Arithmetic Average Density Fusion—Part II: Unified Derivation for Unlabeled and Labeled RFS Fusion

As a fundamental information fusion approach, the arithmetic average (AA) fusion has recently been investigated for various random finite set (RFS) filter fusions in the context of multisensor, multitarget 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 multitarget density. In this article, 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 interfilter 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 building on a single coherent framework are theoretically unified, exact, need no approximation, and greatly enable heterogenous unlabeled and labeled RFS density fusion which is separately demonstrated in companion papers.