Verhaegen, M. H. Round-off error propagation in four generally-applicable, recursive, least-squares estimation schemes. (English) Zbl 0684.93094 Automatica 25, No. 3, 437-444 (1989). Summary: The numerical robustness of four generally-applicable, recursive, least- squares estimation schemes is analysed by means of a theoretical round- off propagation study. This study highlights a number of practical, interesting insights into the widely-used recursive least-squares schemes. These insights have been confirmed in an experimental verification study. Cited in 1 ReviewCited in 8 Documents MSC: 93E25 Computational methods in stochastic control (MSC2010) 65G50 Roundoff error 62J05 Linear regression; mixed models 65C99 Probabilistic methods, stochastic differential equations Keywords:numerical robustness; least-squares estimation schemes; round-off propagation PDFBibTeX XMLCite \textit{M. H. Verhaegen}, Automatica 25, No. 3, 437--444 (1989; Zbl 0684.93094) Full Text: DOI Link References: [1] Åström, K. J.; Borisson, U.; Ljung, L.; Wittenmark, B., Theory and applications of self-tuning regulators, Automatica, 13, 457-476 (1977) · Zbl 0374.93024 [2] Bierman, G. J., (Factorization Methods for Discrete Sequential Estimation (1976), Academic Press: Academic Press New York) [3] Cybenko, G., The numerical stability of the Levison-Durbin algorithm for Toeplitz systems of equations, SIAM J. Sci. Stat. Comput., 1, 3, 303-319 (1980) · Zbl 0474.65026 [4] Gill, P.; Golub, G.; Murray, W.; Saunders, M., Methods for modifying matrix factorizations, Math. Comput., 28, 126, 505-535 (1974) · Zbl 0289.65021 [5] Hägglund, T., New estimation techniques for adaptive control, (Ph.D. dissertation (1983), Lund Institute of Technology: Lund Institute of Technology Sweden) [6] Hughes, D. J.; Jacobs, O. L., Turn-off, escape and probing in non-linear stochastic control, (IFAC Symp. on Stochastic Control (1974)), 343-352 [7] Kulhavy, R., Restricted exponential forgetting in real-time identification, (Seventh IFAC Symp. on Syst. Identification and Parameter Estimation. Seventh IFAC Symp. on Syst. Identification and Parameter Estimation, York, U.K. (1985)) · Zbl 0634.93073 [8] Levinson, N., The Weiner RMS (root mean square) error criterion in filter design and prediction, J. Math. Phys., 25, 261-278 (1947) [9] Ljung, L.; Söderström, T., (Theory and Practice of Recursive Identification (1983), MIT Press: MIT Press Cambridge, Massachusetts) · Zbl 0548.93075 [10] Ljung, S.; Ljung, L., Error propagation properties of recursive least squares adaptation algorithms, Automatica, 21, 2, 157-167 (1985) · Zbl 0575.93068 [11] Sluis, A.van der, Stability of the solutions of linear least squares problems, Numer. Math., 23, 241-254 (1975) · Zbl 0308.65026 [12] Stewart, G. W., Perturbation bounds for the QR factorization of a matrix, SIAM J. Numer. Analysis, 14, 3, 509-518 (1977) · Zbl 0358.65038 [13] Verhaegen, M. H., A new class of algorithms in linear system theory, with application to real-time aerodynamic model identification, (Ph.D. dissertation (1985), Catholic University Leuven: Catholic University Leuven Leuven, Belgium) · Zbl 0669.93071 [14] Verhaegen, M. H.; Van Dooren, P., Numerical aspects of different Kalman filter implementations, IEEE Trans. Aut. Control, AC-31, 10, 907-917 (1986) · Zbl 0601.93053 [15] Wilkinson, J. H., (The Algebraic Eigenvalue Problem (1965), Clarendon Press: Clarendon Press Oxford) · Zbl 0258.65037 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.