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Array algorithms for H^2 and H^∞ estimation

Hassibi, Babak and Kailath, Thomas and Sayed, Ali H. (1999) Array algorithms for H^2 and H^∞ estimation. In: Applied and Computational Control, Signals, and Circuits. Vol.1. Birkhäuser Boston , Boston, MA, pp. 67-120. ISBN 978-1-4612-6822-2. (Unpublished)

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Currently, the preferred method for implementing H^2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H^∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H^∞ filtering. These can be regarded as natural generalizations of their H^2 counterparts, and involve propagating the indefinite square roots of the quantities of interest. The H^∞ square-root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters. These conditions are built into the algorithms themselves so that an H^∞ estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H^2 case, further investigation is needed to determine the numerical behavior of such algorithms.

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Additional Information:© 1999 Birkhäuser Boston. This work was supported in part by DARPA through the Department of Air Force under contract F49620-95-1-0525-P00001 and by the Joint Service Electronics Program at Stanford under contract DAAH04-94-G-0058-P-00003.
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Air Force Office of Scientific Research (AFOSR)F49620-95-1-0525-P00001
Joint Service Electronics Program at StanfordDAAH04-94-G-0058-P-00003
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55077
Deposited By: Shirley Slattery
Deposited On:04 Mar 2015 00:28
Last Modified:10 Nov 2021 20:41

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