Equivalence of measurement space solution data fusion and complete fusion

Many observation systems are operating on space-borne and airborne platforms, as well as from ground-based stations, providing measurements of vertical profiles of atmospheric parameters. When independent measurements of the same profile are available data fusion methods can be used to combine them and exploit all the available information for a more comprehensive and accurate description of the atmospheric state. Several data fusion methods can be used. Among the others, both the measurement space solution data fusion method and the complete fusion method have the remarkable properties of using all the acquired information and of providing results that are independent from a priori information used in the individual retrievals. For this reason, though the two methods use two completely different procedures, it is reasonable to expect that they give the same results and in this paper the rigorous proof of the equivalence of the two methods is given. Therefore, the choice between them is only driven by the advantages of the different implementations.