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Pure Mathematics 2025
一类状态饱和非线性系统的隐私保护分布式最大相关熵滤波：基于状态分解的方法
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Abstract:
本文研究了一类在非高斯噪声影响下的状态饱和系统的分布式隐私保护熵滤波问题。首先，引入变量分解策略结合系统状态饱和的特征设计了一个分布式滤波器，其中考虑的系统遭受的乘性噪声以及非高斯噪声。接下来，结合已有的符合约束条件的时变动态密钥以及分解规则，得到私有误差协方差矩阵与公共协方差矩阵之间的关系以及它们的上界。在此基础上，最小化基于S-t核函数的最大熵准则下的代价函数得到待设计的滤波器增益。最后，通过对比窃听者滤波误差协方差和正常滤波误差协方差，分析了所设计的滤波算法的隐私性。最后利用仿真算例验证了算法的有效性以及安全性。
This paper studies the distributed privacy-preserving entropy filtering problem for a class of state-saturated systems under the influence of non-Gaussian noise. Firstly, a distributed filter is designed by introducing a variable decomposition strategy and considering the characteristics of system state saturation, where the multiplicative noise and non-Gaussian noise suffered by the system are taken into account. Next, by combining the existing time-varying dynamic keys that meet the constraint conditions and the decomposition rules, the relationship between the private error covariance matrix and the public covariance matrix and their upper bounds are obtained. On this basis, the filter gain to be designed is obtained by minimizing the cost function under the maximum entropy criterion based on the S-t kernel function. Finally, the privacy of the designed filtering algorithm is analyzed by comparing the eavesdropper’s filtering error covariance with the normal filtering error covariance. The effectiveness and security of the algorithm are verified by simulation examples.
| [1] | Dunik, J., Biswas, S.K., Dempster, A.G., Pany, T. and Closas, P. (2020) State Estimation Methods in Navigation: Overview and Application. IEEE Aerospace and Electronic Systems Magazine, 35, 16-31. https://doi.org/10.1109/maes.2020.3002001 |
| [2] | Huang, Y., Zhang, Y., Shi, P., Wu, Z., Qian, J. and Chambers, J.A. (2019) Robust Kalman Filters Based on Gaussian Scale Mixture Distributions with Application to Target Tracking. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49, 2082-2096. https://doi.org/10.1109/tsmc.2017.2778269 |
| [3] | Deng, R., Xiao, G., Lu, R., Liang, H. and Vasilakos, A.V. (2017) False Data Injection on State Estimation in Power Systems—Attacks, Impacts, and Defense: A Survey. IEEE Transactions on Industrial Informatics, 13, 411-423. https://doi.org/10.1109/tii.2016.2614396 |
| [4] | 张云涵, 邓涛, 龚琦皓. 基于LSTM-EKF的无人机航迹追踪算法[J]. 导航定位学报, 2024, 12(6): 62-69. |
| [5] | Liu, N., Zhang, K., Xie, X. and Yue, D. (2024) UKF-Based Optimal Tracking Control for Uncertain Dynamic Systems with Asymmetric Input Constraints. IEEE Transactions on Cybernetics, 54, 7224-7235. https://doi.org/10.1109/tcyb.2024.3471987 |
| [6] | Arasaratnam, I., Haykin, S. and Elliott, R.J. (2007) Discrete-Time Nonlinear Filtering Algorithms Using Gauss-Hermite Quadrature. Proceedings of the IEEE, 95, 953-977. https://doi.org/10.1109/jproc.2007.894705 |
| [7] | Chen, B., Liu, X., Zhao, H. and Principe, J.C. (2017) Maximum Correntropy Kalman Filter. Automatica, 76, 70-77. https://doi.org/10.1016/j.automatica.2016.10.004 |
