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
Privacy-Preserving Distributed Maximum Correntropy Filtering for State-Saturation Nonlinear Systems: A State Decomposition Approach
DOI: 10.12677/pm.2025.153102, PDF,    国家自然科学基金支持
作者: 杜 雨：上海理工大学理学院，上海；张志祥, 丁德锐：上海理工大学光电信息与计算机工程学院，上海
关键词: 分布式滤波；最大相关熵；状态分解；状态饱和；S-t核函数；隐私保护；Distributed Filtering； Maximum Correntropy； State Decomposition； State Saturation； S-t Kernel Function； Privacy Protection
摘要: 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。
Abstract: 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.
文章引用：杜雨, 张志祥, 丁德锐. 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[J]. 理论数学, 2025, 15(3): 273-287. https://doi.org/10.12677/pm.2025.153102

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