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An algorithm for Kalman filtering and smoothing with diagonal input covariance matrices
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-3811-062X
1996 (English)In: Computational techniques and applications, CTAC95: proceedings of the Seventh Biennial Conference held at Swinburne University of Technology, Melbourne, July 3--5, 1995 / [ed] Robert L. May; Alan K. Easton, World Scientific Publishing Co Pte Ltd , 1996, p. 709-716Conference paper, Published paper (Refereed)
Abstract [en]

A new square-root algorithm for Kalman filtering and smoothing is derived. The new algorithm is a modification of the information filter presented by Paige and Saunders [C.C. Paige and M.A. Saunders, Least Squares Estimation of Discrete Linear Dynamic System Using Orthogonal Transformations, SIAM J. Num.Anal 12 (1977) pp. 180-193] and can be used when the input covariance matrices are diagonal. Potential ill-conditioning, caused by different sizes of the input covariances, is handled using techniques for solving weighted and constrained least squares problems. That is, the ordinary QR-decomposition that is used in the filter by Paige and Sauders are replaced by a weighted QR-decomposition introduced by Gulliksson and Wedin [M.G. Gulliksson and P.-Å. Wedin, Modyfying the QR Decomposition to Weighted and Constrained Linear Least Squares, SIAM J. Mat.Anal. 13 (1992) pp. 1298-1313]. This technique implies that the new algorithm can handle singular covariance matrices as well as singular information matrices.

Place, publisher, year, edition, pages
World Scientific Publishing Co Pte Ltd , 1996. p. 709-716
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:ltu:diva-28170Local ID: 1df4d8e0-b5e7-11db-bf94-000ea68e967bISBN: 981-02-2820-1 (print)OAI: oai:DiVA.org:ltu-28170DiVA, id: diva2:1001365
Conference
Computational techniques and applications, CTAC95 : 03/07/1995 - 05/07/1995
Note
Godkänd; 1996; 20070206 (kani)Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-03-08Bibliographically approved

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CiteExportLink to record
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