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The Research of Kernel Adaptive Filtering Algorithms

Author: MiaoQiuYuan
Tutor: LiChunGuang
School: Zhejiang University
Course: Circuits and Systems
Keywords: Nuclear methods Renewable kernel Hilbert space Minimum average mixed norm Locally exponentially stable Variable step size Incremental meta-learning
CLC: TN713
Type: Master's thesis
Year: 2012
Downloads: 32
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Abstract


Linear system computing power is limited , usually , the real-world applications involving complex nonlinear relationship . Nuclear is a linear system is a powerful tool extended to nonlinear applications , recently , nuclear methods have been increasingly used in the design of nonlinear adaptive filter . However , compared to the perfect linear adaptive filter system , nuclear nonlinear adaptive filter there are still many aspects need to develop , for example , the processing capability of the algorithm for different environmental noise , increase in speed of convergence of the algorithm . In this thesis , these two aspects of nuclear non-linear adaptive filter design problem . First, for the more general noise environment , the linear adaptive filtering algorithm , the minimum average mixing norm ( LMMN ) algorithm is confirmed that when the noise of the environment has a good performance in the linear combination of the Thrasher distribution and Bobtail distribution of noise . Therefore , in this paper , we study the combination of nuclear technology and LMMN adaptive filtering algorithm is derived out of a renewable the nuclear Hilbert (RKHS) space adaptive filtering algorithm we call nuclear LMMN ( KLMMN) algorithm . Derivation guarantee algorithm is stable learning step size parameter range , and prove that the algorithm is locally exponentially stable . In addition , we give the expression of the the optimal norm mixing parameters to maintain the speed of convergence of the algorithm unchanged . Confirmed the advantages of KLMMN algorithm algorithm is applied to nonlinear system identification when the system noise is Gaussian distribution , and the Bernoulli distribution of linear superposition and chaotic time series forecasting , simulation results show that the algorithm in response to environmental noise for Thrasher distribution and short-tailed distribution of the linear combination of a problem , is indeed able to obtain the convergence of the lower mean square error. Secondly , for improving the convergence rate of the nuclear adaptive filtering algorithm problem , we propose a two Approves variable step size algorithm , a simple convergence analysis of the algorithm , and verify these two algorithms given instance of a channel equalization in under the conditions of the steady-state mean square error (MSE) does not deteriorate greatly improve the speed of convergence of the algorithm .

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CLC: > Industrial Technology > Radio electronics, telecommunications technology > Basic electronic circuits > Filtering techniques,the filter
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