Zonotope-Based Distributed Fusion for 2-D Binary Sensor Systems Under FlexRay Protocols

Lan Lan; Guoliang Wei; Ying Sun

doi:10.1109/JAS.2025.125744

Volume 13 Issue 7

Jul. 2026

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 18.3, Top 1 (SCI Q1)

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(7): 1600-1609

L. Lan, G. Wei, and Y. Sun, “Zonotope-based distributed fusion for 2-D binary sensor systems under FlexRay protocols,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 7, pp. 1600–1609, Jul. 2026. doi: 10.1109/JAS.2025.125744

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L. Lan, G. Wei, and Y. Sun, “Zonotope-based distributed fusion for 2-D binary sensor systems under FlexRay protocols,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 7, pp. 1600–1609, Jul. 2026. doi: 10.1109/JAS.2025.125744

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Zonotope-Based Distributed Fusion for 2-D Binary Sensor Systems Under FlexRay Protocols

doi: 10.1109/JAS.2025.125744

Funds: This work was supported by the National Natural Science Foundation of China (62273239, 62203306, 62273132)

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Author Bio:
Lan Lan received the B.Sc. degree in applied mathematics from Henan Institute of Science and Technology in 2016, and the M.Sc. degree in applied mathematics and the Ph.D. degree in system science from the University of Shanghai for Science and Technology in 2019 and 2025, respectively. She is currently a Teacher with the School of Mathematics and Statistics, Xinyang Normal University. Her research interests include multisensor information fusion, distributed filtering, and networked control systems. She is an active reviewer for many international journals

Guoliang Wei received the B.Sc. degree in mathematics from Henan Normal University in 1997, and the M.Sc. degree in applied mathematics and the Ph.D. degree in control engineering from Donghua University in 2005 and 2008, respectively. He is currently a Professor with the Business School, University of Shanghai for Science and Technology. From March 2010 to May 2011, he was an Alexander von Humboldt Research Fellow with the Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Germany. From March 2009 to February 2010, he was a Postdoctoral Research Fellow with the Department of Information Systems and Computing, Brunel University, UK, sponsored by the Leverhulme Trust of the UK. From June 2007 to August 2007, he was a Research Assistant with the University of Hong Kong, China. From March 2008 to May 2008, he was a Research Assistant with the City University of Hong Kong, China. His research interests include nonlinear systems, stochastic systems, and bioinformatics. He is a very active reviewer for many international journals. He has published more than 100 papers in refereed international journals

Ying Sun received the B.Sc. degree in physics from Harbin Normal University in 2013, and the Ph.D. degree in control science and engineering from University of Shanghai for Science and Technology in 2021. From April 2021 to April 2024, she worked at the Postdoctoral Research Station of Systems Science at the Business School, University of Shanghai for Science and Technology. Since April 2024, she has been serving as a Lecturer in the Department of Systems Science at the Business School, University of Shanghai for Science and Technology. Her current research interests include networked control systems, stochastic control and filtering as well as H_∞, l₂–l_∞ control and filtering. She is an active reviewer for many international journals
Corresponding author: Guoliang Wei, e-mail: guoliang.wei@usst.edu.cn
Received Date: 2025-02-16
Revised Date: 2025-05-12
Accepted Date: 2025-07-16

Available Online: 2026-07-21

Abstract

Abstract

In this paper, a zonotopic distributed fusion estimation problem is investigated for a class of 2-D nonlinear systems subject to unknown-but-bounded noises over a binary sensor network. An auxiliary innovation is constructed to reduce the influence of the less measured information, and FlexRay protocol is employed to schedule the innovation transmission between nodes. By resorting to the set-membership filtering, a variable-independent zonotope is achieved to constrain local estimation error, and gain parameters are obtained by minimizing the upper bound of zonotope in the F-radius sense. Subsequently, a zonotopic distributed fusion scheme is implemented through the matrix-weighted fusion criteria, and an optimized weighted matrix is obtained using the Lagrange Multiple method. Furthermore, the monotonicity of the local zonotope is analyzed with the gain-constraint parameter. Finally, a numerical example is considered to verify the effectiveness of the developed fusion algorithm.
- Binary sensor,
- distributed fusion,
- 2-D nonlinear systems,
- FlexRay protocols,
- zonotope

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References(36)

