Robust Extended Kalman Filter for Graphical Nonlinear Systems with Hybrid Cyber-Attacks

This paper studies the extended Kalman filtering for graphical nonlinear systems with hybrid cyber-attacks. The considered system states and measurement outputs are generated based on graph structures, and the measurement signals are subject to denial-of-service attacks and deception attacks. In order to improve the filtering performance of graphical nonlinear systems subjected to hybrid cyber-attacks, we design an extended Kalman filter with a diagonal gain matrix in the graph frequency domain by means of the graph Fourier transform. The diagonal form of the gain matrix allows the states of each node to be updated independently, thus reducing the iterative accumulation error. Further, we introduce higher-order terms in the first-order Taylor expansion of the nonlinear function to compensate for the linearization error. Finally, we obtain the diagonal Kalman gain matrix by solving two Riccati-like equations. A simulation example on a power system validates the superior performance of the proposed filter against hybrid cyber-attacks.