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 in 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 considered sampling based on time, based on amplitude (event-triggered sampling) and optimal sampling (optimal stopping). We obtained the solution in each case as a constrained optimization problem. We compare the performance of the various sampling schemes and show that the event-triggered sampling performs close to optimal. Implications and extensions are discussed.