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| Noisy data-driven identification for errors-in-variables MISO Hammerstein nonlinearmodels |
| JieHou1,HaoranWang1,PenghuaLi1,HaoSu2 |
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| (College of Automation, Chongqing University of Posts and Telecommunications, No.2 Chongwen Road, Chongqing 400065, Chongqing, China;School of Artificial Intelligence, Beijing University of Posts and Telecommunications, No. 10 Xitucheng Road, Beijing 100876, Beijing, China) |
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| 摘要: |
| In this paper, we consider a multiple-input single-output (MISO) Hammerstein system whose inputs and output are disturbed
by unknown Gaussian white measurement noises. The parameter estimation of such a system is a typical errors-in-variables (EIV) nonlinear system identification problem. This paper proposes a bias-correction least squares (BCLS) identification methods to compute a consistent estimate of EIV MISO Hammerstein systems from noisy data. To obtain the unbiased parameter estimates of EIV MISO Hammerstein system, the analytical expression of estimated bias for the standard least squares (LS) algorithm is derived first, which is a function about the variances of noises. And then a recursive algorithm is proposed to estimate the unknown term of noises variances from noisy data. Finally, based on bias estimation scheme, the bias caused by the correlation between the input–output signals exciting the true system and the corresponding measurement noise, resulting in unbiased parameter estimates of the EIV MISO Hammerstein system. The performance of the proposed method is demonstrated through a simulation example and a chemical continuously stirred tank reactor (CSTR) system. |
| 关键词: Biased-corrected least squares · Errors-in-variables · MISO Hammerstein models · Parameter estimation · System identification |
| DOI：https://doi.org/10.1007/s11768-025-00264-8 |
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| 基金项目:This work was supported in part by the National Natural Science Foundation of China (62373070 and 52272388), in part by the Chongqing Natural Science Foundation (CSTB2024NSCQQCXMX0054, CSTB2022NSCQ-MSX1225 and CSTC2024YCJHBGZXM0042), and in part by the Key Research and Development Project of Anhui Province (202304a05020060). |
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| Noisy data-driven identification for errors-in-variables MISO Hammerstein nonlinearmodels |
| Jie Hou1,Haoran Wang1,Penghua Li1,Hao Su2 |
| (College of Automation, Chongqing University of Posts and Telecommunications, No.2 Chongwen Road, Chongqing 400065, Chongqing, China;School of Artificial Intelligence, Beijing University of Posts and Telecommunications, No. 10 Xitucheng Road, Beijing 100876, Beijing, China) |
| Abstract: |
| In this paper, we consider a multiple-input single-output (MISO) Hammerstein system whose inputs and output are disturbed
by unknown Gaussian white measurement noises. The parameter estimation of such a system is a typical errors-in-variables (EIV) nonlinear system identification problem. This paper proposes a bias-correction least squares (BCLS) identification methods to compute a consistent estimate of EIV MISO Hammerstein systems from noisy data. To obtain the unbiased parameter estimates of EIV MISO Hammerstein system, the analytical expression of estimated bias for the standard least squares (LS) algorithm is derived first, which is a function about the variances of noises. And then a recursive algorithm is proposed to estimate the unknown term of noises variances from noisy data. Finally, based on bias estimation scheme, the bias caused by the correlation between the input–output signals exciting the true system and the corresponding measurement noise, resulting in unbiased parameter estimates of the EIV MISO Hammerstein system. The performance of the proposed method is demonstrated through a simulation example and a chemical continuously stirred tank reactor (CSTR) system. |
| Key words: Biased-corrected least squares · Errors-in-variables · MISO Hammerstein models · Parameter estimation · System identification |
