多重攻击下的事件触发学生t扩展卡尔曼滤波方法

An Event-triggered Student’s t Extended Kalman Filter Under Multiple Attacks

  • 摘要: 网络化系统易受到DoS攻击(Denial of Service Attacks)和FDI攻击(False Data Injection Attacks)等多重攻击,破坏了传感器量测数据的完整性和有效性,降低了滤波器的准确性,甚至使得滤波器发散。此外,系统建模误差、数据传输过程的多径传播等因素,使得过程噪声和量测噪声不再服从标准的高斯分布,呈现厚尾特性,降低了滤波器的估计性能。本文针对一类噪声服从厚尾分布的网络化非线性系统状态估计问题,考虑到系统面临的DoS攻击和FDI攻击等多重攻击导致滤波器估计性能差等问题,提出了基于学生t分布的抗攻击扩展卡尔曼滤波器。首先,借助学生t分布来近似厚尾噪声的概率分布,引入两个二元随机变量分别表征DoS攻击和FDI攻击,使用最小化估计误差协方差上界的方法,计算最优的滤波器增益矩阵,设计了多重攻击下的学生t扩展卡尔曼滤波器;其次,考虑到数据传输带宽有限,数据传输过程中面临的信道堵塞、信息丢失等问题,引入了事件触发机制,提高通信信道利用率,给出了事件触发机制下的学生t扩展卡尔曼滤波;最后,仿真验证了所提方法的有效性。

     

    Abstract: ‍ ‍Wireless network systems are susceptible to various attacks such as DoS (Denial of Service Attacks) and FDI (False Data Injection Attacks), which disrupt the integrity and effectiveness of sensor measurement data. They reduce the accuracy of filter state estimation, and even cause filter divergence. Moreover, the system modeling error, multipath propagation and other factors in the data transmission process make the process noise and measurement noise will not obey the standard Gaussian distribution, showing heavy-tail characteristics. These factors will reduce the estimation performance of filters. Aiming at the problem of state estimation for a class of networked nonlinear systems with heavy tailed noise distribution, considering the poor performance of filter estimation caused by multiple attacks, such as DoS attacks and FDI attacks, an anti-attack extended Kalman filter based on the Student’s t distribution is proposed. Firstly, the Student’s t distribution is used to approximate the probability density function of the heavy tailed noise. Two binary random variables are introduced to represent DoS attacks and FDI attacks, based on the estimation error covariance upper bound minimization method, the optimal filter gain matrix is derived. Then, the Student’s t extended Kalman filter under multiple attacks is obtained; secondly, considering the limited bandwidth and the issues of channel congestion and information loss faced during data transmission, an event trigger mechanism is introduced to improve the channel utilization; finally, simulations verify the effectiveness of the proposed method.

     

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