Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
Indefinite-quadratic estimation and control: a unified approach to H2 and H∞ theories
Indefinite-quadratic estimation and control: a unified approach to H2 and H∞ theories
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
Fast J-Unitary Array Form of the Hyper H∞ Filter
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Adaptive Filters
Gradient-based variable forgetting factor RLS algorithm in time-varying environments
IEEE Transactions on Signal Processing - Part II
Computational Improvement of the Fast H∞ Filter Based on Information of Input Predictor
IEEE Transactions on Signal Processing
An H∞ optimization and its fast algorithm for time-variant system identification
IEEE Transactions on Signal Processing
H∞ optimality of the LMS algorithm
IEEE Transactions on Signal Processing
A New Robust Variable Step-Size NLMS Algorithm
IEEE Transactions on Signal Processing
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The normalized least mean squares (NLMS) and recursive least squares (RLS) algorithms are widely used for adaptive filtering. Interestingly, the NLMS algorithm has been shown to be strictly optimal in the sense of H"~ filtering, whereas the forgetting factor RLS algorithm has not been clearly related to a solution to the H"~ filtering problem. This paper describes a method for further optimizing the solutions to the ordinary H"~ filtering problem over an assumed system model set and a predetermined norm weight set. The extended H"~ filtering problem offers a framework for constructing a unified view of adaptive algorithms for finite impulse response (FIR) filters. The framework enables a discussion of the relationships among the NLMS algorithm, the forgetting factor RLS algorithm, and the H"~ filter over the common parameter space, and facilitates the development of new fast adaptive algorithms that outperform the existing algorithms, such as the NLMS and the fast RLS algorithms. The validity of the discussion based on the H"~ framework is verified using numerical examples.