Distributed Parameter Estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication

The paper studies the problem of distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and imperfect inter-sensor communication. We introduce the concept of \emph{separably estimable} observation models, which generalize the observability condition for linear centralized estimation to nonlinear distributed estimation. We study the algorithms $\mathcal{NU}$ (with its linear counterpart $\mathcal{LU}$) and $\mathcal{NLU}$ for distributed estimation in separably estimable models. We prove consistency (all sensors reach consensus almost sure and converge to the true parameter value), asymptotic unbiasedness and asymptotic normality of these algorithms. Both the algorithms are characterized by appropriately chosen decaying weight sequences in the estimate update rule. While the algorithm $\mathcal{NU}$ is analyzed in the framework of stochastic approximation theory, the algorithm $\mathcal{NLU}$ exhibits mixed time-scale behavior and biased perturbations and require a different approach, which we develop in the paper.