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Optimal filtering and smoothing algorithms for linear discrete-time distributed parameter systems are derived by a unified approach based on the Wiener-Hopf theory. The Wiener-Hopf equation for the estimation problems is derived using the least-squares estimation error criterion. Using the basic equation, three types of the optimal smoothing estimators are derived, namely, fixed-point, fixed-interval, and fixed-lag smoothers. Finally, the results obtained are applied to estimation of atmospheric sulfur dioxide concentrations in the Tokushima prefecture of Japan.