On smoothing in linear discrete systems with time delays†

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Abstract
An algorithm is presented for optimal linear fixed-point and fixed-lag smoothing in non-stationary linear discrete systems with multiple time delays. Relations derived previously in the problem of filtering are used directly to obtain the fixed-point and fixed-lag smoothing filters. The smoothing error covariance matrix is obtained via a recursive matrix equation. For the particular case of systems without delay terms, the algorithm defines new smoothing procedures.

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