Maximum correntropy EKF for stochastic nonlinear systems under measurement model with multiplicative false data cyber attacks and non-Gaussian noises

The weighted maximum correntropy extended Kalman filtering (WMC-EKF) problem is addressed in this article for a class of stochastic nonlinear systems under cyber attacks, considering the noises are non-Gaussian of system and measurement. A measurement model is established to characterize both denial-of-service (DoS) attacks and false data injection (FDI) attacks, where the false data has a multiplicative effect on the original measurement. Both deterministic and stochastic nonlinear functions are taken into account. Since the standard Kalman filter only utilizes second-order signal information, it may not be optimal in non-Gaussian environments. By leveraging the advantages of correntropy in handling non-Gaussian signals, formulas for calculating the filter gains and upper bound of the filter error covariance are derived using the weighted maximum correntropy criterion, Taylor series expansion, and fixed-point iterative update rule. Finally, two numerical simulations demonstrate the effectiveness of WMC-EKF under hybrid cyber attacks with non-Gaussian process and measurement noises.