Fixed-lag smoothing estimator for a linear distributed parameter system

The fixed-lag smoothing estimator for a linear distributed parameter system with a noisy observation at discrete points on the spatial domain or its boundary is derived from the Wiener-Hopf theoretical viewpoint. The new feature of this paper is that the derivation of the optimal smoothing estimator is based only on the Wiener-Hopf theory. Using the Wiener-Hopf equations both for the optimal smoothing problem and for the optimal filtering problem, the optimal fixed-lag smoothing estimator which corresponds to the results obtained by using Kalman's limiting procedure is derived