Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article An Adaptive Nonlinear Filter for System Identiﬁcation | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2009 Article ID 859698 7 pages doi 2009 859698 Research Article An Adaptive Nonlinear Filter for System Identification Ifiok J. Umoh EURASIP Member and Tokunbo Ogunfunmi Department of Electrical Engineering Santa Clara University Santa Clara CA 95053 USA Correspondence should be addressed to Tokunbo Ogunfunmi togunfunmi@ Received 12 March 2009 Accepted 8 May 2009 Recommended by Jonathon Chambers The primary difficulty in the identification of Hammerstein nonlinear systems a static memoryless nonlinear system in series with a dynamic linear system is that the output of the nonlinear system input to the linear system is unknown. By employing the theory of affine projection we propose a gradient-based adaptive Hammerstein algorithm with variable step-size which estimates the Hammerstein nonlinear system parameters. The adaptive Hammerstein nonlinear system parameter estimation algorithm proposed is accomplished without linearizing the systems nonlinearity. To reduce the effects of eigenvalue spread as a result of the Hammerstein system nonlinearity a new criterion that provides a measure of how close the Hammerstein filter is to optimum performance was used to update the step-size. Experimental results are presented to validate our proposed variable step-size adaptive Hammerstein algorithm given a real life system and a hypothetical case. Copyright 2009 I. J. Umoh and T. Ogunfunmi. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Nonlinear system identification has been an area of active research for decades. Nonlinear systems research has led to the discovery of numerous types of nonlinear systems such as Volterra Hammerstein and Weiner nonlinear systems 1-4 . This work will focus on the .