Communication efficient distributed weighted non-linear least squares estimation

Abstract

Abstract The paper addresses design and analysis of communication-efficient distributed algorithms for solving weighted non-linear least squares problems in multi-agent networks. Communication efficiency is highly relevant in modern applications like cyber-physical systems and the Internet of things, where a significant portion of the involved devices have energy constraints in terms of limited battery power. Furthermore, non-linear models arise frequently in such systems, e.g., with power grid state estimation. In this paper, we develop and analyze a non-linear communication-efficient distributed algorithm dubbed CREDO−Nℒ $\mathcal {CREDO-NL}$ (non-linear CREDO $\mathcal {CREDO}$). CREDO−Nℒ $\mathcal {CREDO-NL}$ generalizes the recently proposed linear method CREDO $\mathcal {CREDO}$ (Communication efficient REcursive Distributed estimatOr) to non-linear models. We establish for a broad class of non-linear least squares problems and generic underlying multi-agent network topologies CREDO−Nℒ $\mathcal {CREDO-NL}$’s strong consistency. Furthermore, we demonstrate communication efficiency of the method, both theoretically and by simulation examples. For the former, we rigorously prove that CREDO−Nℒ $\mathcal {CREDO-NL}$ achieves significantly faster mean squared error rates in terms of the elapsed communication cost over existing alternatives. For the latter, the considered simulation experiments show communication savings by at least an order of magnitude.

Keywords

• Distributed estimation
• Stochastic approximation
• Statistical inference
• Non-linear least squares