References

[1]	Y. Bar-Shalom, X.-R. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software. New York, USA: Wiley, 2001.
[2]	G. Battistelli, L. Chisci, and D. Selvi, “A distributed Kalman filter with event-triggered communication and guaranteed stability,” Automatica, vol. 93, pp. 75–82, Jul. 2018. doi: 10.1016/j.automatica.2018.03.005
[3]	C. Fantacci, B.-N. Vo, B.-T. Vo, G. Battistelli, and L. Chisci, “Robust fusion for multisensor multiobject tracking,” IEEE Signal Process. Lett., vol. 25, no. 5, pp. 640–644, May 2018. doi: 10.1109/LSP.2018.2811750
[4]	H. Geng, H. Liu, L. Ma, and X. Yi, “Multi-sensor filtering fusion meets censored measurements under a constrained network environment: Advances, challenges and prospects,” Int. J. Syst. Sci., vol. 52, no. 16, pp. 3410–3436, Nov. 2021. doi: 10.1080/00207721.2021.2005178
[5]	S. Sun, H. Lin, J. Ma, and X. Li, “Multi-sensor distributed fusion estimation with applications in networked systems: A review paper,” Inform. Fusion, vol. 38, pp. 122–134, Nov. 2017. doi: 10.1016/j.inffus.2017.03.006
[6]	R. Caballero-Águila and J. Linares-Pérez, “Distributed fusion filtering for uncertain systems with coupled noises, random delays and packet loss prediction compensation,” Int. J. Syst. Sci., vol. 54, no. 2, pp. 371−390, 2023.
[7]	B. Chen, G. Hu, D. W. C. Ho, and L. Yu, “Distributed covariance intersection fusion estimation for cyber-physical systems with communication constraints,” IEEE Trans. Autom. Control, vol. 61, no. 12, pp. 4020–4026, Dec. 2016. doi: 10.1109/TAC.2016.2539221
[8]	J. Li, Z. Wang, J. Hu, H. Dong, and H. Liu, “Cubature Kalman fusion filtering under amplify- and-forward relays with randomly varying channel parameters,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 2, pp. 356–368, Feb. 2025. doi: 10.1109/JAS.2024.124590
[9]	J. Hu, J. Li, H. Yan, and H. Liu, “Optimized distributed filtering for saturated systems with amplify-and-forward relays over sensor networks: A dynamic event-triggered approach,” IEEE Trans. Neural Netw. Learn. Syst., vol. 35, no. 12, pp. 17742–17753, Dec. 2024. doi: 10.1109/TNNLS.2023.3308192
[10]	M. Xie, D. Ding, G. Wei, and X. Yi, “H_∞ fusion estimation of time-delayed nonlinear systems with energy constraints: The finite-horizon case,” Nonlinear Dyn., vol. 107, no. 3, pp. 2583–2598, Feb. 2022. doi: 10.1007/s11071-021-07098-4
[11]	L. Xie, D.-H. Choi, S. Kar, and H. V. Poor, “Fully distributed state estimation for wide-area monitoring systems,” IEEE Trans. Smart Grid, vol. 3, no. 3, pp. 1154–1169, Sep. 2012. doi: 10.1109/TSG.2012.2197764
[12]	K. Zhu, Z. Wang, Q.-L. Han, and G. Wei, “Distributed set-membership fusion filtering for nonlinear 2-D systems over sensor networks: An encoding-decoding scheme,” IEEE Trans. Cybern., vol. 53, no. 1, pp. 416–427, Jan. 2023. doi: 10.1109/TCYB.2021.3110587
[13]	Z. Zhao, Z. Wang, L. Zou, Y. Chen, and W. Sheng, “Zonotopic distributed fusion for nonlinear networked systems with bit rate constraint,” Inform. Fusion, vol. 90, pp. 174–184, Feb. 2023. doi: 10.1016/j.inffus.2022.09.014
[14]	C. Hu, S. Ding, and X. Xie, “Event-based distributed set-membership estimation for complex networks under deception attacks,” IEEE Trans. Autom. Sci. Eng., vol. 21, no. 3, pp. 3719–3729, Jul. 2024. doi: 10.1109/TASE.2023.3284448
[15]	S. Liu, Z. Wang, L. Wang, and G. Wei, “Recursive set-membership state estimation over a FlexRay network,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 52, no. 6, pp. 3591–3601, Jun. 2022. doi: 10.1109/TSMC.2021.3071390
[16]	X. Li, F. Han, N. Hou, H. Dong, and H. Liu, “Set-membership filtering for piecewise linear systems with censored measurements under round-robin protocol,” Int. J. Syst. Sci., vol. 51, no. 9, pp. 1578–1588, Jul. 2020. doi: 10.1080/00207721.2020.1768453
[17]	F. Qu, X. Zhao, X. Wang, and E. Tian, “Probabilistic-constrained distributed fusion filtering for a class of time-varying systems over sensor networks: A torus-event-triggering mechanism,” Int. J. Syst. Sci., vol. 53, no. 6, pp. 1288–1297, Apr. 2022. doi: 10.1080/00207721.2021.1998721
