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Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search
Research Article | Published: 14 April 2025
IECE Transactions on Intelligent Systematics Volume 2, Issue 2, 2025: 76-84
Volume 2, Issue 2, IECE Transactions on Intelligent Systematics
Volume 2, Issue 2, 2025
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Seifedine Kadry
Seifedine Kadry
Noroff University College, Norway
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IECE Transactions on Intelligent Systematics, Volume 2, Issue 2, 2025: 76-84

Free to Read | Research Article | 14 April 2025
Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search
by
Siyu Liu Siyu Liu 1
Feng Ding Feng Ding 2 *
1 College of Engineering, Zhejiang Normal University, Jinhua 321004, China
2 School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China
* Corresponding Author: Feng Ding, [email protected]
DOI: 10.62762/TIS.2024.155941
Received: 02 November 2024, Accepted: 26 March 2025, Published: 14 April 2025  
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Abstract
This study addresses the challenge of estimating parameters iteratively in bilinear state-space systems affected by stochastic noise. A Newton iterative (NI) algorithm is introduced by utilizing the Newton search and iterative identification theory for identifying the system parameters. Following the estimation of the unknown parameters, we create a bilinear state observer (BSO) using the Kalman filtering principle for state estimation. Subsequently, we propose the BSO-NI algorithm for simultaneous parameter and state estimation. An iterative algorithm based on gradients is given for comparisons to illustrate the effectiveness of the proposed algorithms.
Graphical Abstract
Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search
Keywords
newton search
bilinear system
parameter estimation
system identification
iterative method
Data Availability Statement
Data will be made available on request.
Funding
This work was supported by the Young Scientists Fund of the National Natural Science Foundation of Zhejiang Province, China under Grant LQN25F030017.
Conflicts of Interest
The authors declare no conflicts of interest. 
Ethical Approval and Consent to Participate
Not applicable.
References
  1. Ljung, L. (1999). System identification: Theory for the user. (2nd ed.). Prentice Hall, Englewood Cliffs, New Jersey. http://dx.doi.org/10.1109/MRA.2012.2192817
    [Google Scholar]
  2. Miao, G., Ding, F., Liu, Q., & Yang, E. (2023). Iterative parameter identification algorithms for transformed dynamic rational fraction input–output systems. Journal of Computational and Applied Mathematics, 434, 115297.
    [CrossRef]   [Google Scholar]
  3. Benesty, J., Paleologu, C., Dogariu, L. M., & Ciochină, S. (2021). Identification of linear and bilinear systems: A unified study. Electronics, 10(15), 1790.
    [CrossRef]   [Google Scholar]
  4. Li, F., Zhang, M., Yu, Y., & Li, S. (2024). Deep belief network-based hammerstein nonlinear system for wind power prediction. IEEE Transactions on Instrumentation and Measurement, 73, 1-12. 2024. 73:6505912.
    [CrossRef]   [Google Scholar]
  5. Chen, J., Mao, Y., Gan, M., Wang, D., & Zhu, Q. (2023). Greedy search method for separable nonlinear models using stage Aitken gradient descent and least squares algorithms. IEEE Transactions on Automatic Control, 68(8), 5044-5051.
    [CrossRef]   [Google Scholar]
  6. Chen, J., Ma, J., Gan, M., & Zhu, Q. (2022). Multidirection gradient iterative algorithm: A unified framework for gradient iterative and least squares algorithms. IEEE Transactions on Automatic Control, 67(12), 6770-6777.
    [CrossRef]   [Google Scholar]
  7. Khodarahmi, M., & Maihami, V. (2023). A review on Kalman filter models. Archives of Computational Methods in Engineering, 30(1), 727-747.
    [CrossRef]   [Google Scholar]
  8. An, S., He, Y., & Wang, L. (2023). Maximum likelihood based multi‐innovation stochastic gradient identification algorithms for bilinear stochastic systems with ARMA noise. International Journal of Adaptive Control and Signal Processing, 37(10), 2690-2705.
