The paper studies distributed static parameter (vector) estimation in sensor
networks with nonlinear observation models and noisy inter-sensor
communication. It introduces \emph{separably estimable} observation models that
generalize the observability condition in linear centralized estimation to
nonlinear distributed estimation. It studies two distributed estimation
algorithms in separably estimable models, the NU (with its linear
counterpart LU) and the NLU. Their update rule combines
a \emph{consensus} step (where each sensor updates the state by weight
averaging it with its neighbors' states) and an \emph{innovation} step (where
each sensor processes its local current observation.) This makes the three
algorithms of the \textit{consensus + innovations} type, very different from
traditional consensus. The paper proves consistency (all sensors reach
consensus almost surely and converge to the true parameter value,) efficiency,
and asymptotic unbiasedness. For LU and NU, it proves
asymptotic normality and provides convergence rate guarantees. The three
algorithms are characterized by appropriately chosen decaying weight sequences.
Algorithms LU and NU are analyzed in the framework of
stochastic approximation theory; algorithm NLU exhibits mixed
time-scale behavior and biased perturbations, and its analysis requires a
different approach that is developed in the paper.Comment: IEEE Transactions On Information Theory, Vol. 58, No. 6, June 201