Optimum Linear Estimation for Random Processes as the Limit of Estimates Based on Sampled Data

摘要

A generalized form of the problem of optimum linear filtering and prediction for random processes is considered. It is shown that, under very general conditions, the optimum linear estimation based on the received signal, observed continuously for a finite interval is the limit of optimum linear estimation based on sampled data. This yields a method for obtaining the optimum linear estimation in cases where the conventional generalized Wiener-Hopf integral equation technique has not been shown to yield a solution. The relationship between the sampled-data solution and the Wiener-Hopf integral equation solution is discussed. A problem is posed concerning the rate at which the error variance of optimum sampled-data estimates approaches the error variance of the optimum estimate based on continuous observation, as the sampled points become denser in the observation interval. This problem is solved in one case.