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Published January 1996 | Published
Journal Article Open

Linear estimation in Krein spaces. I. Theory

Abstract

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.

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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