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State estimation for a nonlinear fractional-order system with correlated noises considering influence of initial value

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Abstract

This paper investigates the influence of initial value (IIV) aiming at nonlinear continuous-time fractional-order systems (FOSs), which contain the correlated noises via fractional-order hybrid extended-cubature Kalman filters (HECKFs). Typically, the choice of initial values for the estimated system greatly affects the accuracy of state estimation; hence, the model transformation method is used to weaken IIV. The continuous-time FOS is discretized by using the Grünwald–Letnikov difference to obtain the difference equation. By utilizing the third-degree spherical-radial rule and the cubature points to represent nonlinear functions in the state equation and output equation, a fractional-order HECKF to deal with the correlated noise is proposed to achieve an effective state estimation. Finally, the effectiveness of the proposed algorithm is verified with two simulation examples.

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No data were used for the research described in the article.

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Funding

This work was supported by the Shenyang Young and Middle-Aged Scientific and Technological Innovation Talents Support Program under Grant RC210082, the Liaoning Revitalization Talents Program under Grant XLYC1807229, and the Scientific Research Fund of Liaoning Provincial Education Department, China under Grant LJC202010.

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, People’s Republic of China

    Chuang Yang

  2. College of Light Industry, Liaoning University, Shenyang, 110036, People’s Republic of China

    Zhe Gao

  3. School of Mathematics and Statistics, Liaoning University, Shenyang, 110036, People’s Republic of China

    Zhe Gao & Haoyu Chai

  4. College of Science, Qiqihar University, Qiqihar, 161006, People’s Republic of China

    Chuang Yang & Yang Han

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  1. Chuang Yang
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Correspondence to Zhe Gao.

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Yang, C., Gao, Z., Chai, H. et al. State estimation for a nonlinear fractional-order system with correlated noises considering influence of initial value. Nonlinear Dyn 111, 22443–22456 (2023). https://doi.org/10.1007/s11071-023-09030-4

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  • DOI: https://doi.org/10.1007/s11071-023-09030-4

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