Distributed information fusion in tangle networks

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.