\r\nwith variable regularization parameter. The proposed algorithms

\r\ndynamically update the regularization parameter that is fixed in the

\r\nconventional regularized APA (R-APA) using a gradient descent

\r\nbased approach. By introducing the normalized gradient, the proposed

\r\nalgorithms give birth to an efficient and a robust update scheme for

\r\nthe regularization parameter. Through experiments we demonstrate

\r\nthat the proposed algorithms outperform conventional R-APA in

\r\nterms of the convergence rate and the misadjustment error.","references":"[1] B. Widrow and S. D. Sterns, Adaptive Signal Processing, Englewood\r\nCliffs, NJ: Prentice Hall, 1985.\r\n[2] S. Haykin, Adaptive Filter Theory, Englewood Cliffs, NJ: Prentice Hall,\r\n2002.\r\n[3] A. H. Sayed, Fundamentals of Adaptive Filtering, Englewood Cliffs,\r\nNJ: Prentice Hall, 2003.\r\n[4] K. Ozeki and T. Umeda, \u201cAn adaptive filtering algorithm using an\r\northogonal projection to an affine subspace and its properties,\u201d Electro.\r\nCommun. Jpn., vol. 67-A, no. 5, pp. 19\u201327, 1984.\r\n[5] H.-C. Shin and A. H. Sayed, \u201cMean-square peformance of a family of\r\naffine projection algorithms,\u201d IEEE Trans. Signal Processing, vol. 52,\r\npp. 90\u2013102, Jan. 2004.\r\n[6] V. Myllyl\u00a8a and G. Schmidt, \u201cPsedo-optimal regulariztion for affine\r\nprojection algorithms,\u201d in Proc. IEEE Int. Conf. on Accoustics, Speech,\r\nand Signal Processing, ICASSP\u201902, Orlando, Florida, May 2002,\r\npp. 1917\u20131920.\r\n[7] S. C. Douglas, \u201cGeneralized gradient adaptive step sizes for stochastic\r\ngradient adaptive filters,\u201d in Proc. IEEE Int. Conf. on Accoustics, Speech,\r\nand Signal Processing, ICASSP\u201995, vol. 2, pp. 1396\u20131399, 1995.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 109, 2016"}