$\mathcal{CIRFE}$: A Distributed Random Fields Estimator

TL;DR

This paper introduces $ ext{CIRFE}$, a communication-efficient distributed algorithm for high-dimensional parameter estimation in multi-agent networks, where each agent estimates only relevant components, ensuring convergence and optimal performance.

Contribution

The paper proposes $ ext{CIRFE}$, a novel distributed estimation algorithm that handles high-dimensional parameters with sparse agent interest, providing convergence guarantees and performance analysis.

Findings

Almost sure convergence of estimates to true parameters.

Asymptotic covariance depends on the number of agents estimating each component.

Simulation results confirm the algorithm's effectiveness.

Abstract

This paper presents a communication efficient distributed algorithm, $\mathcal{CIRFE}$ of the \emph{consensus}+\emph{innovations} type, to estimate a high-dimensional parameter in a multi-agent network, in which each agent is interested in reconstructing only a few components of the parameter. This problem arises for example when monitoring the high-dimensional distributed state of a large-scale infrastructure with a network of limited capability sensors and where each sensor is tasked with estimating some local components of the state. At each observation sampling epoch, each agent updates its local estimate of the parameter components in its interest set by simultaneously processing the latest locally sensed information~(\emph{innovations}) and the parameter estimates from agents~(\emph{consensus}) in its communication neighborhood given by a time-varying possibly sparse graph. Under minimal conditions on the inter-agent communication network and the sensing models, almost sure convergence of the estimate sequence at each agent to the components of the true parameter in its interest set is established. Furthermore, the paper establishes the performance of $\mathcal{CIRFE}$ in terms of asymptotic covariance of the estimate sequences and specifically characterizes the dependencies of the component wise asymptotic covariance in terms of the number of agents tasked with estimating it. Finally, simulation experiments demonstrate the efficacy of $\mathcal{CIRFE}$.