Generalized Kernel Normalized Mixed-Norm Algorithm: Analysis and Simulations

  • Shujian Yu
  • Xinge You
  • Xiubao Jiang
  • Weihua Ou
  • Ziqi Zhu
  • Yixiao Zhao
  • C. L. Philip Chen
  • Yuanyan Tang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9490)


This paper is a continuation and extension of our previous research where kernel normalized mixed-norm (KNMN) algorithm, a combination of the kernel trick with the mixed-norm strategy, was proposed to demonstrate superior performance for system identification under non-Gaussian environment. Meanwhile, we also introduced a naive adaptive mixing parameter (AMP) updating mechanism to make KNMN more robust under nonstationary scenarios. The main contributions of this paper are threefold: firstly, the \(\ell _p\)-norm is substituted for the \(\ell _4\)-norm in the cost function, which can be viewed as a generalized version to the form of mixed-norms; secondly, instead of using the original AMP proposed in our previous work, a novel time-varying AMP is employed to provide better tracking behavior to the nonstationarity; and thirdly, the mean square convergence analysis is conducted, where the second moment behavior of weight error vector is elaborately studied. Simulations are conducted on two benchmark system identification problems, and different kinds of additive noises are added respectively to verify the effectiveness of improvements.


KNMN algorithm Generalized KNMN algorithm Adaptive mixing parameter System identification 



This work is supported partially by the National Natural Science Foundation of China (no.61402122) and the 2014 Ph.D. Recruitment Program of Guizhou Normal University.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Shujian Yu
    • 1
  • Xinge You
    • 2
  • Xiubao Jiang
    • 2
  • Weihua Ou
    • 3
  • Ziqi Zhu
    • 4
  • Yixiao Zhao
    • 1
  • C. L. Philip Chen
    • 5
  • Yuanyan Tang
    • 2
    • 5
  1. 1.Department of Electrical and Computer EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.School of Electronic Information and CommunicationsHuazhong University of Science and TechnologyWuhanChina
  3. 3.School of Mathematics and Computer ScienceGuizhou Normal UniversityGuiyangChina
  4. 4.School of Computer Science and TechnologyWuhan University of Science and TechnologyWuhanChina
  5. 5.The Faculty of Science and TechnologyUniversity of MacauMacauChina

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