  This work presents a distributed estimation algorithm that efficiently uses
the available communication resources. The approach is based on Bayesian
filtering that is distributed across a network by using the logarithmic opinion
pool operator. Communication efficiency is achieved by having only agents with
high Value of Information (VoI) share their estimates, and the algorithm
provides a tunable trade-off between communication resources and estimation
error. Under linear-Gaussian models the algorithm takes the form of a censored
distributed Information filter, which guarantees the consistency of agent
estimates. Importantly, consistent estimates are shown to play a crucial role
in enabling the large reductions in communication usage provided by the VoI
censoring approach. We verify the performance of the proposed method via
complex simulations in a dynamic network topology and by experimental
validation over a real ad-hoc wireless communication network. The results show
the validity of using the proposed method to drastically reduce the
communication costs of distributed estimation tasks.
