A Family of Minimal Residual Based Algorithm for Adaptive Filtering

Authors: Noor Atinah Ahmad

Abstract:

The Minimal Residual (MR) is modified for adaptive filtering application. Three forms of MR based algorithm are presented: i) the low complexity SPCG, ii) MREDSI, and iii) MREDSII. The low complexity is a reduced complexity version of a previously proposed SPCG algorithm. Approximations introduced reduce the algorithm to an LMS type algorithm, but, maintain the superior convergence of the SPCG algorithm. Both MREDSI and MREDSII are MR based methods with Euclidean direction of search. The choice of Euclidean directions is shown via simulation to give better misadjustment compared to their gradient search counterparts.

Keywords: Adaptive filtering, Adaptive least square, Minimalresidual method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061715

References:

[1] G. K. Boray and M. D. Srinath, "Conjugate gradient techniques for adaptive filtering", IEEE Trans. Circuits Syst., vol. 39, Jan. 1992, pp. 1- 10.
[2] P. S. Chang and A. N. Wilson, Jr., "Analysis of conjugate gradient method for adaptive filtering", IEEE Trans. Signal Processing, vol. 48, no. 2, Feb. 2000.
[3] N. A. Ahmad, "A globally convergent stochastic pairwise conjugate gradient based adaptive filtering algorithm", IEEE Signal Process. Lett., vol. 15, Dec. 2008, pp. 914-917.
[4] Y. Saad, Iterative Methods for Sparse Linear Systems. Boston, MA: PWS-Kent, 1996.
[5] S. Haykin, Adaptive Filter Theory, Englewood Cliffs, NJ: Prentice-Hall, 1991.
[6] N. A. Ahmad, ÔÇÿLow Complexity Stochastic Pairwise Conjugate Gradient Based Adaptive Filtering Algorithm-, (to be published).
[7] G. F. Xu, T. Bose and J. Schroeder, "The Euclidean direction search algorithm for adaptive filtering", Proceedings of the 1999 IEEE Int. Symp. on Circuits and Systems, 3:146 - 149, 1999.