Abstract
We consider the problem of the global convergence of the output error identification scheme in the presence of colored noise. The adaptation scheme utilizes at each step a projection of the parameter estimate vector onto a compact, convex set known to contain the true parameter. We establish convergence of the scheme for infinite order moving average noise with geometrically decaying weights.
The research reported here has been supported by the U.S. Army Research Office under Contract No. DAAL-03–88-K0046, and by the Joint Services Electronics Program under Contract No. N00014–90-J-1270. The work or the first author was supported by an International Paper Company Fellowship.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. R. Johnson, Jr., “Adaptive IIR filtering, Current results and open issues,” IEEE Transactions on Information Theory, vol. IT-30, pp. 237–250, 1984.
I. D. Landau, “Unbiased recursive identification using model reference adaptive techniques,” IEEE Transactions on Automatic Control, vol. AC-21, pp. 194–202, 1976.
W. Ren and P. R. Kumar, “The convergence of output error identification and adaptive IIR filtering algorithms in the presence of colored noise,” in Proceedings of the 29th Conference on Decision and Control, December 5–7 1990. Honolulu, HI.
K. Knopp, Infinite Sequences and Series. New York, NY: Dover, 1956.
W. Ren and P. R. Kumar, “On stochastic parallel model adaptative problems,” tech. rep., University of Illinois, 1990. In preparation.
T. L. Lai and C. Z. Wei, “Least squares estimate in stochastic regression with applications to identification and control of dynamic systems,” Ann. Math. Statist, vol. 10, pp. 154–166, 1982.
B. E. Ydstie, “Stability of discrete MRAC- revisited,” Systems and Control Letters, vol. 13, pp. 429–439, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Ren, W., Kumar, P.R. (1993). The Convergence of output Error Recursions in Infinite Order Moving Average Noise. In: Brillinger, D., Caines, P., Geweke, J., Parzen, E., Rosenblatt, M., Taqqu, M.S. (eds) New Directions in Time Series Analysis. The IMA Volumes in Mathematics and its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9296-5_18
Download citation
DOI: https://doi.org/10.1007/978-1-4613-9296-5_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-9298-9
Online ISBN: 978-1-4613-9296-5
eBook Packages: Springer Book Archive