On a consistent procedure for distributed recursive nonlinear least-squares estimation

This paper studies recursive nonlinear least squares parameter estimation in inference networks with observations distributed across multiple agents and sensed sequentially over time. Conforming to a given inter-agent communication or interaction topology, distributed recursive estimators of the consensus + innovations type are 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 rather weak conditions on the connectivity of the inter-agent communication and a global observability criterion, it is shown that the proposed algorithms lead to consistent parameter estimates at each agent. Furthermore, under standard smoothness assumptions on the sensing nonlinearities, the distributed estimators are shown to yield order-optimal convergence rates, i.e., as far as the order of pathwise convergence is concerned, the local agent estimates are as good as the optimal centralized nonlinear least squares estimator having access to the entire network observation data at all times.