Efficient Sampling for Keeping Track of an Ornstein-Uhlenbeck Process

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 communications. We identify as a typical representative for such problems tracking of a process when the number and type of measurements 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.