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

TL;DR

This paper develops and analyzes distributed algorithms for nonlinear parameter estimation in sensor networks with noisy communication, proving their consistency, efficiency, and asymptotic properties.

Contribution

It introduces the concept of separably estimable models and proposes three novel consensus + innovations algorithms with rigorous convergence analysis.

Findings

Algorithms achieve consensus and converge to true parameters.

Proven asymptotic normality and convergence rates for key algorithms.

Analysis extends stochastic approximation theory to nonlinear, biased, and mixed time-scale settings.

Abstract

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 $\mathcal{NU}$ (with its linear counterpart $\mathcal{LU}$) and the $\mathcal{NLU}$. 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 $\mathcal{LU}$ and $\mathcal{NU}$, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms $\mathcal{LU}$ and $\mathcal{NU}$ are analyzed in the framework of stochastic approximation theory; algorithm $\mathcal{NLU}$ exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in the paper.