[18]	T. Chevet, T. N. Dinh, J. Marzat, Z. Wang, and T. Raïssi, “Zonotopic Kalman filter-based interval estimation for discrete-time linear systems with unknown inputs,” IEEE Control Syst. Lett., vol. 6, pp. 806−811, 2022.
[19]	Q. Li, Y. Zhi, H. Tan, and W. Sheng, “Zonotopic set-membership state estimation for multirate systems with dynamic event-triggered mechanisms,” ISA Trans., vol. 130, pp. 667–674, Nov. 2022. doi: 10.1016/j.isatra.2022.07.023
[20]	X. Yang and J. K. Scott, “A comparison of zonotope order reduction techniques,” Automatica, vol. 95, pp. 378–384, Sep. 2018. doi: 10.1016/j.automatica.2018.06.006
[21]	L. van Hien, H. Trinh, and N. T. Lan-Huong, “Delay-dependent energy-to-peak stability of 2-D time-delay Roesser systems with multiplicative stochastic noises,” IEEE Trans. Autom. Control, vol. 64, no. 12, pp. 5066–5073, Dec. 2019. doi: 10.1109/TAC.2019.2907888
[22]	M. Li and J. Liang, “Set-membership estimation for nonlinear 2-D systems with missing measurements,” IEEE Trans. Circuits Syst. II: Exp. Briefs, vol. 70, no. 1, pp. 146–150, Jan. 2023.
[23]	F. Wang, J, Liang, J. Lam, J. Yang, and C. Zhao, “Robust filtering for 2-D systems with uncertain-variance noises and weighted try-once-discard protocols,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 53, no. 5, pp. 2914–2924, May 2023. doi: 10.1109/TSMC.2022.3219919
[24]	L. Yang, Z. Fei, Z. Wang, and C. Ki Ahn, “Zonotope-based interval estimation for 2-D FMLSS systems using an event-triggered mechanism,” IEEE Trans. Autom. Control, vol. 68, no. 3, pp. 1655–1666, Mar. 2023. doi: 10.1109/TAC.2022.3168167
[25]	M. Casini, A. Garulli, and A. Vicino, “Set membership state estimation for discrete-time linear systems with binary sensor measurements,” Automatica, vol. 159, Art. no. 111396, Jan. 2024.
[26]	Z. Hu, B. Chen, Y. Zhang, and L. Yu, “Kalman-like filter under binary sensors,” IEEE Trans. Instrum. Meas., vol. 71, Art. no. 9503111, Feb. 2022.
[27]	T. Wang, H. Zhang, and Y. Zhao, “Consensus of multi-agent systems under binary-valued measurements and recursive projection algorithm,” IEEE Trans. Autom. Control, vol. 65, no. 6, pp. 2678–2685, Jun. 2020. doi: 10.1109/TAC.2019.2942569
[28]	X. Ge, Q.-L. Han, X.-M. Zhang, L. Ding, and F. Yang, “Distributed event-triggered estimation over sensor networks: A survey,” IEEE Trans. Cybern., vol. 50, no. 3, pp. 1306–1320, Mar. 2020. doi: 10.1109/TCYB.2019.2917179
[29]	H. Song, D. Ding, B. Shen, and H. Dong, “Jointly distributed filtering based on generalized maximum correntropy criterion: Memory-based event-triggered cases,” IEEE Trans. Industr. Inform., vol. 19, no. 10, pp. 10024–10033, Oct. 2023. doi: 10.1109/TII.2022.3231429
[30]	X. Li, G. Wei, D. Ding, and S. Liu, “Recursive filtering for time-varying discrete sequential systems subject to deception attacks: Weighted try-once-discard protocol,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 52, no. 6, pp. 3704–3713, Jun. 2022. doi: 10.1109/TSMC.2021.3064653
[31]	H. Tan, B. Shen, Q. Li, and H. Liu, “Recursive filtering for stochastic systems with filter-and-forward successive relays,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1202–1212, May 2024. doi: 10.1109/JAS.2023.124110
[32]	J. Liu, S. Wang, J. Liu, X. Xie, and E. Tian, “FlexRay protocol-based event-triggered secure filtering for IT-2 fuzzy systems with fading measurements over high-rate communication networks: The finite-horizon case,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 54, no. 10, pp. 6055–6067, Oct. 2024. doi: 10.1109/TSMC.2024.3416900
[33]	C. Combastel, “Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence,” Automatica, vol. 55, pp. 265–273, May 2015. doi: 10.1016/j.automatica.2015.03.008
[34]	V. T. H. Le, C. Stoica, T. Alamo, E. F. Camacho, and D. Dumur, Zonotopes: From Guaranteed State-Estimation to Control. London, UK: ISTE Ltd, 2013.
[35]	T. Kaczorek, Two-Dimensional Linear Systems. Berlin, Germany: Springer, 1985.
[36]	F. Wang, Z. Wang, J. Liang, and C. Silvestre, “A recursive algorithm for secure filtering for two-dimensional state-saturated systems under network-based deception attacks,” IEEE Trans. Netw. Sci. Eng., vol. 9, no. 2, pp. 678–688, Mar.–Apr. 2022. doi: 10.1109/TNSE.2021.3130297