This paper focuses on the problem of recursive nonlinear least squaresparameter estimation in multi-agent networks, in which the individual agentsobserve sequentially over time an independent and identically distributed(i.i.d.) time-series consisting of a nonlinear function of the true but unknownparameter corrupted by noise. A distributed recursive estimator of the\emph{consensus} + \emph{innovations} type, namely $\mathcal{CIWNLS}$, isproposed, in which the agents update their parameter estimates at eachobservation sampling epoch in a collaborative way by simultaneously processingthe latest locally sensed information~(\emph{innovations}) and the parameterestimates from other agents~(\emph{consensus}) in the local neighborhoodconforming to a pre-specified inter-agent communication topology. Under ratherweak conditions on the connectivity of the inter-agent communication and a\emph{global observability} criterion, it is shown that at every network agent,the proposed algorithm leads to consistent parameter estimates. Furthermore,under standard smoothness assumptions on the local observation functions, thedistributed estimator is shown to yield order-optimal convergence rates, i.e.,as far as the order of pathwise convergence is concerned, the local parameterestimates at each agent are as good as the optimal centralized nonlinear leastsquares estimator which would require access to all the observations across allthe agents at all times. In order to benchmark the performance of the proposeddistributed $\mathcal{CIWNLS}$ estimator with that of the centralized nonlinearleast squares estimator, the asymptotic normality of the estimate sequence isestablished and the asymptotic covariance of the distributed estimator isevaluated. Finally, simulation results are presented which illustrate andverify the analytical findings.
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