A square-root fixed-interval discrete-time smoother

T PRVAN*, Michael R. Osborne

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The square-root fixed-interval discrete-time smoother has been used extensively in discrete recursive estimation since it was first developed by Rauch, Tung and Streibel [10]. Various people, for example Bierman [2], [3], have recognized the inherent instability in employing this kind of smoother in its original form; they have investigated implementing the recursion more stably. Bierman's paper [3] is one such contribution. In this paper we plan to present a more comprehensive development of Bierman's approach, and to show that this algorithm can be implemented more stably as a square-root smoother. Throughout this paper the fixed-interval discrete-time smoother will be referred to as the RTS smoother. Numerical results are given for the usual form of the RTS smoother, Bierman's algorithm and our square-root formulation of his algorithm. These confirm that the square-root formulation is more desirable than Bierman's algorithm, which performs better than the usual implementation of the RTS smoother.
Original languageEnglish
Pages (from-to)57-68
Number of pages12
JournalJournal of the Australian Mathematical Society Series B-Applied Mathematics
Issue number1
Publication statusPublished - Jul 1988
Externally publishedYes


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