Distributed Averaging of Exponential-Class Densities With Discrete-Time Event-Triggered Consensus

The paper addresses discrete-time event-driven consensus on exponential-class probability densities (including Gaussian, binomial, Poisson, Rayleigh, Wishart, Inverse Wishart, and many other distributions of interest) completely specified by a finite-dimensional vector of so-called natural parameters. First, it is proved how such exponential classes are closed under Kullback-Leibler fusion (average), and how the latter is equivalent to a weighted arithmetic average over the natural parameters. Then, a novel event-driven transmission strategy is proposed in order to trade off the data-communication rate and, hence, energy consumption, versus consensus speed and accuracy. A theoretical analysis of the convergence properties of the proposed algorithm is provided by exploiting the Fisher metric as a local approximation of the Kullback-Leibler divergence. Some numerical examples are presented in order to demonstrate the effectiveness of the proposed event-driven consensus. It is expected that the latter can be successfully exploited for energy-and/or bandwidth-efficient networked state estimation.