Tackling heavy-tailed noise in distributed estimation: Asymptotic performance and tradeoffs
This work addresses robust parameter estimation in distributed systems like IoT, but it appears incremental as it builds on existing consensus+innovation methods with added nonlinearities.
The paper tackles the problem of distributed estimation under heavy-tailed observation and communication noises, common in IoT and sensor networks, by proposing a consensus+innovation algorithm with nonlinearities to mitigate noise effects, achieving almost sure convergence and asymptotic normality.
We present an algorithm for distributed estimation of an unknown vector parameter $\boldsymbolθ^\ast \in {\mathbb R}^M$ in the presence of heavy-tailed observation and communication noises. Heavy-tailed noises frequently appear, e.g., in densely deployed Internet of Things (IoT) or wireless sensor network systems. The presented algorithm falls within the class of \emph{consensus+innovation} estimators and combats the effect of the heavy-tailed noises by adding general nonlinearities in the consensus and innovations update parts. We present results on almost sure convergence and asymptotic normality of the estimator. In addition, we provide novel analytical studies that reveal interesting tradeoffs between the system noises and the underlying network topology.