Optimal filtering, smoothing and prediction in linear distributed-parameter systems

This paper extends the optimal linear filtering and prediction theory of Kalman and Bucy to a general class of linear distributed-parameter systems. The filter equations for the optimal estimate and its variance are replaced by partial integrodifferential equations, the complexity of which depends on the form of the particular system under investigation. A solution to the smoothing problem for the same class of distributed systems, analogous to that suggested by Kwakernaak, is given, and the problem of integrating the filtering and smoothing equations is discussed.