Privacy-Preserving Distributed Extended Kalman Filtering for Graphical Nonlinear Systems

In this article, a privacy-preserving distributed extended Kalman filter based on average consensus information fusion is designed for graphical nonlinear systems. The privacy-preserving approach adopted is realized based on a combination of state decomposition and noise injection methods. On the one hand, the Laplacian matrix of the graphical nonlinear system is utilized to design a distributed filter in the graph frequency domain, featuring a diagonal gain matrix that significantly enhances filtering performance; on the other hand, a recursive least squares filter is applied at the sensor nodes to filter out the privacy-preserving noise, thus making the eavesdropper's observation mismatch with the iterative update of the sensor state, which effectively improves the filtering and privacy performance. Subsequently, the boundedness of the filtering error is shown, and the privacy performance against eavesdroppers is discussed. Finally, a simulation example of a power system demonstrates the superiority of our proposed algorithm.