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Study on initial value problem for fractional-order cubature Kalman filters of nonlinear continuous-time fractional-order systems

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Abstract

To realize the state estimation of nonlinear continuous-time fractional-order systems, two types of fractional-order cubature Kalman filters are designed to solve problem on the initial value influence. For the first type of cubature Kalman filter (CKF), the initial value of the estimated system is also regarded as the augmented state, and the augmented state equation is constructed to obtain the CKF based on Grünwald–Letnikov difference. For the second type of CKF, the fractional-order hybrid extended-cubature Kalman filter is proposed to weaken the influence of initial value by the first-order Taylor expansion and the third-order spherical-radial rule. These two methods can reduce the influence of initial value on the state estimation effectively. Finally, the effectiveness of the proposed CKFs is verified by two simulation examples.

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Funding

This work was supported by Liaoning Revitalization Talents Program under Grant XLYC1807229, China Postdoctoral Science Foundation Funded Project under Grant 2019M651 206, Scientific Research Fund of Liaoning Provincial Education Department, China, under Grant LJC202010 and Liaoning University Science Research Fund LDGY2019020.

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Authors and Affiliations

  1. School of Mathematics, Liaoning University, Shenyang, 110036, People’s Republic of China

    Chuang Yang, Zhe Gao, Yue Miao & Tao Kan

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

    Zhe Gao

  3. Department of Control Science and Engineering, Jilin University, Changchun, 130025, People’s Republic of China

    Zhe Gao

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  1. Chuang Yang
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  2. Zhe Gao
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  4. Tao Kan
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Correspondence to Zhe Gao.

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Yang, C., Gao, Z., Miao, Y. et al. Study on initial value problem for fractional-order cubature Kalman filters of nonlinear continuous-time fractional-order systems. Nonlinear Dyn 105, 2387–2403 (2021). https://doi.org/10.1007/s11071-021-06726-3

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  • DOI: https://doi.org/10.1007/s11071-021-06726-3

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