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.

翻译：作为基础信息融合方法，算术平均融合近期在多传感器多目标跟踪场景中被研究用于各类随机有限集滤波器融合。该融合并非将普通密度算术平均融合直接扩展到随机有限集分布，而是必须保持融合多目标密度的形式。本文首先提出统计概念——概率假设密度一致性，并阐释如何通过PHD-AA融合实现该一致性，从而更准确、鲁棒地检测与定位现有目标。这为在保留融合随机有限集滤波器形式的同时执行滤波器间PHD算术平均融合/共识提供了兼具理论严谨性与技术合理性的依据。随后，基于（标记）PHD算术平均/一致性原理，推导并分析了现有无标记/标记随机有限集滤波器的合理算术平均融合公式。这些推导在理论上具有统一性、精确性且无需近似，极大促进了异质无标记与标记随机有限集密度融合——该成果将在两篇后续配套论文中分别展示。