A unified view of adaptive algorithms for finite impulse response filters using the H infinity framework

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 infinity H infinity filtering, whereas the forgetting factor RLS algorithm has not b...

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Bibliographic Details
Published in:Signal processing 2014-04, Vol.97, p.55-63
Main Author: Nishiyama, Kiyoshi
Format: Article
Language:English
Subjects:
Adaptive algorithms
Adaptive filters
Algorithms
Filtering
Filtration
Mathematical analysis
Mathematical models
Optimization
Online Access:Get full text
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Summary: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 infinity H infinity filtering, whereas the forgetting factor RLS algorithm has not been clearly related to a solution to the H infinity H infinity filtering problem. This paper describes a method for further optimizing the solutions to the ordinary H infinity H infinity filtering problem over an assumed system model set and a predetermined norm weight set. The extended H infinity H infinity 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 infinity H infinity 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 infinity H infinity framework is verified using numerical examples.
ISSN:0165-1684
DOI:10.1016/j.sigpro.2013.10.007