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<p>In this paper, the identification of fractional order Wiener output error auto-regressive moving average (OEARMA) systems is discussed. The dynamic part of the Wiener OEARMA system is an OEARMA structure, and the static part is two-stage nonlinearity. The identification expression is obtained by key term separation technique and definition of the Grünwald Letnikov factional differential. Then, the hierarchical extended stochastic gradient (H-ESG) and hierarchical multi-innovation extended stochastic gradient (H-MIESG) methods are proposed for identification of the unknown parameter in the system and the the convergence is verified. Through numerical simulations, the feasibility of the derived algorithms is studied. The identification accuracy of H-MIESG is satisfactory, which reflects its excellent identification efficiency.</p>

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Hierarchical gradient parameter estimation algorithms for fractional order Wiener OEARMA system

  • 期刊论文

  • 发表日期：

    2025年4月22日

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  • Junhong Li,
  • Hongrui Zhang,
  • Kang Xiao,
  • Juping Gu

摘要

In this paper, the identification of fractional order Wiener output error auto-regressive moving average (OEARMA) systems is discussed. The dynamic part of the Wiener OEARMA system is an OEARMA structure, and the static part is two-stage nonlinearity. The identification expression is obtained by key term separation technique and definition of the Grünwald Letnikov factional differential. Then, the hierarchical extended stochastic gradient (H-ESG) and hierarchical multi-innovation extended stochastic gradient (H-MIESG) methods are proposed for identification of the unknown parameter in the system and the the convergence is verified. Through numerical simulations, the feasibility of the derived algorithms is studied. The identification accuracy of H-MIESG is satisfactory, which reflects its excellent identification efficiency.