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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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  • [1]
    M. V. Basin, A. G. Loukianov, and M. Hernandez-Gonzalez, “Joint state and parameter estimation for uncertain stochastic nonlinear polynomial systems,” Int. J. Systems Science, vol. 44, no. 7, pp. 1200–1208, 2013. doi: 10.1080/00207721.2012.670309
    R. Caballero-Águila, A. Hermoso-Carazo, and J. Linares-Pérez, “Distributed fusion filters from uncertain measured outputs in sensor networks with random packet losses,” Information Fusion, vol. 34, pp. 70–79, 2017. doi: 10.1016/j.inffus.2016.06.008
    H. R. Karimi and H. Gao, “New delay-dependent exponential H synchronization for uncertain neural networks with mixed time delays,” IEEE Trans. Systems,Man,and Cybernetics,Part B-Cybernetics, vol. 40, no. 1, pp. 173–185, Feb. 2010. doi: 10.1109/TSMCB.2009.2024408
    W. Li, Y. Jia, and J. Du, “Recursive state estimation for complex networks with random coupling strength,” Neurocomputing, vol. 219, pp. 1–8, 2017. doi: 10.1016/j.neucom.2016.08.095
    D. Liu, Y. Liu, and F. Alsaadi, “Recursive state estimation based-on the outputs of partial nodes for discrete-time stochastic complex networks with switched topology,” J. Franklin Institute, vol. 355, no. 11, pp. 4686–4707, Jul. 2018. doi: 10.1016/j.jfranklin.2018.04.029
    Q. Liu and Z. Wang, “Moving-horizon estimation for linear dynamic networks with binary encoding schemes,” IEEE Trans. Automatic Control, 2020. DOI: 10.1109/TAC.2020.2996579
    B. Shen, Z. Wang, D. Wang, J. Luo, H. Pu, and Y. Peng, “Finite-horizon filtering for a class of nonlinear time-delayed systems with an energy harvesting sensor,” Automatica, vol. 100, no. 2, pp. 144–152, Feb. 2019.
    S. Sun, T. Tan, and H. Lin, “Optimal linear estimators for systems with finite-step correlated noises and packet dropout compensations,” IEEE Trans. Signal Processing, vol. 64, no. 21, pp. 5672–5681, 2016. doi: 10.1109/TSP.2016.2576420
    F. Wang and J. Liang, “Constrained H estimation for time-varying networks with hybrid incomplete information,” Int. J. Robust and Nonlinear Control, vol. 28, no. 2, pp. 699–715, 2018. doi: 10.1002/rnc.3894
    Y. Xu, R. Lu, P. Shi, H. Li, and S. Xie, “Finite-time distributed state estimation over sensor networks with round-robin protocol and fading channels,” IEEE Trans. Cybernetics, vol. 48, no. 1, pp. 336–345, Jan. 2018. doi: 10.1109/TCYB.2016.2635122
    D. Zhang, Z. Xu, H. R. Karimi, and Q. Wang, “Distributed filtering for switched linear systems with sensor networks in presence of packet dropouts and quantization,” IEEE Trans. Circuits and Systems I-Regular Papers, vol. 64, no. 10, pp. 2783–2796, 2017. doi: 10.1109/TCSI.2017.2695481
    D. Zhao, S. X. Ding, H. R. Karimi, Y. Li, and Y. Wang, “On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: A least squares method,” Automatica, vol. 99, pp. 203–212, 2019. doi: 10.1016/j.automatica.2018.10.029
    L. Zou, Z. Wang, J. Hu, and D. Zhou, “Moving horizon estimation with unknown inputs under dynamic quantization effects,” IEEE Trans. Automatic Control, 2020. DOI: 10.1109/TAC.2020.2968975
    R. Caballero-Águila, I. García-Garrido, and J. Linares-Pérez, “Information fusion algorithms for state estimation in multi-sensor systems with correlated missing measurements,” Applied Mathematics and Computation, vol. 226, pp. 548–563, 2014. doi: 10.1016/j.amc.2013.10.068
    H. Fang, N. Tian, Y. Wang, M. Zhou, and M. A. Haile, “Nonlinear bayesian estimation: From Kalman filtering to a broader horizon,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 401–417, Mar. 2018. doi: 10.1109/JAS.2017.7510808
    Q. Li, Z. Wang, N. Li, and W. Sheng, “A dynamic event-triggered approach to recursive filtering for complex networks with switching topologies subject to random sensor failures,” IEEE Trans. Neural Networks and Learning Systems, vol. 31, no. 10, pp. 4381–4388, 2020. doi: 10.1109/TNNLS.2019.2951948
    L. Zou, Z. Wang, Q.-L. Han, and D. Zhou, “Recursive filtering for timevarying systems with random access protocol,” IEEE Trans. Automatic Control, vol. 64, no. 2, pp. 720–727, Feb. 2019.
