Distributed averaging of exponential-class densities with discrete-time event-triggered consensus

The paper addresses discrete-time event-driven con- sensus on exponential-class probability densities (including Gaus- sian, 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 so as to tradeoff data communication rate, and hence energy consump- tion, 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.