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

Wei Xue; Xiaoli Luan; Shunyi Zhao; Fei Liu

doi:10.1109/JAS.2021.1004389

Volume 9 Issue 4

Apr. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(4): 709-718

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

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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

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

doi: 10.1109/JAS.2021.1004389

Wei Xue^1
,,
Xiaoli Luan^{1
,
,},
Shunyi Zhao^{1
,
,},
Fei Liu^1
,

Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Jiangsu 214000, China

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)

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Author Bio:
Wei Xue (Member, IEEE) received B.E. degree from the Department of Automation, Northeastern University, Qinhuangdao, China, in 2018. He is currently a Ph.D. candidate at the Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University. His research interests include state estimation and Bayesian estimation theory

Xiaoli Luan received the B.Sc. degree in industrial automation from Jiangnan University, China, in 2002; the M.Sc. degree in control theory and control engineering from Jiangnan University, China, in 2006; and the Ph.D. degree in control theory and control engineering from Jiangnan University, China, in 2010. Now she is a Professor of the Institute of Automation, Jiangnan University. In 2016, she was a Visiting Professor at the University of Alberta, Canada. Her research interests include robust control and optimization of complex industrial process. She has authored or coauthored more than 80 articles in professional journals, conference proceedings, and technical reports in these related areas. She hosted and participated several research programs funded by National Natural Science Foundation, and served as reviewer of a number of international journals

Shunyi Zhao (Senior Member, IEEE) received the Ph.D. degree in control theory and application from the Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi, China, in 2015. From 2013 to 2014, he was a Visiting Student in the Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada, where he was a Postdoctoral Fellow from 2015 to 2018. In 2015, he joined Jiangnan University as an Associate Professor, and is currently a Professor. His research interests include statistical signal processing, Bayesian estimation theory, and fault detection and diagnosis. He is the recipient of the Alexander von Humboldt Research Fellowship in Germany, the excellent Ph.D. thesis award (2016) in Jiangsu Province, China, and has received a nomination for excellent doctoral thesis from Chinese Association of Automation (CAA) in 2016

Fei Liu received the B.Sc. degree in electrical technology from Wuxi Institute of Light Industry, China, in 1987; the M.Sc. degree in industrial automation from Wuxi Institute of Light Industry, China, in 1990; and the Ph.D. degree in control science and control engineering from Zhejiang University, China, in 2002. From 1990 to 1999, he was an Assistant, Lecturer, and Associate Professor in Wuxi Institute of Light Industry. Since 2003, he has been a Professor of the Institute of Automation, Jiangnan University. From 2005 to 2006, he was a Visiting Professor with the University of Manchester, UK. His research interests include advanced control theory and applications, batch process control engineering, statistical monitoring and diagnosis in industrial process, and intelligent technique with emphasis on fuzzy and neural systems
Corresponding author: Xiaoli Luan, e-mail: xlluan@jiangnan.edu.cn; Shunyi Zhao, e-mail: shunyi.s.y@gmail.com
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: \begin{document}$ f'(x') = \frac{\partial f(x)}{\partial x}\big|_{x = x'} $\end{document}, Numerical gradient – \begin{document}$f'(x') = $\end{document} \begin{document}$ \frac{f(x'+\delta)-f(x'-\delta)}{2\delta} $\end{document}
Received Date: 2021-01-26
Revised Date: 2021-06-10
Accepted Date: 2021-08-16

Available Online: 2021-09-15

Abstract

Abstract

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.
- Fusion filter,
- influence function,
- Kalman filter (KF),
- robustness,
- unbiased finite impulse response (FIR)

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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} $

References(37)

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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.

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

doi: 10.1109/JAS.2021.1004389

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