Unscented Kalman filter of graph signals

We consider the nonlinear filtering problem of graph signals, where the measurements are generated based on graph topology. We propose a graph-based unscented Kalman filter (UKF) by using the decomposition of graph Laplacian matrix in the design of Kalman gain matrix. We demonstrate that the graph-based UKF reduces to the UKF for the graph Fourier transform of signals with a diagonal Kalman gain matrix, so that each vertex signal can be updated independently and more accurate results can be derived to reduce accumulation errors. Simulation results are provided to verify the effectiveness of the proposed filter.