The potential of a decentralized/distributed system to behave intelligently as a whole hinges on the capacity of its constituents to exchange and process information. In sensor networks and multiagent platforms this may be realized by means of distributed information fusion techniques. The very nature of these approaches demands specifying, or at least approximating, the statistical interdependencies between individual entities in the network. This, however, becomes impractical with the increase in network size. In the past years a number of scalable techniques have been devised, which relax this constraint while yet maintaining a number of desired statistical properties like consistency and convergence to consensus. Here, we present a methodological approach for designing and analyzing information fusion in potentially large-scale networks. Tangle networks, the objects of study in our formalism, are flexible diagrammatic models that capture key properties of scalable information fusion. A tangle network comes equipped with a natural notion of equivalence: two networks are equivalent if they can be transformed one into the other by successive application of local deformations. Any such deformation preserves the information content and consistency of estimators in the network. We derive novel particle-filtering-based algorithms for distributed information fusion over tangle networks and analyze their performance in various settings. The algebraic properties of tangle networks are shown to bear resemblance to algebraic properties of graphs. In particular, we show that the agreement between estimators in the network is governed by the spectral gap of the network’s associated matrix, the analog of a graph Laplacian. The utility of the framework is demonstrated through comparison with state-of-the-art distributed information fusion techniques.

分散/分布式系统整体上智能运行的潜力取决于其组成部分交换和处理信息的能力。在传感器网络和多代理平台中，这可以通过分布式信息融合技术来实现。这些方法的本质要求指定或至少近似网络中各个实体之间的统计相互依赖性。然而，随着网络规模的增加，这变得不切实际。在过去的几年中，已经设计出了许多可伸缩的技术，这些技术在减轻约束的同时又保持了许多所需的统计特性，如一致性和收敛性。在这里，我们提出了一种在潜在的大规模网络中设计和分析信息融合的方法论方法。缠结网络是我们形式主义的研究对象，是灵活的图表模型，可捕获可伸缩信息融合的关键属性。缠结网络具有自然的等效概念：如果可以通过连续应用局部变形将两个网络转换为另一个，则两个网络是等效的。任何此类变形都会保留网络中估算器的信息内容和一致性。我们推导了基于新颖的基于粒子过滤的算法，用于在缠结网络上进行分布式信息融合，并分析了它们在各种环境下的性能。缠结网络的代数性质显示为与图的代数性质相似。特别是，我们证明了网络中估算器之间的一致性受网络相关矩阵的频谱间隙支配，图拉普拉斯算子的类似物。通过与最新的分布式信息融合技术进行比较，证明了该框架的实用性。