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A square-root fixed-interval discrete-time smoother

Published online by Cambridge University Press:  17 February 2009

Tania Prvan  and
M. R. Osborne
Tania Prvan
Affiliation:
Dept. of Pure and Applied Mathematics, Washington State University, Pullman, 99164-2930, WA, USA.
M. R. Osborne
Affiliation:
Dept. of Statistics, Institute of Advanced Studies, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 1 , July 1988 , pp. 57 - 68
Copyright
Copyright © Australian Mathematical Society 1988

References

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