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On nonlinear filters for mixed H^2/H^∞ estimation

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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ACC.1997.611970DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=611970PublisherArticle
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.
Funders:
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)F49620-95-l-0525-PO0001
Joint Service Electronics ProgramDAAH04-94-G-0058-P00003
Record Number:CaltechAUTHORS:20150302-162239004
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150302-162239004
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ID Code:55439
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:03 Mar 2015 01:40
Last Modified:03 Oct 2019 08:05

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