Multiple Sampling for Estimation on a Finite Horizon

We discuss some multiple sampling problems that arise in finite horizon real-time estimation when there is an upper limit on the number of allowable samples. Measuring estimation quality by the aggregate squared error, we compare the performances of the best deterministic, level-triggered and the optimal sampling schemes. We restrict the signal to be either a Wiener or an Ornstein-Uhlenbeck process. For the Wiener process, we provide closed form expressions and series expansions, whereas for the Ornstein Uhlenbeck process, procedures for numerical computation. Our results indicate that the best level-triggered sampling is almost optimal when the signal is stable.