Nonlinear weighted measurement fusion Unscented Kalman Filter with asymptotic optimality

For the general nonlinear systems, a universal weighted measurement fusion (WMF) algorithm is presented via the Taylor series expansion method. Based on the proposed fusion algorithm and the well-known Unscented Kalman Filter (UKF), the WMF-UKF is presented. It is proven that the proposed WMF-UKF asymptotically approaches to the centralized measurement fusion UKF (CMF-UKF) with the increase of the order of Taylor series expansion. So it has the asymptotical global optimality. We find that WMF-UKF has less computational cost than the CMF-UKF does with the increase of the number of sensors. Two examples are given to show the effectiveness of the proposed algorithms.