random field whose mean is unknown and covariance is known up to a scaling parameter. The Bayesian posterior predictive entropy provides a direct mapping between the locations of a new set of point measurements and the uncertainty of the resulting estimate of the model parameters. Since the posterior predictive entropy and its gradient are not amenable to distributed computation, we propose an alternative objective function based on a Taylor series approximation. We present a distributed strategy for sequential design which ensures that measurements at each timestep are taken at local minima of the objective function. The technical approach builds on a novel reformulation of the posterior predictive entropy.