A recent trend in distributed multisensor fusion is to use random finite-set filters at the sensor nodes and fuse the filtered distributions algorithmically using their exponential mixture densities (EMDs). Fusion algorithms that extend covariance intersection and consensus-based approaches are such examples. In this paper, we analyze the variational principle underlying EMDs and show that the EMDs of finite-set distributions do not necessarily lead to consistent fusion of cardinality distributions. Indeed, we demonstrate that these inconsistencies may occur with overwhelming probability in practice, through examples with Bernoulli, Poisson, and independent identically distributed cluster processes. We prove that pointwise consistency of EMDs does not imply consistency in global cardinality and vice versa. Then, we redefine the variational problems underlying fusion and provide iterative solutions thereby establishing a framework that guarantees cardinality consistent fusion.

中文翻译：

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有限集分布的融合：逐点一致性和全局基数

分布式多传感器融合的最新趋势是在传感器节点使用随机有限集滤波器，并使用指数混合密度 (EMD) 以算法方式融合滤波后的分布。扩展协方差交集的融合算法和基于共识的方法就是这样的例子。在本文中，我们分析了 EMD 的变分原理，并表明有限集分布的 EMD 不一定会导致基数分布的一致融合。事实上，我们通过伯努利、泊松和独立同分布集群过程的例子证明了这些不一致在实践中可能以压倒性的概率发生。我们证明 EMD 的逐点一致性并不意味着全局基数的一致性，反之亦然。然后，