ON OPTIMAL SMOOTHING OF CONTINUOUS TIME KALMAN PROCESSES

In their fundamental paper Kalman and Bucy solved the problem of explicitly designing the optimal estimator of the state of a certain type of Markov process at the time T + h (h ≥ 0) given observations of a certain number of linear combinations of the states for a certain observation time (0, T). The problem with h = 0 is currently known as the filtering problem and the one with h > 0 as the prediction problem. Below is given a solution of the smoothing or interpolation problem (0 < A ≤ T), which is left open in their paper. This problem has been tackled by many authors, but it is believed that the method of the present paper has some points of interest. © 1969.