Distributed Consensus Algorithms in Sensor Networks with Higher-Order Topology

Information aggregation in distributed sensor networks has received significant attention from researchers in various disciplines. Distributed consensus algorithms are broadly developed to accelerate the convergence to consensus under different communication and/or energy limitations. Non-Bayesian social learning strategies are representative algorithms for distributed agents to learn progressively an underlying state of nature by information communications and evolutions. This work designs a new non-Bayesian social learning strategy named the hypergraph social learning by introducing the higher-order topology as the underlying communication network structure, with its convergence as well as the convergence rate theoretically analyzed. Extensive numerical examples are provided to demonstrate the effectiveness of the framework and reveal its superior performance when applying to sensor networks in tasks such as cooperative positioning. The designed framework can assist sensor network designers to develop more efficient communication topology, which can better resist environmental obstructions, and also has theoretical and applied values in broad areas such as distributed parameter estimation, dispersed information aggregation and social networks.