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A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise

Author

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  • Xiao Zhang

    (Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China)

  • Feng Ding

    (Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China
    College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, China)

  • Ling Xu

    (Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China)

  • Ahmed Alsaedi

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Tasawar Hayat

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

This paper is concerned with the joint state and parameter estimation methods for a bilinear system in the state space form, which is disturbed by additive noise. In order to overcome the difficulty that the model contains the product term of the system input and states, we make use of the hierarchical identification principle to present new methods for estimating the system parameters and states interactively. The unknown states are first estimated via a bilinear state estimator on the basis of the Kalman filtering algorithm. Then, a state estimator-based recursive generalized least squares (RGLS) algorithm is formulated according to the least squares principle. To improve the parameter estimation accuracy, we introduce the data filtering technique to derive a data filtering-based two-stage RGLS algorithm. The simulation example indicates the efficiency of the proposed algorithms.

Suggested Citation

  • Xiao Zhang & Feng Ding & Ling Xu & Ahmed Alsaedi & Tasawar Hayat, 2019. "A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise," Mathematics, MDPI, vol. 7(4), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:356-:d:223482
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    References listed on IDEAS

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    1. N. Chopin & P. E. Jacob & O. Papaspiliopoulos, 2013. "SMC-super-2: an efficient algorithm for sequential analysis of state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 397-426, June.
    2. repec:dau:papers:123456789/7305 is not listed on IDEAS
    3. Fengying Ma & Yankai Yin & Min Li, 2019. "Start-Up Process Modelling of Sediment Microbial Fuel Cells Based on Data Driven," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, January.
    4. Jian Pan & Hao Ma & Xiao Jiang & Wenfang Ding & Feng Ding, 2018. "Adaptive Gradient-Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique," Complexity, Hindawi, vol. 2018, pages 1-11, July.
    5. Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
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    Cited by:

    1. Feng Ding & Jian Pan & Ahmed Alsaedi & Tasawar Hayat, 2019. "Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data," Mathematics, MDPI, vol. 7(5), pages 1-15, May.

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