Distributed parameter estimation with exponential family statistics: Asymptotic efficiency

This paper studies the problem of distributed parameter estimation in multi-agent networks with exponential family observation statistics. Conforming to a given inter-agent communication topology, a distributed recursive estimator of the consensus-plus-innovations type is presented in which at every observation sampling epoch the network agents exchange a single round of messages with their communication neighbors and recursively update their local parameter estimates by simultaneously processing the received neighborhood data and the new information (innovation) embedded in the observation sample. Under global observability of the networked sensing model and mean connectivity of the inter-agent communication network, the proposed estimator is shown to yield consistent parameter estimates at each network agent. Furthermore, it is shown that the distributed estimator is asymptotically efficient, in that, the asymptotic covariances of the agent estimates coincide with that of the optimal centralized estimator, i.e., the inverse of the centralized Fisher information rate.