Extended Kalman filtering for stochastic nonlinear systems with randomly occurring cyber attacks.

This paper is concerned with the extended Kalman filtering problem for a class of stochastic nonlinear systems under cyber attacks, wherein the discussed cyber attacks occur in a random way in the data transmission from sensor nodes to remote filter nodes. A novel cyber attack model is established in a unified representation to account for both the false data injection attacks and the denial of service (DoS) attacks. Moreover, a more general nonlinear description that stands for both the deterministic and stochastic nonlinearities is put forward. By virtue of the recurrence on the stochastic analysis approach, the upper bound of filtering error covariance is obtained, and it can be minimized at each time instant via solving an optimization problem. Furthermore, a sufficient condition is provided to ensure the stochastic boundedness of filtering error in the simultaneous presence of randomly occurring cyber attacks and nonlinearities. Eventually, one example is presented to verify the validity of the suggested filtering scheme.