Modified Kalman Filtering for Stochastic Nonlinear Systems Under Non-Gaussian–Lévy Noise and Cyber Attacks

This article studies the filtering problem for a class of stochastic nonlinear system under non-Gaussian–Lévy noise and cyber attacks, where the denial-of-service (DoS) attacks and the false data-injection (FDI) attacks are both considered. Since the covariance of the Lévy noise is unknown and infinite, the standard Kalman filter fails to estimate system states. By exploiting saturation functions, a modified Kalman filter is proposed, where the extremely large values of the measurement outputs caused by the Lévy noises can be clipped. In the presence of Lévy noise and cyber attacks, an upper bound for the error covariance is guaranteed and can be minimized via designing the filter parameter. Besides, a sufficient condition is provided to guarantee the boundedness of the upper bound, and the convergence analysis of the filtering error is presented. Finally, the simulation results are given to verify the algorithm.