Security Protection for Vessel Positioning in Smart Waterway Systems Based on Extended Kalman Dynamic Encoding

TANG Fengjian; YAN Xia; SUN Zeyi; ZHU Zhaowei; YANG Wen

doi:10.11999/JEIT250846

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2025 >

TANG Fengjian, YAN Xia, SUN Zeyi, ZHU Zhaowei, YANG Wen. Security Protection for Vessel Positioning in Smart Waterway Systems Based on Extended Kalman Dynamic Encoding[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250846

Citation:

TANG Fengjian, YAN Xia, SUN Zeyi, ZHU Zhaowei, YANG Wen. Security Protection for Vessel Positioning in Smart Waterway Systems Based on Extended Kalman Dynamic Encoding[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250846

Citation:

PDF( 1552 KB)

Security Protection for Vessel Positioning in Smart Waterway Systems Based on Extended Kalman Dynamic Encoding

doi: 10.11999/JEIT250846 cstr: 32379.14.JEIT250846

1.
Shanghai Channel Department of Changjiang Waterway Bureau, Shanghai 200011, China
2.
School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China
3.
Jiangsu Guoxin Jingjiang Power Generation Co., Ltd., Jingjiang 214500, China

Funds: National Key Research and Development Program of China (2023YFF1204805),Key Program of the National Natural Science Foundation of China (62336005)

Accepted Date: 2025-11-17
Rev Recd Date: 2025-11-17

Available Online: 2025-11-26

Abstract

Abstract

Objective With the rapid development of intelligent shipping systems, vessel positioning data faces severe privacy leakage risks during wireless transmission. Traditional privacy-preserving methods such as differential privacy and homomorphic encryption suffer from issues like data distortion, high computational overhead, or reliance on costly communication links, making it difficult to achieve both data integrity and efficient protection. This paper addresses the characteristics of vessel stabilization systems and proposes a dynamic encoding scheme enhanced by time-varying perturbations. By integrating Extended Kalman Filter (EKF) and introducing unstable temporal perturbations during encoding, the scheme utilizes receiver-side acknowledgments (ACK feedback) to achieve reference time synchronization and independently generates synchronized perturbations via a shared random seed. Theoretical analysis and simulations demonstrate that the proposed method enables nearly zero precision loss in state estimation for legitimate receivers while causing eavesdroppers’ decoding errors to grow exponentially after a single packet loss, effectively countering both single and multi-channel eavesdropping attacks. The shared seed synchronization mechanism avoids complex key management and significantly reduces communication and computational costs, making it suitable for resource-constrained maritime wireless sensor networks. Methods The proposed dynamic encoding scheme incorporates a time-varying perturbation term into the encoding process. The perturbation is governed by an unstable matrix to ensure exponential error growth for eavesdroppers. The encoding mechanism uses the difference between the current state estimate and a time-scaled reference state, plus the perturbation term. A shared random seed between legitimate parties enables deterministic and synchronized generation of the perturbation sequence without online key exchange. The decoding process at the legitimate receiver cancels out the perturbation, enabling accurate state recovery. The system employs Extended Kalman Filtering for local state estimation at each sensor node, and the entire communication process is reinforced by acknowledgment-based synchronization to maintain consistency between sender and receiver. Results and Discussions Simulations were conducted in a wireless sensor network with four sensors tracking vessel states such as position, velocity, and heading. The results show that legitimate receivers achieve nearly zero estimation error (Fig.3), while eavesdroppers experience exponentially growing errors after a single packet loss (Fig.4). The error growth rate correlates with the instability of the perturbation matrix, confirming the theoretical divergence. In multi-channel scenarios, independent perturbation sequences per channel prevent cross-channel correlation attacks (Fig.5). The scheme maintains low communication and computational overhead, making it practical for maritime environments. Furthermore, the method demonstrates strong adaptability to packet loss and channel variations, fulfilling SOLAS requirements for data integrity and reliability. Conclusions This paper proposes a dynamic encoding scheme with time-varying perturbations for privacy-preserving vessel state estimation. The method integrates EKF with an unstable perturbation mechanism to ensure high precision for legitimate users and exponential error growth for eavesdroppers. Key contributions include: (1) A novel encoding framework that ensures zero precision loss for legitimate receivers; (2) A lightweight synchronization mechanism based on shared seeds, eliminating complex key management; (3) Theoretical guarantees of exponential error divergence for eavesdroppers under single or multi-channel attacks. The scheme is robust against packet loss and channel asynchrony, complies with SOLAS data integrity requirements, and is suitable for resource-limited maritime networks. Future work will extend the method to nonlinear vessel dynamics, adaptive perturbation optimization, and real-world maritime communication validation.
- Vessel positioning,
- Privacy protection,
- Extended Kalman Filter (EKF),
- Dynamic encoding,
- Distributed estimation

