New computationally efficient formula for backward-pass fixed-interval smoother and its UD factorisation algorithm

K. Watanabe, S. G. Tzafestas

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13 Citations (Scopus)


A new UD factorization-based backward-pass fixed-interval smoother that is numerically reliable and stable is derived for linear stochastic discrete-time systems. A computationally efficient recursion of a classic backforward-pass smoother is first obtained, so that the smoother can exclude the well known shortcomings of the classic version and utilize the outputs of a forward-pass information filter. This recursion formula is then applied to construct the UD smoother using three fundamental UD algorithms. It is shown that, compared with Bierman's backward-pass UD smoother, the present UD smoother can provide an improvement in computation speed and computer storage for time-invariant systems, as well as the forward-pass UD smoother, but cannot avoid the computation of an inversion of the state-transition matrix for time-varying systems.

Original languageEnglish
Pages (from-to)73-78
Number of pages6
JournalIEE Proceedings D: Control Theory and Applications
Issue number2
Publication statusPublished - Jan 1 1989
Externally publishedYes


ASJC Scopus subject areas

  • Engineering(all)

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