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Stability of the distributed Kalman filter using general random coefficients

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Abstract

In this paper, we propose a distributed Kalman filter (DKF) for the dynamical system with general random coefficients. In the proposed method, each estimator shares local innovation pairs with its neighbors to collectively complete the estimation task. Further, we introduce a collective random observability condition by which the Lp-stability of the covariance matrix and the Lp-exponential stability of the homogeneous part of the estimation error equation can be established. In contrast, the stringent conditions on the coefficient matrices, such as independency and stationarity are not required. Besides, the stability of the DKF, i.e., the boundedness of the filtering errors, can be established. Finally, from the simulation result, we demonstrate the cooperative effect of the sensors.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11688101) and National Key R&D Program of China (Grant No. 2018YFA0703800).

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Die Gan & Zhixin Liu

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China

    Die Gan & Zhixin Liu

  3. The Department of Electrical and Computer Engineering, Wayne State University, Detroit, 48202, USA

    Siyu Xie

Authors
  1. Die Gan
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  2. Siyu Xie
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  3. Zhixin Liu
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Correspondence to Zhixin Liu.

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Gan, D., Xie, S. & Liu, Z. Stability of the distributed Kalman filter using general random coefficients. Sci. China Inf. Sci. 64, 172204 (2021). https://doi.org/10.1007/s11432-020-2962-9

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  • DOI: https://doi.org/10.1007/s11432-020-2962-9

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