FullText(HTML)

References(27)

References

[1]	LI Song, HAN Jinguang, TONG Deyu, et al. Redactable signature-based public auditing scheme with sensitive data sharing for cloud storage[J]. IEEE Systems Journal, 2022, 16(3): 3613–3624. doi: 10.1109/JSYST.2022.3159832.
[2]	SUGIURA G, ITO K, and KASHIMA K. Bayesian differential privacy for linear dynamical systems[J]. IEEE Control Systems Letters, 2022, 6: 896–901. doi: 10.1109/LCSYS.2021.3087096.
[3]	XUE Qiao, ZHU Youwen, and WANG Jian. Joint distribution estimation and Naïve Bayes classification under local differential privacy[J]. IEEE Transactions on Emerging Topics in Computing, 2021, 9(4): 2053–2063. doi: 10.1109/TETC.2019.2959581.
[4]	DOMINGO-FERRER J. A provably secure additive and multiplicative privacy homomorphism[C]. Proceedings of the 5th International Conference on Information Security, Sao Paulo, Brazil, 2002: 471–483. doi: 10.1007/3-540-45811-5_37.
[5]	TERANISHI K, KOGISO K, and TANAKA T. Faithful and privacy-preserving implementation of average consensus[C]. Proceedings of 2025 American Control Conference (ACC), Denver, USA, 2025: 2937–2942. doi: 10.23919/ACC63710.2025.11107548.
[6]	SHU Haoyu, ZHOU Jiayu, YANG Wen, et al. Distortion-based state security codes for distributed sensor networks[J]. Automatica, 2023, 151: 110904. doi: 10.1016/j.automatica.2023.110904.
[7]	LIN Y H, CHANG S Y, and SUN H M. CDAMA: Concealed data aggregation scheme for multiple applications in wireless sensor networks[J]. IEEE Transactions on Knowledge and Data Engineering, 2013, 25(7): 1471–1483. doi: 10.1109/TKDE.2012.94.
[8]	YANG Wen, LI Dengke, ZHANG Heng, et al. An encoding mechanism for secrecy of remote state estimation[J]. Automatica, 2020, 120: 109116. doi: 10.1016/j.automatica.2020.109116.
[9]	TSIAMIS A, GATSIS K, and PAPPAS G J. State-secrecy codes for networked linear systems[J]. IEEE Transactions on Automatic Control, 2020, 65(5): 2001–2015. doi: 10.1109/TAC.2019.2927459.
[10]	TSIAMIS A, GATSIS K, and PAPPAS G J. State-secrecy codes for stable systems[C]. Proceedings of 2018 Annual American Control Conference (ACC), Milwaukee, USA, 2018: 171–177. doi: 10.23919/ACC.2018.8431642.
[11]	YANG Wen, LI Dengke, ZHANG Heng, et al. An encoding mechanism for secrecy of remote state estimation[J]. Automatica, 2020, 120: 109116. doi: 10.1016/j.automatica.2020.109116. (查阅网上资料,本条文献与第8条文献重复,请确认).
[12]	YANG Lixin, XU Yong, LV Weijun, et al. Optimal transmission scheduling over multihop networks: Structural results and reinforcement learning[J]. IEEE Transactions on Automatic Control, 2024, 69(3): 1826–1833. doi: 10.1109/TAC.2023.3327622.
[13]	HUANG Zenghong, CHEN Zijie, XU Yong, et al. Distributed receding horizon estimation for time invariant discrete time linear systems based on substate decomposition[J]. IEEE Transactions on Network Science and Engineering, 2025. doi: 10.1109/TNSE.2025.3590754. (查阅网上资料,未找到本条文献卷期页码信息,请确认).
[14]	YU Yan, YANG Wen, DING Wenjie, et al. Reinforcement learning solution for cyber-physical systems security against replay attacks[J]. IEEE Transactions on Information Forensics and Security, 2023, 18: 2583–2595. doi: 10.1109/TIFS.2023.3268532.
