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<p>This paper studies the parameter identification problem of the fractional order Hammerstein output error autoregressive (FO-H-OEAR) model. First, the fractional order is introduced into the polynomial operator of the Hammerstein model. Then the key term separation technology is used in the model derivation process to obtain the FO-H-OEAR model. Second, this paper integrates the recursive technique into the maximum likelihood principle and proposes the fractional order maximum likelihood recursive least squares (ML-RLS) algorithm. Then the forgetting factor stochastic gradient (F-SG) algorithm is proposed as a comparative algorithm. Finally, two simulation examples are given. The results of the two simulation experiments show that the ML-RLS algorithm has higher accuracy and smaller identification error compared with the F-SG algorithm. Therefore, the ML-RLS algorithm can effectively estimate the parameters of the FO-H-OEAR model.</p>

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Recursive Parameter Estimation of Fractional Order Hammerstein Output Error Autoregressive Model

  • 期刊论文

  • 发表日期：

    2025年2月20日

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  • Yanan Li,
  • Junhong Li,
  • Fuchao Li,
  • Yaqi Duan

摘要

This paper studies the parameter identification problem of the fractional order Hammerstein output error autoregressive (FO-H-OEAR) model. First, the fractional order is introduced into the polynomial operator of the Hammerstein model. Then the key term separation technology is used in the model derivation process to obtain the FO-H-OEAR model. Second, this paper integrates the recursive technique into the maximum likelihood principle and proposes the fractional order maximum likelihood recursive least squares (ML-RLS) algorithm. Then the forgetting factor stochastic gradient (F-SG) algorithm is proposed as a comparative algorithm. Finally, two simulation examples are given. The results of the two simulation experiments show that the ML-RLS algorithm has higher accuracy and smaller identification error compared with the F-SG algorithm. Therefore, the ML-RLS algorithm can effectively estimate the parameters of the FO-H-OEAR model.