Convergence of distributed flooding and its application for distributed Bayesian filtering

Distributed flooding is a fundamental information sharing method to obtaining network consensus via peer-to-peer communication. However, a unified consensus-oriented formulation of the algorithm and its convergence performance are not explicitly available in the literature. To fill this void in this paper, set-theoretic flooding rules are defined by encapsulating the information of interest in finite sets (one set per node), namely distributed set-theoretic information flooding (DSIF). This leads to a new type of consensus called 'collecting consensus,' which aims to ensure that all nodes get the same information. Convergence and optimality analyses are provided based on a consistent measure of the degree of consensus of the network. Compared with the prevailing averaging consensus, the proposed DSIF protocol benefits from avoiding repeated use of any information and offering the highest converging efficiency for network consensus while being exposed to increasing node-storage requirements against communication iterations and higher communication load. The protocol has been advocated for distributed nonlinear Bayesian filtering, where each node operates a separate particle filter, and the collecting consensus is sought on the sensor data alone or jointly with intermediate local filter estimates. Simulations are provided to demonstrate the theoretical findings.