VC-EKF for Graphical Nonlinear Systems

This paper investigates the issue of extended Kalman filtering (EKF) for graphical nonlinear systems. For the signals that have a nonlinear relationship with the graph Laplacian matrix, we introduce a variance-constrained (VC)-EKF, leveraging the graph Fourier transform (GFT), aimed at enhancing the filtering performance. In this paper, the GFT is applied for system variables and the updated estimate is designed with a diagonal gain matrix for the transformed system, then the higher-order terms are introduced into the predicted error and the updated error, and the diagonal gain matrix can be acquired through the solution of two Riccati-like equations. The advantages of the GFT-VC-EKF are that, the gain matrix represented by a diagonal matrix enables the node signal to be updated independently, thus reducing the iterative cumulative error, and the introduction of higher-order terms makes it possible to compensate for the linearization error caused by the fact that the EKF containing only first-order Taylor expansion term. A simulation example on a power system proves the superiority of the proposed filter.