Distributed Bayesian Estimation of Continuous Variables Over Time-Varying Directed Networks

Abstract

This letter presents a distributed Bayesian estimation algorithm for time-varying directed sensor networks. We consider a network of sensing agents aiming to estimate continuous variables of interest using direct observations as well as communication across the network. We aim to obtain a probability density function for the unknown variables that best explains the collectively gathered data. To account for point-to-point and broadcast communication, our formulation considers uniformly and strongly connected digraphs. Each agent pools neighbor densities via a weighted geometric average to achieve consensus. We deal with continuous variables via a novel application of large deviation analysis to the estimated probability ratios. Our analysis captures a large class of probability density functions, including Gaussian mixtures, and guarantees that the mode of the estimated density converges to the true parameter value at an exponential rate. The consistency and convergence rate of our algorithm are demonstrated in cooperative localization and distributed target tracking simulations.