Linear estimation in Krein spaces. II. Applications

Author

Hassibi, Babak ; Sayed, Ali H. ; Kailath, Thomas

Author_Institution

Inf. Syst. Lab., Stanford Univ., CA, USA

Volume

41

Issue

1

fYear

1996

fDate

1/1/1996 12:00:00 AM

Firstpage

34

Lastpage

49

Abstract

We have shown that several interesting problems in H^∞-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in Part I. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties. The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns

Keywords

H^∞ control; Kalman filters; adaptive filters; filtering theory; recursive estimation; state estimation; state-space methods; H^∞-filtering; Krein spaces; error Gramians; finite memory adaptive filtering; generalizations; linear estimation; quadratic game theory; risk sensitive control; second-order forms; state space models; varying sliding patterns; Adaptive filters; Art; Cost function; Filtering theory; Game theory; Kalman filters; Nonlinear filters; Riccati equations; State estimation; State-space methods;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.481606

Filename

481606