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This paper is concerned witn the fixed-point optimal smoothing problems for linear distributed parameter systems with a noisy observation at discrete points on the spatial domain or its boundary. The approach adopted here is that we use both the optimal filter and the orthogonal projection lemma to treat the smoothing problems. By solving the Wiener-Hopf equations for the filtering and the smoothing problems, we derive the fixed-point optimal smoothing mechanisms which are more suitable for the practical computations than those obtained before by the formal procedures. Finally, for the convenience of numerical conputations, we rewrite the results for the distributed parameter systems by using the Fourier expansion methods.
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