Multiple Sampling for Estimation on a Finite Horizon

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