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Robust State Estimation for Uncertain Discrete Linear Systems with Delayed Measurements

Author

Listed:
  • Zhijun Li

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China)

  • Minxing Sun

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China)

  • Qianwen Duan

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China)

  • Yao Mao

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China)

Abstract

Measurement delays and model parametric uncertainties are meaningful issues in actual systems. Addressing the simultaneous existence of random model parametric uncertainties and constant measurement delay in the discrete-time linear systems, this study proposes a novel robust estimation method based on the combination of Kalman filter regularized least-squares (RLS) framework and state augmentation. The state augmentation method is elaborately designed, and the cost function is improved by considering the influence of modelling errors. A recursive program similar to the Kalman filter is derived. Meanwhile, the asymptotic stability conditions of the proposed estimator and the boundedness conditions of its error covariance are analyzed theoretically. Numerical simulation results show that the proposed method has a better processing capability for measurement delay and better robustness to model parametric uncertainties than the Kalman filter based on nominal parameters.

Suggested Citation

  • Zhijun Li & Minxing Sun & Qianwen Duan & Yao Mao, 2022. "Robust State Estimation for Uncertain Discrete Linear Systems with Delayed Measurements," Mathematics, MDPI, vol. 10(9), pages 1-24, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1365-:d:797215
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    References listed on IDEAS

    as
    1. Hua-Ming Qian & Wei Huang & Biao Liu, 2014. "Finite-Horizon Robust Kalman Filter for Uncertain Attitude Estimation System with Star Sensor Measurement Delays," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, February.
    2. Konstantin Belyaev & Andrey Kuleshov & Ilya Smirnov & Clemente A. S. Tanajura, 2021. "Generalized Kalman Filter and Ensemble Optimal Interpolation, Their Comparison and Application to the Hybrid Coordinate Ocean Model," Mathematics, MDPI, vol. 9(19), pages 1-15, September.
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