Distributed consensus-based Bayesian estimation: sufficient conditions for performance characterization

The paper considers the framework of distributed Bayesian linear estimation. We introduce some consensus-based estimation strategies that are equivalent to centralized ones pending knowledge of some parameters, e.g. number of agents in the network. If such parameters are not known, agents can estimate them locally or exploit prior knowledge. We show that in this case the performance depends on parameter uncertainty in such a way that, in case of large errors, the distributed estimator can perform worse than the local one. Then, we find some sufficient conditions on the error magnitude which ensure that the distributed scheme behaves better than the local one.