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Adaptive filtering algorithms designed using control Liapunov functions

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2 Author(s)
Diene, O. ; Dept. of Electr. Eng., NACAD-COPPE/Fed. Univ. of Rio de Janeiro., Rio De Janeiro, Brazil ; Bhaya, Amit

The standard conjugate gradient (CG) method uses orthogonality of the residues to simplify the formulas for the parameters necessary for convergence. In adaptive filtering, the sample-by-sample update of the correlation matrix and the cross-correlation vector causes a loss of the residue orthogonality in a modified online algorithm, which, in turn, results in loss of convergence and an increase of the filter quadratic mean error. This letter extends a recently proposed control Liapunov function analysis of the CG method viewed as a dynamic system in the standard feedback configuration to the case of adaptive filtering.

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Signal Processing Letters, IEEE  (Volume:13 ,  Issue: 4 )