Distributed Constrained Recursive Nonlinear Least-Squares Estimation: Algorithms and Asymptotics

This paper focuses on recursive nonlinear least-squares parameter estimation in multiagent networks, where the individual agents observe sequentially over time an independent and identically distributed time-series consisting of a nonlinear function of the true but unknown parameter corrupted by noise. A distributed recursive estimator of the consensus+ innovations type, namely CIWNLS, is proposed, in which the agents update their parameter estimates at each observation sampling epoch in a collaborative way by simultaneously processing the latest locally sensed information (innovations) and the parameter estimates from other agents (consensus) in the local neighborhood conforming to a prespecified interagent communication topology. Under rather weak conditions on the connectivity of the interagent communication and a global observability criterion, it is shown that, at every network agent, CIWNLS leads to consistent parameter estimates. Furthermore, under standard smoothness assumptions on the local observation functions, the distributed estimator is shown to yield order-optimal convergence rates, i.e., as far as the order of pathwise convergence is concerned, the local parameter estimates at each agent are as good as the optimal centralized nonlinear least-squares estimator that requires access to all the observations across all the agents at all times. To benchmark the performance of the CIWNLS estimator with that of the centralized nonlinear least-squares estimator, the asymptotic normality of the estimate sequence is established, and the asymptotic covariance of the distributed estimator is evaluated. Finally, simulation results are presented that illustrate and verify the analytical findings.