Consistent Kalman filters for nonlinear uncertain systems over sensor networks
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RESEARCH ARTICLE
Consistent Kalman filters for nonlinear uncertain systems over sensor networks Xingkang He1 · Wenchao Xue2,3 · Haitao Fang2,3 · Xiaoming Hu4 Received: 23 August 2020 / Revised: 8 September 2020 / Accepted: 9 September 2020 © South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we study how to design filters for nonlinear uncertain systems over sensor networks. We introduce two Kalmantype nonlinear filters in centralized and distributed frameworks. Moreover, the tuning method for the parameters of the filters is established to ensure the consistency, i.e., the mean square error is upper bounded by a known parameter matrix at each time. We apply the consistent filters to the track-to-track association analysis of multi-targets with uncertain dynamics. A novel track-to-track association algorithm is proposed to identify whether two tracks are from the same target. It is proven that the resulting probability of mis-association is lower than the desired threshold. Numerical simulations on track-to-track association are given to show the effectiveness of the methods. Keywords Kalman filter · Consistency · Distributed filter · Track-to-track association
1 Introduction With the development of networked systems in recent years, all kinds of network-related estimation, learning, control and optimization issues are emerging. In recent years, more and more attention of researchers are given to the study of networked systems, including robotic networks, sensor networks, transportation systems, etc. The learning and estimation over sensor networks are essential to the sensing-based decision-making or system control, like observer-based control and model predicted con-
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Wenchao Xue [email protected] Xingkang He [email protected]
1
Division of Decision and Control Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
2
LSC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
4
Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
trol. In practice, there are many uncertainties [1], such as measurement bias, process disturbances, sensing noise, and unmodeled dynamics. For the systems with uncertainties, the design and analysis of estimation algorithms usually face difficulties resulted from imperfect model knowledge. For example, the sensor measurement bias, resulted from calibration error, sensor drift, and registration error, can directly influence the estimation consistency (see Definition 1) as well as the stability of filters. To deal with the system uncertainties over sensor networks, some traditional centralized robust estimation methods, such as H∞ filters, set-valued filters [2, 3], and robu
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