IEEE Transactions on Signal Processing · 1993 · 492 citations · 32 references
Numerical AnalysisEngineeringMachine LearningConvergence BehaviorAnalysis Of AlgorithmComputational ComplexityFilter (Signal Processing)Statistical Signal ProcessingFiltering TechniqueRegularization (Mathematics)Approximation TheoryConvergence AnalysisAdaptive FilterComputer ScienceAdaptive AlgorithmAlgorithmic Information TheoryWhite Input SignalSignal ProcessingNormalized Lms AlgorithmsRobust ModelingInput Signal StatisticsInput Signal Vectors
It is shown that the normalized least mean square (NLMS) algorithm is a potentially faster converging algorithm compared to the LMS algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics. A very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the LMS and NLMS algorithms is proposed. Using this model, answers can be obtained to questions for which no answers are currently available using other (perhaps more realistic) models. Examples are given to illustrate that even quantitatively, the answers obtained can be good approximations. It is emphasized that the convergence of the NLMS algorithm can be speeded up significantly by employing a time-varying step size. The optimal step-size sequence can be specified a priori for the case of a white input signal with arbitrary distribution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Adaptive filtering, prediction and control
Pétros Ioannou · Automatica · 1985 · 4.5K citations
Stationary and nonstationary learning characteristics of the LMS adaptive filter
Bernard Widrow, J. McCool, M. Larimore et al. · Proceedings of the IEEE · 1976 · 1.3K citations