Performance Analysis for Distributed Fusion with Different Dimensional Data

Different sensors or estimators may have different capability to provide data. Some sensors can provide a relatively higher dimensional data, while other sensors can only provide part of them. Some estimators can estimate full dimensional quantity of interest, while others may only estimate part of it due to some constraints. How is such kind of data with different dimensions fused? How do the common part and the uncommon part affect each other during fusion? To answer these questions, a fusion algorithm based on linear minimum mean-square error (LMMSE) estimation is provided in this paper. Then the fusion performance is analyzed, which is the main contribution of this work. The conclusions are as follows. First, the fused common part is not affected by the uncommon part. Second, the fused uncommon part will benefit from the common part through the cross-correlation. Finally, under certain conditions, both the more accurate common part and the stronger correlation can result in more accurate fused uncommon part. The conclusions are all supported by some tracking application examples.