| [8] | Chang, L., Hu, B., Chang, G. and Li, A. (2012) Huber-Based Novel Robust Unscented Kalman Filter. IET Science, Measurement & Technology, 6, 502-509. https://doi.org/10.1049/iet-smt.2011.0169 |
| [9] | Song, H., Ding, D., Dong, H. and Han, Q. (2022) Distributed Maximum Correntropy Filtering for Stochastic Nonlinear Systems under Deception Attacks. IEEE Transactions on Cybernetics, 52, 3733-3744. https://doi.org/10.1109/tcyb.2020.3016093 |
| [10] | Chen, B., Zhu, Y., Hu, J. and Principe, J.C. (2013) System Parameter Identification: Information Criteria and Algorithms. Newnes, 51-55. |
| [11] | Huang, Y., Zhang, Y., Li, N. and Chambers, J. (2016) Robust Student’s T Based Nonlinear Filter and Smoother. IEEE Transactions on Aerospace and Electronic Systems, 52, 2586-2596. https://doi.org/10.1109/taes.2016.150722 |
| [12] | Song, H., Ding, D., Dong, H. and Yi, X. (2022) Distributed Filtering Based on Cauchy-Kernel-Based Maximum Correntropy Subject to Randomly Occurring Cyber-Attacks. Automatica, 135, Article ID: 110004. https://doi.org/10.1016/j.automatica.2021.110004 |
| [13] | Wang, H., Li, X., Bi, D., Xie, X. and Xie, Y. (2021) A Robust Student’s t-Based Kernel Adaptive Filter. IEEE Transactions on Circuits and Systems II: Express Briefs, 68, 3371-3375. https://doi.org/10.1109/tcsii.2021.3074643 |
| [14] | 罗贞. 基于卡尔曼滤波器的系统状态估计和故障检测[D]: [博士学位论文]. 武汉: 华中科技大学, 2013. |
| [15] | Tran, H., Hu, J. and Pota, H.R. (2023) A Privacy-Preserving State Estimation Scheme for Smart Grids. IEEE Transactions on Dependable and Secure Computing, 20, 3940-3956. https://doi.org/10.1109/tdsc.2022.3210017 |
| [16] | Zhou, J., Yang, W., Ding, W., Zheng, W.X. and Xu, Y. (2023) Watermarking-Based Protection Strategy against Stealthy Integrity Attack on Distributed State Estimation. IEEE Transactions on Automatic Control, 68, 628-635. https://doi.org/10.1109/tac.2022.3171422 |
| [17] | Wen, C., Wang, Z., Liu, Q. and Alsaadi, F.E. (2018) Recursive Distributed Filtering for a Class of State-Saturated Systems with Fading Measurements and Quantization Effects. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48, 930-941. https://doi.org/10.1109/tsmc.2016.2629464 |
| [18] | Shen, B., Wang, X. and Zou, L. (2023) Maximum Correntropy Kalman Filtering for Non-Gaussian Systems with State Saturations and Stochastic Nonlinearities. IEEE/CAA Journal of Automatica Sinica, 10, 1223-1233. https://doi.org/10.1109/jas.2023.123195 |
| [19] | Zhao, P., Ding, D., Dong, H., Liu, H. and Yi, X. (2024) Secure Distributed State Estimation for Microgrids with Eavesdroppers Based on Variable Decomposition. IEEE Transactions on Circuits and Systems I: Regular Papers, 71, 3307-3316. https://doi.org/10.1109/tcsi.2024.3357523 |
| [20] | Izanloo, R., Fakoorian, S.A., Yazdi, H.S. and Simon, D. (2016). Kalman Filtering Based on the Maximum Correntropy Criterion in the Presence of Non-Gaussian Noise. 2016 Annual Conference on Information Science and Systems (CISS), Princeton, 16-18 March 2016, 500-505. https://doi.org/10.1109/ciss.2016.7460553 |
| [21] | Theodor, Y. and Shaked, U. (1996) Robust Discrete-Time Minimum-Variance Filtering. IEEE Transactions on Signal Processing, 44, 181-189. https://doi.org/10.1109/78.485915 |
