Optimal filtering in linear systems with time delays
H. Kwakernaak · IEEE Transactions on Automatic Control · 1967
The optimal linear filtering theory of Kalman and Bucy is extended to include linear systems with multiple time delays as well as the smoothing problem. The (ordinary) filter differential equation and variance equation of the Kalman-Bucy theory are replaced by partial differential equations. An explicit solution is given of the smoothing problem for systems without time delays.