Hassibi, Babak and Kailath, Thomas (1997) On nonlinear filters for mixed H^2/H^∞ estimation. In: Proceedings of the American Control Conference, 1997. Vol.5. IEEE , Piscataway, NJ, pp. 2820-2824. ISBN 0-7803-3832-4. https://resolver.caltech.edu/CaltechAUTHORS:20150302-162239004
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Abstract
We study the problem of mixed least-mean-squares H^∞ -optimal (or mixed H^2/H^∞-optimal) estimation of signals generated by discrete-time, finite-dimensional, linear state-space models. The major result is that, for finite-horizon problems, and when the stochastic disturbances have Gaussian distributions, the optimal solutions have finite-dimensional (i.e., bounded-order) nonlinear state-space structure of order 2n+1 (where n is the dimension of the underlying state-space model). Being nonlinear, the filters do not minimize an H2 norm subject to an H^∞ constraint, but instead minimize the least-mean-squares estimation error (given a certain a priori probability distribution on the disturbances) subject to a given constraint on the maximum energy gain from disturbances to estimation errors. The mixed filters therefore have the property of yielding the best average (least-mean-squares) performance over all filters that achieve a certain worst-case (H^∞) bound
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 1997 IEEE. This work was supported in part by DARPA through the Department of Air Force under contract F49620-95-l-0525-PO0001 and by the Joint Service Electronics Program at Stanford under contract DAAH04-94-G-0058-P00003. | |||||||||
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| DOI: | 10.1109/ACC.1997.611970 | |||||||||
| Record Number: | CaltechAUTHORS:20150302-162239004 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150302-162239004 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 55439 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Shirley Slattery | |||||||||
| Deposited On: | 03 Mar 2015 01:40 | |||||||||
| Last Modified: | 10 Nov 2021 20:45 |
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