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Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances

Received: 7 September 2018     Accepted: 19 September 2018     Published: 4 January 2019
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Abstract

This paper addresses the design of robust Kalman estimators (filter, predictor and smoother) for the time-varying system with uncertain noise variances. According to the unbiased linear minimum variance (ULMV) optimal estimation rule, the robust time-varying Kalman estimators are presented. Specially, two robust Kalman smoothing algorithms are presented by the augmented and non-augmented state approaches, respectively. They have the robustness in the sense that their actual estimation error variances are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved by the Lyapunov equation approach, and their robust accuracy relations are proved. The corresponding steady-state robust Kalman estimators are also presented for the time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.

Published in Mathematics and Computer Science (Volume 3, Issue 6)
DOI 10.11648/j.mcs.20180306.11
Page(s) 113-128
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Uncertain System, Uncertain Noise Variance, Robust Kalman Filtering, Minimax Estimator, Robust Accuracy, Lyapunov Equation Approach, Convergence

References
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Cite This Article
  • APA Style

    Wenjuan Qi, Zunbing Sheng. (2019). Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances. Mathematics and Computer Science, 3(6), 113-128. https://doi.org/10.11648/j.mcs.20180306.11

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    ACS Style

    Wenjuan Qi; Zunbing Sheng. Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances. Math. Comput. Sci. 2019, 3(6), 113-128. doi: 10.11648/j.mcs.20180306.11

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    AMA Style

    Wenjuan Qi, Zunbing Sheng. Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances. Math Comput Sci. 2019;3(6):113-128. doi: 10.11648/j.mcs.20180306.11

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  • @article{10.11648/j.mcs.20180306.11,
      author = {Wenjuan Qi and Zunbing Sheng},
      title = {Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances},
      journal = {Mathematics and Computer Science},
      volume = {3},
      number = {6},
      pages = {113-128},
      doi = {10.11648/j.mcs.20180306.11},
      url = {https://doi.org/10.11648/j.mcs.20180306.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20180306.11},
      abstract = {This paper addresses the design of robust Kalman estimators (filter, predictor and smoother) for the time-varying system with uncertain noise variances. According to the unbiased linear minimum variance (ULMV) optimal estimation rule, the robust time-varying Kalman estimators are presented. Specially, two robust Kalman smoothing algorithms are presented by the augmented and non-augmented state approaches, respectively. They have the robustness in the sense that their actual estimation error variances are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved by the Lyapunov equation approach, and their robust accuracy relations are proved. The corresponding steady-state robust Kalman estimators are also presented for the time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances
    AU  - Wenjuan Qi
    AU  - Zunbing Sheng
    Y1  - 2019/01/04
    PY  - 2019
    N1  - https://doi.org/10.11648/j.mcs.20180306.11
    DO  - 10.11648/j.mcs.20180306.11
    T2  - Mathematics and Computer Science
    JF  - Mathematics and Computer Science
    JO  - Mathematics and Computer Science
    SP  - 113
    EP  - 128
    PB  - Science Publishing Group
    SN  - 2575-6028
    UR  - https://doi.org/10.11648/j.mcs.20180306.11
    AB  - This paper addresses the design of robust Kalman estimators (filter, predictor and smoother) for the time-varying system with uncertain noise variances. According to the unbiased linear minimum variance (ULMV) optimal estimation rule, the robust time-varying Kalman estimators are presented. Specially, two robust Kalman smoothing algorithms are presented by the augmented and non-augmented state approaches, respectively. They have the robustness in the sense that their actual estimation error variances are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved by the Lyapunov equation approach, and their robust accuracy relations are proved. The corresponding steady-state robust Kalman estimators are also presented for the time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.
    VL  - 3
    IS  - 6
    ER  - 

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Author Information
  • School of Mechnical and Electronical Engineering, Heilongjiang University, Harbin, China

  • School of Mechnical and Electronical Engineering, Heilongjiang University, Harbin, China

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