    N. M. Alyazidi and M. S. Mahmoud, “Distributed H2/H filter design for discrete-time switched systems,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 158–168, Jan. 2020. doi: 10.1109/JAS.2019.1911630
    Y. Shen, Z. Wang, B. Shen, and F. E. Alsaadi, “H state estimation for multi-rate artificial neural networks with integral measurements: A switched system approach,” Information Sciences, vol. 539, pp. 434–446, Oct. 2020. doi: 10.1016/j.ins.2020.06.021
    Y. Liu, B. Shen, and Q. Li, “State estimation for neural networks with Markov-based nonuniform sampling: The partly unknown transition probability case,” Neurocomputing, vol. 357, pp. 261–270, Sept. 2019. doi: 10.1016/j.neucom.2019.04.065
    X. Wan, Z. Wang, M. Wu, and X. Liu, “State estimation for discrete timedelayed genetic regulatory networks with stochastic noises under the Round-Robin protocols,” IEEE Trans. NanoBioscience, vol. 17, no. 2, pp. 145–154, Apr. 2018. doi: 10.1109/TNB.2018.2797124
    S. Wang, L. Chen, D. Gu, and H. Hu, “Cooperative localization of AUVs using moving horizon estimation,” IEEE/CAA J. Autom. Sinica, vol. 1, no. 1, pp. 68–76, Jan. 2014. doi: 10.1109/JAS.2014.7004622
    L. Zou, Z. Wang, Q.-L. Han, and D. Zhou, “Moving horizon estimation for networked time-delay systems under Round-Robin protocol,” IEEE Trans. Automatic Control, vol. 64, no. 12, pp. 5191–5198, Dec. 2019. doi: 10.1109/TAC.2019.2910167
    L. Zou, Z. Wang, Q.-L. Han, and D. Zhou, “Moving horizon estimation of networked nonlinear systems with random access protocol,” IEEE Trans. Systems,Man,and Cyberneics-Systems, 2019. DOI: 10.1109/TSMC.2019.2918002
    S. Liu, G. Wei, Y. Song, and D. Ding, “Set-membership state estimation subject to uniform quantization effects and communication constraints,” J. Franklin Institute - Engineering and Applied Methematics, vol. 354, no. 15, pp. 7012–7027, Oct. 2017. doi: 10.1016/j.jfranklin.2017.08.012
    F. Yang, N. Xia, and Q.-L. Han, “Event-based networked islanding detection for distributed solar PV generation systems,” IEEE Trans. Industrial Informatics, vol. 13, no. 1, pp. 322–329, Feb. 2017. doi: 10.1109/TII.2016.2607999
    W. Chen, D. Ding, H. Dong, and G. Wei, “Distributed resilient filtering for power systems subject to denial-of-service attacks,” IEEE Trans. Systems,Man,and Cyberneics-Systems, vol. 49, no. 8, pp. 1688–1697, Aug. 2019. doi: 10.1109/TSMC.2019.2905253
    J. Mao, D. Ding, G. Wei and H. Liu, “Networked recursive filtering for time-delayed nonlinear stochastic systems with uniform quantisation under Round-Robin protocol,” Int. J. Systems Science, vol. 50, no. 4, pp. 871–884, Mar. 2019. doi: 10.1080/00207721.2019.1586002
    F. Han, Z. Wang, H. Dong, and H. Liu, “Partial-nodes-based scalable H-consensus filtering with censored measurements over sensor networks,” IEEE Trans. Systems,Man,and Cyberneics-Systems, 2019. DOI: 10.1109/TSMC.2019.2907649
    H. S. Witsenhausen, “Sets of possible states of linear systems given perturbed observations,” IEEE Trans. Automatic Control, vol. 13, no. 5, pp. 556–558, Oct. 1968. doi: 10.1109/TAC.1968.1098995
    X. Ge, Q.-L. Han, and Z. Wang, “A dynamic event-triggered transmission scheme for distributed set-membership estimation over wireless sensor networks,” IEEE Trans. Cybernetics, vol. 49, no. 1, pp. 171–183, Jan. 2019. doi: 10.1109/TCYB.2017.2769722
    D. Shi, T. Chen, and L. Shi, “On set-valued Kalman filtering and its application to event-based state estimation,” IEEE Trans. Automatic Control, vol. 60, no. 5, pp. 1275–1290, May 2015. doi: 10.1109/TAC.2014.2370472
    G. Wei, S. Liu, Y. Song, and Y. Liu, “Probability-guaranteed setmembership filtering for systems with incomplete measurements,” Automatica, vol. 60, pp. 12–16, Oct. 2015. doi: 10.1016/j.automatica.2015.06.037
    N. Xia, F. Yang, and Q.-L. Han, “Distributed event-triggered networked set-membership filtering with partial information transmission,” IET Control Theory and Applications, vol. 11, no. 2, pp. 155–163, Jan. 2017. doi: 10.1049/iet-cta.2016.0781
    F. Yang and Y. Li, “Set-membership filtering for discrete-time systems with nonlinear equality constraints,” IEEE Trans. Automatic Control, vol. 54, no. 10, pp. 2480–2486, Oct. 2009. doi: 10.1109/TAC.2009.2029403
    A. D. Akkaya and M. L. Tiku, “Robust estimation in multiple linear regression model with non-Gaussian noise,” Automatica, vol. 44, no. 2, pp. 407–417, Feb. 2008. doi: 10.1016/j.automatica.2007.06.029
    A. Alessandri and M. Awawdeh, “Moving-horizon estimation with guaranteed robustness for discrete-time linear systems and measurements subject to outliers,” Automatica, vol. 67, pp. 85–93, May 2016. doi: 10.1016/j.automatica.2016.01.015
    A. Alessandri and L. Zaccarian, “Stubborn state observers for linear timeinvariant systems,” Automatica, vol. 88, pp. 1–9, Feb. 2018. doi: 10.1016/j.automatica.2017.10.022
    A. Gabriel, J. I. Nieto, and E. M. Nebot, “An outlier-robust Kalman filter,” in Proc. IEEE Int. Conf. Robotics and Automation, Shanghai, China, pp. 1151–1158, May 2011.
