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Volume 8 Issue 2
Feb.  2021

IEEE/CAA Journal of Automatica Sinica

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Lei Zou, Zidong Wang, Hang Geng and Xiaohui Liu, "Set-Membership Filtering Subject to Impulsive Measurement Outliers: A Recursive Algorithm," IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 377-388, Feb. 2021. doi: 10.1109/JAS.2021.1003826
Citation: Lei Zou, Zidong Wang, Hang Geng and Xiaohui Liu, "Set-Membership Filtering Subject to Impulsive Measurement Outliers: A Recursive Algorithm," IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 377-388, Feb. 2021. doi: 10.1109/JAS.2021.1003826

Set-Membership Filtering Subject to Impulsive Measurement Outliers: A Recursive Algorithm

doi: 10.1109/JAS.2021.1003826
Funds:  This work was supported in part by the National Natural Science Foundation of China (61703245, 61873148, 61933007), the China Postdoctoral Science Foundation (2018T110702), the Postdoctoral Special Innovation Foundation of of Shandong Province of China (201701015), the European Union’s Horizon 2020 Research and Innovation Programme (820776 (INTEGRADDE)), the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany
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  • This paper is concerned with the set-membership filtering problem for a class of linear time-varying systems with norm-bounded noises and impulsive measurement outliers. A new representation is proposed to model the measurement outlier by an impulsive signal whose minimum interval length (i.e., the minimum duration between two adjacent impulsive signals) and minimum norm (i.e., the minimum of the norms of all impulsive signals) are larger than certain thresholds that are adjustable according to engineering practice. In order to guarantee satisfactory filtering performance, a so-called parameter-dependent set-membership filter is put forward that is capable of generating a time-varying ellipsoidal region containing the true system state. First, a novel outlier detection strategy is developed, based on a dedicatedly constructed input-output model, to examine whether the received measurement is corrupted by an outlier. Then, through the outcome of the outlier detection, the gain matrix of the desired filter and the corresponding ellipsoidal region are calculated by solving two recursive difference equations. Furthermore, the ultimate boundedness issue on the time-varying ellipsoidal region is thoroughly investigated. Finally, a simulation example is provided to demonstrate the effectiveness of our proposed parameter-dependent set-membership filtering strategy.


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    • A new model is established to characterize the measurement outlier
    • A new algorithm is proposed to find the measurements corrupted by outliers
    • A new set-membership filter is designed to guarantee the filtering performance
    • Rigorous analysis is provided on the ultimate boundedness of the filtering error


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