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Linear estimation in Krein spaces. I. Theory

Hassibi, Babak and Sayed, Ali H. and Kailath, Thomas (1996) Linear estimation in Krein spaces. I. Theory. IEEE Transactions on Automatic Control, 41 (1). pp. 18-33. ISSN 0018-9286. doi:10.1109/9.481605.

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The authors develop a self-contained theory for linear estimation in Krein spaces. The derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between Krein space projection and the recursive computation of the stationary points of certain second-order (or quadratic) forms. The authors use the innovations process to obtain a general recursive linear estimation algorithm. When specialized to a state-space structure, the algorithm yields a Krein space generalization of the celebrated Kalman filter with applications in several areas such as H ∞-filtering and control, game problems, risk sensitive control, and adaptive filtering.

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Additional Information:© 1996 IEEE. Reprinted with permission. Manuscript received March 4, 1994; revised June 16, 1995. Recommended by Associate Editor at Large, B. Pasik-Duncan. This work was supported in part by the Advanced Research Projects Agency of the Department of Defense monitored by the Air Force Office of Scientific Research under Contract F49620-93-1-0085 and in part by a grant from NSF under award MIP-9409319. The authors would like to thank P. P. Khargonekar and D. J. N. Limebeer for helpful discussions during the preparation of this manuscript. Seminars by P. Park on the KYP Lemma were also helpful in leading us to begin the research.
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Advanced Research Projects Agency (ARPA)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F49620-93-1-0085
Subject Keywords:Kalman filters, matrix algebra, recursive estimation, state estimation, state-space methods, H∞-filtering
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Record Number:CaltechAUTHORS:HASieeetac96a
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2239
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Deposited On:17 Mar 2006
Last Modified:08 Nov 2021 19:46

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