    M. A. Gandhi and L. Mili, “Robust Kalman filter based on a generalized maximum-likelihood-type estimator,” IEEE Trans. Signal Processing, vol. 58, no. 5, pp. 2509–2520, May 2010. doi: 10.1109/TSP.2009.2039731
    R. G. Gibbs, “New Kalman filter and smoother consistency tests,” Automatica, vol. 49, no. 10, pp. 3141–3144, Oct. 2013. doi: 10.1016/j.automatica.2013.07.013
    C. Xu, S. Zhao, B. Huang, and F. Liu, “Distributed Student’s t filtering algorithm for heavy-tailed noises,” Int. J. Adaptive Control and Signal Processing, vol. 32, no. 6, pp. 875–890, Jun. 2018. doi: 10.1002/acs.2873
    L. Chang and K. Li, “Unified form for the robust Gaussian information filtering based on M-estimate,” IEEE Signal Processing Letters, vol. 24, no. 4, pp. 412–416, Feb. 2017. doi: 10.1109/LSP.2017.2669238
    S. C. Chan, Z. G. Zhang, and K. W. Tse, “A new robust Kalman filter algorithm under outliers and system uncertainties,” in Proc. IEEE Int. Symp. Circuits and Systems, Kobe, Japan, pp. 4317–4320, May 2005.
    Y. Huang, Y. Zhang, N. Li, and J. Chambers, “Robust Student’s t based nonlinear filter and smoother,” IEEE Trans. Aerospace and Electronic Systems, vol. 52, no. 5, pp. 2586–2596, Oct. 2016. doi: 10.1109/TAES.2016.150722
    Z. Sun and H. Sun, “Stacked denoising autoencoder with density-grid based clustering method for detecting outlier of wind turbine components,” IEEE Access, vol. 7, pp. 13078–13091, 2019. doi: 10.1109/ACCESS.2019.2893206
    Z. Yao, J. Xie, Y. Tian, and Q. Huang, “Using hampel identifier to eliminate profile-isolated outliers in laser vision measurement,” J. Sensors, vol. 2019, pp. 1–12, 2019. doi: 10.1155/2019/3823691
    S. Cabuk, “Simple test of hypotheses on system availability and mean time to repair,” IEEE Trans. Reliability, vol. 35, no. 5, pp. 581–583, Dec. 1986. doi: 10.1109/TR.1986.4335552
    Y. Dai, Y. Zhou, and Y. Jia, “Distribution of time between failures of machining center based on type I censored data,” Reliability Engineering and System Safety, vol. 79, no. 3, pp. 377–379, Mar. 2003. doi: 10.1016/S0951-8320(02)00243-0
    K. Reif, S. Günther, E. Yaz, and R. Unbehauen, “Stochastic stability of the discrete-time extended Kalman filter,” IEEE Trans. Automatic Control, vol. 44, no. 4, pp. 714–728, Apr. 1999. doi: 10.1109/9.754809
    L. El Ghaoui and G. Calafiore, “Robust filtering for discrete-time systems with bounded noise and parametric uncertainty,” IEEE Trans. Automatic Control, vol. 46, no. 7, pp. 1302–1313, Jul. 2001.
    S. Liu, Z. Wang, G. Wei, and M. Li, “Distributed set-membership filtering for multi-rate systems under the Round-Robin scheduling over sensor networks,” IEEE Trans. Cybernetics, vol. 50, no. 5, pp. 1910–1920, May 2020. doi: 10.1109/TCYB.2018.2885653
    N. Xia, F. Yang, and Q.-L. Han, “Distributed networked set-membership filtering with ellipsoidal state estimations,” Information Sciences, vol. 432, pp. 52–62, Mar. 2018. doi: 10.1016/j.ins.2017.12.010
    G. Xiao and F. Liu, “Distributed fault-tolerant model predictive control for intermittent faults,” IET Control Theory and Applications, vol. 13, no. 10, pp. 1554–1563, Jul. 2019. doi: 10.1049/iet-cta.2018.5800


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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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