On functional equivalence of two measurement fusion methods

Currently there exist two optimal measurement fusion methods for Kalman filtering-based multi-sensor data fusion.The first is the centralized measurement fusion method,which combines the multi-sensor data by increasing the dimension of the measurement vector,whereas the second is the distributed measurement fusion method which combines the multi-sensor data by the weighting based on a linear minimum variance criterion,but the dimension of the measurement vector is not changed.By the Kalman filtering method,this paper shows that the two measurement fusion methods are completely functionally equivalent if the sensors used for data fusion have identical measurement matrices,i.e.the Kalman estimators(filter,predictor,smoother),signal estimators,and white noise estimators obtained by two methods are numerically equal,respectively.In this case,the second method not only gives the globally optimal fused estimation as given by the first method,but also obviously reduces the computational burden for real time applications.Finally,a numerical example shows its validity.