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Cubature Kalman filters for nonlinear continuous-time fractional-order systems with uncorrelated and correlated noises

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Abstract

This paper presents cubature Kalman filters for nonlinear continuous-time fractional-order systems involving the uncorrelated and correlated process and measurement noises. A continuous-time fractional-order system is discretized by the Grümwald–Letnikov difference to gain a difference equation. By using the third-degree spherical–radial rule, the nonlinear functions in the state equation and output equation are performed by the cubature points. Based on these cubature points, the Kalman filters for the uncorrelated and correlated noises are given to achieve the effective state estimation. Besides, the estimation for unknown parameters in the investigated nonlinear fractional-order system is also discussed. Finally, three illustrative examples are provided to verify the proposed cubature Kalman filters in this paper.

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Funding

This study was funded by the National Natural Science Foundation of China (Grant Number 61304094, 61673198 and 61773187), Natural Science Foundation of Liaoning Province, China (Grant Number 20180520009), and Opening Fund of Liaoning Province Key Laboratory of Intelligent and Networked Measurement & Control Technology (Grant Number 1010131008101).

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Authors and Affiliations

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

    Zhe Gao

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

    Zhe Gao

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  1. Zhe Gao
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Correspondence to Zhe Gao.

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Gao, Z. Cubature Kalman filters for nonlinear continuous-time fractional-order systems with uncorrelated and correlated noises. Nonlinear Dyn 96, 1805–1817 (2019). https://doi.org/10.1007/s11071-019-04885-y

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  • DOI: https://doi.org/10.1007/s11071-019-04885-y

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