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Extended Kalman Filters for Continuous-time Nonlinear Fractional-order Systems Involving Correlated and Uncorrelated Process and Measurement Noises

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  • Control Theory and Applications
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Abstract

In order to improve the estimation accuracy of the state information and save the computing time for fractional-order systems containing correlated and uncorrelated process and measurement noises, this paper investigates fractional-order extended Kalman filters for continuous-time nonlinear fractional-order systems using the method of fractional-order average derivative. Compared with Grünwald-Letnikov difference, the estimation accuracy is improved via the fractional-order average derivative method. Meanwhile, the computing time in the state estimation is saved. To deal with the correlated and uncorrelated process and measurement noises, two kinds of extended Kalman filters for nonlinear fractional-order systems are given. Finally, the effectiveness of the proposed fractional-order extended Kalman filters based on fractional-order average derivative is validated by two examples.

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Authors and Affiliations

  1. School of Mathematics, Liaoning University, Shenyang, 110036, China

    Fanghui Liu, Chao Yang & Ruicheng Ma

  2. College of Light Industry, Liaoning University, Shenyang, 110036, China

    Zhe Gao

  3. Department of Control Science and Engineering, Jilin University, Changchun, 130025, China

    Zhe Gao

Authors
  1. Fanghui Liu
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  2. Zhe Gao
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  3. Chao Yang
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  4. Ruicheng Ma
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Correspondence to Zhe Gao.

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Recommended by Associate Editor Xiangpeng Xie under the direction of Editor Jessie (Ju H.) Park. This work was supported in part by Liaoning Revitalization Talents Program Grant XLYC1807229, in part by the Natural Science Foundation of Liaoning Province, China under Grant 20180520009, and in part by China Postdoctoral Science Foundation Funded Project under Grant 2019M651206, Liaoning University Science Research Fund under Grant LDGY2019020.

Fanghui Liu received her B.S. degree in School of Mathematics and System Science, Shandong Normal University, Jinan, China in 2016. Currently she is a Postgraduate with the School of Mathematics, Liaoning University, Shenyang, China. Her research interests include fractional-order system, state estimation, and Kalman filter.

Zhe Gao received his Ph.D. degree in Control Theory and Control Engineering from Beijing Institute of Technology in 2012. He is currently an associate professor at the Department of Electrical Engineering and Automation, College of Light Industry, Liaoning University, China. His research interests include control, state estimation and identification of fractional-order systems.

Chao Yang received her B.S. degree in School of Mathematics and Computer Science, Datong University, Datong, China in 2016. Currently she is a Postgraduate with the School of Mathematics, Liaoning university, Shenyang, China. Her research interests include fractional-order system, state estimation, and Kalman filter.

Ruicheng Ma received his M.S. degree in applied mathematics from Liaoning University, China, in 2008. He completed his Ph.D. degree in control theory and control engineering from Northeastern University, China, in 2012. He is currently a professor with the School of Mathematics, Liaoning University, China. His research interests include switched systems, hybrid control, nonlinear systems and robust control.

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Liu, F., Gao, Z., Yang, C. et al. Extended Kalman Filters for Continuous-time Nonlinear Fractional-order Systems Involving Correlated and Uncorrelated Process and Measurement Noises. Int. J. Control Autom. Syst. 18, 2229–2241 (2020). https://doi.org/10.1007/s12555-019-0353-5

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  • DOI: https://doi.org/10.1007/s12555-019-0353-5

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