### Abstract

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 language | English |
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Pages (from-to) | 57-68 |

Number of pages | 12 |

Journal | Journal of the Australian Mathematical Society Series B-Applied Mathematics |

Volume | 30 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 1988 |

Externally published | Yes |

## Cite this

PRVAN, T., & Osborne, M. R. (1988). A square-root fixed-interval discrete-time smoother.

*Journal of the Australian Mathematical Society Series B-Applied Mathematics*,*30*(1), 57-68. https://doi.org/10.1017/S0334270000006032