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Volume 9 Issue 4
Apr.  2022

IEEE/CAA Journal of Automatica Sinica

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Article Contents
W. Xue, X. L. Luan, S. Y. Zhao, and F. Liu, “A fusion Kalman filter and UFIR estimator using the influence function method,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 4, pp. 709–718, Apr. 2022. doi: 10.1109/JAS.2021.1004389
Citation: W. Xue, X. L. Luan, S. Y. Zhao, and F. Liu, “A fusion Kalman filter and UFIR estimator using the influence function method,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 4, pp. 709–718, Apr. 2022. doi: 10.1109/JAS.2021.1004389

A Fusion Kalman Filter and UFIR Estimator Using the Influence Function Method

doi: 10.1109/JAS.2021.1004389
Funds:  This work was supported in part by the National Natural Science Foundation of China (61973136, 61991402, 61833007) and the Natural Science Foundation of Jiangsu Province (BK20211528)
More Information
  • In this paper, the Kalman filter (KF) and the unbiased finite impulse response (UFIR) filter are fused in the discrete-time state-space to improve robustness against uncertainties. To avoid the problem where fusion filters may give up some advantages of UFIR filters by fusing based on noise statistics, we attempt to find a way to fuse without using noise statistics. The fusion filtering algorithm is derived using the influence function that provides a quantified measure for disturbances on the resulting filtering outputs and is termed as an influence finite impulse response (IFIR) filter. The main advantage of the proposed method is that the noise statistics of process noise and measurement noise are no longer required in the fusion process, showing that a critical feature of the UFIR filter is inherited. One numerical example and a practice-oriented case are given to illustrate the effectiveness of the proposed method. It is shown that the IFIR filter has adaptive performance and can automatically switch from the Kalman estimate to the UFIR estimates according to operating conditions. Moreover, the proposed method can reduce the effects of optimal horizon length on the UFIR estimate and can give the state estimates of best accuracy among all the compared methods.

     

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  • 1 The value of this may not be as small as previously described. Since this value is a scalar, it will be eliminated without affecting the final result and can be taken as any real value except 0.
    2 Analytical derivative: $ f'(x') = \frac{\partial f(x)}{\partial x}\big|_{x = x'} $, Numerical gradient – $f'(x') = $ $ \frac{f(x'+\delta)-f(x'-\delta)}{2\delta} $
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    Highlights

    • In this work, a novel fusion filter with KF and UFIR filters as sub-filters is proposed for a discrete-time state space model. Influence finite impulse response (IFIR) filter inherits the advantages of KF and UFIR filters. The main advantage of the proposed method is that the error covariance matrix is not required in the fusion process.
    • Compared to the existing fusion methods proposed, the most significant contribution of our paper is that it does not use the statistics of noise. It indicates that the critical feature of the UFIR filter is inherited ultimately.
    • The proposed algorithm serves as a new fusion approach to fuse the UFIR filter and the KF without calculating error covariances.
    • The proposed method inherits the advantages of the KF and UFIR filter, and can automatically change its performance from optimality to robustness to accommodate its operating environment.
    • Since noise statistics are no longer required in the fusion step, the proposed method is insensitive to the statistical error of noise and yields significant improvements over existing fusion methods in different scenarios.

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