  As a fundamental information fusion approach, the arithmetic average (AA)
fusion has recently been investigated for various random finite set (RFS)
filter fusion in the context of multi-sensor multi-target tracking. It is not a
straightforward extension of the ordinary density-AA fusion to the RFS
distribution but has to preserve the form of the fusing multi-target density.
In this work, we first propose a statistical concept, probability hypothesis
density (PHD) consistency, and explain how it can be achieved by the PHD-AA
fusion and lead to more accurate and robust detection and localization of the
present targets. This forms a both theoretically sound and technically
meaningful reason for performing inter-filter PHD AA-fusion/consensus, while
preserving the form of the fusing RFS filter. Then, we derive and analyze the
proper AA fusion formulations for most existing unlabeled/labeled RFS filters
basing on the (labeled) PHD-AA/consistency. These derivations are theoretically
unified, exact, need no approximation and greatly enable heterogenous unlabeled
and labeled RFS density fusion which is separately demonstrated in two
consequent companion papers.
