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H∞ bounds for least-squares estimators

Hassibi, Babak and Kaliath, Thomas (2001) H∞ bounds for least-squares estimators. IEEE Transactions on Automatic Control, 46 (2). pp. 309-314. ISSN 0018-9286. doi:10.1109/9.905700.

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We obtain upper and lower bounds for the H∞ norm of the Kalman filter and the recursive-least-squares (RLS) algorithm, with respect to prediction and filtered errors. These bounds can be used to study the robustness properties of such estimators. One main conclusion is that, unlike H∞-optimal estimators which do not allow for any amplification of the disturbances, the least-squares estimators do allow for such amplification. This fact can be especially pronounced in the prediction error case, whereas in the filtered error case the energy amplification is at most four. Moreover, it is shown that the H∞ norm for RLS is data dependent, whereas for least-mean-squares (LMS) algorithms and normalized LMS, the H∞ norm is simply unity.

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Additional Information:© Copyright 2001 IEEE. Reprinted with permission. Manuscript received October 9, 1997; revised June 3, 2000. Recommended by Associate Editor H. Katayama. This work was supported in part by the U.S. Air Force through under Contract F49620-95-1-0525-P00001 and in part by the Joint Service Electronics Program at Stanford University, Stanford, CA, under Contract DAAH04-94-G-0058-P00003.
Subject Keywords:Estimation, H∞, least-squares, robustness
Issue or Number:2
Record Number:CaltechAUTHORS:HASieeetac01
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6484
Deposited By: Archive Administrator
Deposited On:11 Dec 2006
Last Modified:08 Nov 2021 20:34

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