Efficient Sampling for Keeping Track of an Ornstein-Uhlenbeck Process

Abstract—We consider estimation and tracking problems in sensor networks with constraints in the hierarchy of inference making, on the sharing of data and inter-sensor communica-tions. We identify as a typical representative for such problems tracking of a process when the number and type of measure-ments are constrained. As the simplest representative of such problems, which still encompasses all the key issues involved, we analyze efficient sampling schemes for tracking an Ornstein-Uhlenbeck process. We consider sampling based on time, based on amplitude (event-triggered sampling) and optimal sampling (optimal stopping). We obtain the best sampling rule in each case as the solution to a constrained optimization problem. We compare the performances of the various sampling schemes and show that the event-triggered sampling performs close to optimal. Implications and extensions are discussed. I