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Round-off error propagation in four generally-applicable, recursive, least-squares estimation schemes. (English) Zbl 0684.93094

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.

MSC:

93E25 Computational methods in stochastic control (MSC2010)
65G50 Roundoff error
62J05 Linear regression; mixed models
65C99 Probabilistic methods, stochastic differential equations
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[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
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