Distributed Bayesian Estimation of Linear Models with Unknown Observation Covariances

In this paper, we address the problem of distributed Bayesian estimation in networks of agents over a given undirected graph. The agents observe data represented by a general linear model with unknown covariance matrices. The agents try to reach consensus on the belief on the unknown linear parameters based on their private signals and information provided by their neighbors. The belief is defined by the posterior distribution of the parameters. After deriving the Bayesian belief held by a fictitious fusion center, we present a consensus-based solution where the agents reach the belief of the fusion center. According to our scheme, at every time instant, each agent carries out three operations: a) receives private noisy measurements; b) exchanges information about its belief with its neighbors; and c) updates its belief with the new information. We show that with the proposed method, the Kullback-Leibler divergence between the beliefs of the agents and the fusion center converges to zero. We demonstrate the performance of the method by computer simulations.