Journal ArticleDOI
Linear estimation in Krein spaces. II. Applications
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TLDR
The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns, and by considering the appropriate state space models and error Gramians, the Krein-space estimation theory.Abstract:
We have shown that several interesting problems in H/sup /spl infin//-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.read more
Citations
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Journal ArticleDOI
H/sup /spl infin// optimality of the LMS algorithm
TL;DR: It is shown that the celebrated least-mean squares (LMS) adaptive algorithm is H/sup /spl infin// optimal, and it is established that it is a minimax filter, which minimizes the maximum energy gain from the disturbances to the predicted errors.
Journal ArticleDOI
Linear estimation in Krein spaces. I. Theory
TL;DR: The authors develop a self-contained theory for linear estimation in Krein spaces 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.
Journal ArticleDOI
A time-domain feedback analysis of filtered-error adaptive gradient algorithms
Markus Rupp,Ali H. Sayed +1 more
TL;DR: It is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes and extended the so-called transfer function approach to a general time-variant scenario without any approximations.
Journal ArticleDOI
Fast communication: H-infinity filtering for a class of nonlinear discrete-time systems based on unscented transform
Wenling Li,Yingmin Jia +1 more
TL;DR: Simulation results for the frequency modulation demodulation and bearings-only tracking are presented to illustrate the effectiveness of the proposed unscented transform technique into the extended H"~ filter structure.
Journal ArticleDOI
Robust estimation of a single complex sinusoid in white noise-H/sub /spl infin// filtering approach
TL;DR: Simulations demonstrate that the HSE is more robust to the nature of observation noise {v/sub k/} than the Kalman sinusoidal estimator (KSE), which is an improved version of the nonlinear filter previously proposed by the author.
References
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Journal ArticleDOI
State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Journal Article
Optimal Filtering
TL;DR: This book helps to fill the void in the market and does that in a superb manner by covering the standard topics such as Kalman filtering, innovations processes, smoothing, and adaptive and nonlinear estimation.
Proceedings ArticleDOI
State-space solutions to standard H 2 and H ∞ control problems
TL;DR: In this article, simple state-space formulas are presented for a controller solving a standard H∞-problem, where the controller has the same state-dimension as the plant, its computation involves only two Riccati equations, and it has a separation structure reminiscent of classical LQG theory.