    [CrossRef]   [Google Scholar]
  9. Zhang, Q., Wang, H., & Liu, X. (2025). Auxiliary model maximum likelihood least squares-based iterative algorithm for multivariable autoregressive output-error autoregressive moving average systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 09596518241280323.
    [CrossRef]   [Google Scholar]
  10. An, S., Wang, L., & He, Y. (2023). Filtering-based maximum likelihood hierarchical recursive identification algorithms for bilinear stochastic systems. Nonlinear Dynamics, 111(13), 12405-12420.
    [CrossRef]   [Google Scholar]
  11. Gu, Y., Dai, W., Zhu, Q., & Nouri, H. (2023). Hierarchical multi-innovation stochastic gradient identification algorithm for estimating a bilinear state-space model with moving average noise. Journal of Computational and Applied Mathematics, 420, 114794.
    [CrossRef]   [Google Scholar]
  12. Xu, L. (2021). Separable multi-innovation Newton iterative modeling algorithm for multi-frequency signals based on the sliding measurement window. Circuits, Systems, and Signal Processing, 41(2), 805-830.
    [CrossRef]   [Google Scholar]
  13. Xu, L. (2022). Separable Newton recursive estimation method through system responses based on dynamically discrete measurements with increasing data length. International Journal of Control, Automation and Systems, 20(2), 432-443.
    [CrossRef]   [Google Scholar]
  14. Pan, Z., Luan, X., & Liu, F. (2022). Confidence set-membership state estimation for LPV systems with inexact scheduling variables. ISA Transactions, 122, 38-48.
    [CrossRef]   [Google Scholar]
  15. Pan, Z., Luan, X., & Liu, F. (2022). Set-membership state and parameter estimation for discrete time-varying systems based on the constrained zonotope. International Journal of Control, 96(12), 3226-3238.
    [CrossRef]   [Google Scholar]
  16. Chen, J., Zhu, Q., & Liu, Y. (2020). Modified Kalman filtering based multi-step-length gradient iterative algorithm for ARX models with random missing outputs. Automatica, 118, 109034.
    [CrossRef]   [Google Scholar]
  17. Pan, Z., Zhao, S., Huang, B., & Liu, F. (2023). Confidence set-membership FIR filter for discrete time-variant systems. Automatica, 157, 111231.
    [CrossRef]   [Google Scholar]
  18. Pan, Z., & Liu, F. (2022). Nonlinear set‐membership state estimation based on the Koopman operator. International Journal of Robust and Nonlinear Control, 33(4), 2703-2721.
    [CrossRef]   [Google Scholar]
  19. Yang, D., Liu, Y., Ding, F., & Yang, E. (2023). Hierarchical gradient-based iterative parameter estimation algorithms for a nonlinear feedback system based on the hierarchical identification principle. Circuits, Systems, and Signal Processing, 43(1), 124-151.
    [CrossRef]   [Google Scholar]
  20. Xu, F., Chen, J., Cheng, L., & Zhu, Q. (2025). Variable fractional order Nesterov accelerated gradient algorithm for rational models with missing inputs using interpolated model. Mechanical Systems and Signal Processing, 224, 111944.
    [CrossRef]   [Google Scholar]
  21. Xu, F., Cheng, L., Chen, J., & Zhu, Q. (2024). The Nesterov accelerated gradient algorithm for auto-regressive exogenous models with random lost measurements: Interpolation method and auxiliary model method. Information Sciences, 659, 120055.
    [CrossRef]   [Google Scholar]
Cite This Article
APA Style
Liu, S., & Ding, F. (2025). Iterative Estimation Algorithm for Bilinear Stochastic Systems by Using the Newton Search. IECE Transactions on Intelligent Systematics, 2(2), 76–84. https://doi.org/10.62762/TIS.2024.155941
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