An efficient algorithm for continuous-discrete linear estimation problems

A new solution is given to the continuous-discrete linear estimation problem of a signal process under the assumption that the autocorrelation function of the signal is known. This approach is based on approximate series expansions of a stochastic process and it is valid for the entire class of measurable, smooth signals defined on half-open intervals of the real line. It includes as particular cases all earlier solutions based on the approximate Karhunen-Loeve expansions. The main advantage of the solution obtained is that it can be derived through an efficient algorithm similar to the Kalman filter.