Abstract
Adaptive filtering of a scalar signal corrupted by noise is considered. In particular, the signal to be estimated is modeled as a linear regression depending on a drifting parameter. The mean-square and worst-case performances of the Normalized Least Mean Squares, Kalman, and central H ∞-filters are studied. The analysis shows that a compromise between performance and robustness should be pursued, for instance by applying the central H ∞-filter with the design parameter γ used as a tuning knob.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Åström, K.J. (1980) Design principles for self-tuning regulators. In Methods and Applications in Adaptive Control, U. Unbenhauen Ed., Springer, Berlin, 1–20.
Bernstein, D.S., Haddad, W.M. (1989) Steady-state Kalman filtering with an H ∞ error bound. Systems and Control Letters, 12, 9–16.
Bolzern, P., Colaneri, P., De Nicolao, G. (1997) Robustness in adaptive filtering: how much is enough? Proc. 36th Conf. on Decision and Control, San Diego, USA, 4677–4679.
Bolzern, P., Colaneri, P., De Nicolao, G. (1999) H ∞ robustness of adaptive filters against measurement noise and parameter drift. To appear in Automatica.
Bolzern, P., Colaneri, P., De Nicolao, G. (1999) Tradeoff between mean-square and worst-case performances in adaptive filtering. Submitted to European J. Control.
Bolzern, P., Colaneri, P., De Nicolao, G. (1999) γ-recalibration of a class of H ∞-filters. IEEE American Control Conference, San Diego, USA.
Colaneri, P., Geromel, J.C., Locatelli, A. (1997) Control Theory and Design — An RH 2 and RH ∞ viewpoint. Academic Press, San Diego, USA.
Didinsky, G., Pan, Z., Basar, T. (1995) Parameter identification for uncertain plants using H ∞ methods. Automatica, 31, N.9, 1227–1250.
Grimble, M.J., Hashim, R., Shaked, U. (1992) Identification algorithms based on H ∞ state-space filtering techniques. Proc. 31st Conference on Decision and Control, Tucson, USA, 2287–2292.
Guo, L., Ljung, L. (1995) Performance analysis of general tracking algorithms, IEEE Trans. Automatic Control, AC-40, N.8, 1388–1402.
Guo, L., Xia, L., Moore, J.B. (1991) Tracking randomly varying parameters — Analysis of a standard algorithm. Mathematics of Control, Signal and Systems, 4, N.1, 1–16.
Hassibi, B. (1996) Indefinite metric spaces in estimation, control and adaptive filtering. PhD Thesis, Stanford University.
Hassibi, B., Sayed, A.H., Kailath, T. (1996) H ∞ optimality of the LMS algorithm. IEEE Trans. Signal Processing, AC-44, 267–280.
Hassibi, B., Sayed, A.H., Kailath, T. (1996) Linear estimation in Krein spaces — Part II: Applications. IEEE Trans. Automatic Control, AC-41, N.1, 34–49.
Kulhavy, R., Karny, M. (1984) Tracking of slowly varying parameters by directional forgetting. Proc. 9 th Triennal IFAC World Congress, Budapest, Hungary, 79–83.
Ljung, L., Gunnarsson, S. (1990) Adaptation and tracking in system identification — a survey. Automatica, 26, N.1, 7–21.
Nagpal, K.M., Khargonekar, P.P. (1991) Filtering and smoothing in an H ∞ setting. IEEE Trans. Automatic Control, AC-36, N.2, 152–166.
Rupp, M., Sayed, A.H. (1996) A time-domain feedback analysis of filtered-error adaptive gradient algorithms. IEEE Trans. Signal Processing, AC-44, N.6, 1428–1439.
Sayed, A.H., Kailath, T. (1994) A state-space approach to adaptive RLS filtering. IEEE Signal Processing Magazine, 11, 18–60.
Sayed, A.H., Rupp, M. (1997) An l 2-stable feedback structure for nonlinear adaptive filtering and identification. Automatica, 33, N.1, 13–30.
Theodor, Y., Shaked, U., Berman, N. (1996) Time-domain H ∞ identification. IEEE Trans. Automatic Control, AC-41, 1019–1024.
Yaesh, I., Shaked, U. (1991) H ∞-optimal estimation — the discrete-time case. Proc. Symp. MTNS, Kobe, Japan, 261–267.
Yaesh, I., Shaked, U. (1991) A transfer function approach to the problems of discrete-time systems: H ∞-optimal linear control and filtering. IEEE Trans. Automatic Control, AC-36, N.11, 1264–1271.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag London Limited
About this paper
Cite this paper
Bolzern, P., Colaneri, P., De Nicolao, G. (1999). Robustness and performance in adaptive filtering. In: Garulli, A., Tesi, A. (eds) Robustness in identification and control. Lecture Notes in Control and Information Sciences, vol 245. Springer, London. https://doi.org/10.1007/BFb0109868
Download citation
DOI: https://doi.org/10.1007/BFb0109868
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-179-5
Online ISBN: 978-1-84628-538-7
eBook Packages: Springer Book Archive