[15]	SHNAIN A H, SRUTHI P, SUBBURAM S, et al. Privacy-preserving data aggregation in IoT networks using homomorphic encryption[C]. Proceedings of 2024 International Conference on IoT, Communication and Automation Technology (ICICAT), Gorakhpur, India, 2024: 1387–1391. doi: 10.1109/ICICAT62666.2024.10923462.
[16]	YU Longxin, YU Wenwu, and LV Yuezu. Multi-dimensional privacy-preserving average consensus in wireless sensor networks[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2022, 69(3): 1104–1108. doi: 10.1109/TCSII.2021.3095952.
[17]	AGARWAL G K, KARMOOSE M, DIGGAVI S, et al. Distortion-based lightweight security for cyber-physical systems[J]. IEEE Transactions on Automatic Control, 2021, 66(4): 1588–1601. doi: 10.1109/TAC.2020.3006814.
[18]	金敏捷, 赵瑜颢. 舰船通信网络隐私信息安全加密方法研究[J]. 舰船科学技术, 2024, 46(10): 166–169. doi: 10.3404/j.issn.1672-7649.2024.10.029. JIN Minjie and ZHAO Yuhao. Research on privacy information security encryption methods for ship communication networks[J]. Ship Science and Technology, 2024, 46(10): 166–169. doi: 10.3404/j.issn.1672-7649.2024.10.029.
[19]	卞璐. 船舶通信网络主动防御下隐私信息保护研究[J]. 舰船科学技术, 2021, 43(3A): 151–153. BIAN Lu. Research on the protection of privacy information in ship communication network[J]. Ship Science and Technology, 2021, 43(3A): 151–153.
[20]	孙宝全, 颜冰, 姜润翔, 等. 船舶静态电场跟踪的渐进更新扩展卡尔曼滤波器[J]. 国防科技大学学报, 2018, 40(6): 134–140. doi: 10.11887/j.cn.201806019. SUN Baoquan, YAN Bing, JIANG Runxiang, et al. A progressive update extended Kalman filter for ship tracking with static electric field[J]. Journal of National University of Defense Technology, 2018, 40(6): 134–140. doi: 10.11887/j.cn.201806019.
[21]	KENNEDY J M, FORD J J, QUEVEDO D E, et al. Innovation-based remote state estimation secrecy with no acknowledgments[J]. IEEE Transactions on Automatic Control, 2024, 69(11): 7433–7448. doi: 10.1109/TAC.2024.3385315.
[22]	CHEN Peipei, YANG Wen, LIU Yun, et al. Dynamic encoding scheme for state estimation over wireless sensor networks[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2023, 70(11): 4098–4102. doi: 10.1109/TCSII.2023.3275175.
[23]	蒋瀚, 刘怡然, 宋祥福, 等. 隐私保护机器学习的密码学方法[J]. 电子与信息学报, 2020, 42(5): 1068–1078. doi: 10.11999/JEIT190887. JIANG Han, LIU Yiran, SONG Xiangfu, et al. Cryptographic approaches for privacy-preserving machine learning[J]. Journal of Electronics & Information Technology, 2020, 42(5): 1068–1078. doi: 10.11999/JEIT190887.
[24]	耿普, 祝跃飞. 浮点数比较分支的混淆方法研究[J]. 电子与信息学报, 2020, 42(12): 2857–2864. doi: 10.11999/JEIT190743. GENG Pu and ZHU Yuefei. An branch obfuscation research on path branch which formed by floating-point comparison[J]. Journal of Electronics & Information Technology, 2020, 42(12): 2857–2864. doi: 10.11999/JEIT190743.
[25]	LIN X, ZHU Y, LI M, et al. Stability of extended Kalman filtering for nonlinear systems: A survey[J]. Automatica, 2021, 134: 109948. (查阅网上资料, 未找到本条文献信息, 请确认).
[26]	SHI Xiasheng and LI Zhongmei. Fully distributed adaptive practical fixed-time optimal consensus for multi-agent systems[J]. IEEE Control Systems Letters, 2025, 9: 1958–1963. doi: 10.1109/LCSYS.2025.3589617.
[27]	PAN Zhuorui, REN Wei, and SUN Ximing. Distributed event-triggered observer-based control for linear networked multi-agent systems[C]. Proceedings of 2024 European Control Conference (ECC), Stockholm, Sweden, 2024: 1171–1176. doi: 10.23919/ECC64448.2024.10591233.