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 mathcal {CREDO-NL} (non-linear mathcal {CREDO}). mathcal {CREDO-NL} generalizes the recently proposed linear method 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 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 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.
Highlights
We consider distributed non-linear least squares estimation in networked systems
We propose and analyze a communication efficient distributed estimator for non-linear observation models that we refer to as CREDO − N L
We propose the non-linear distributed estimator CREDO − N L that works for a broad class of non-linear observation models and where the model information in terms of the node i’s sensing function and noise statistic is only available at the individual agent i itself
Summary
We consider distributed non-linear least squares estimation in networked systems. The networked system considered consists of heterogeneous networked entities or agents where the inter-agent collaboration conforms to a pre-assigned possibly sparse communication graph. The agents acquire their local, noisy, non-linear observations about the unknown phenomenon (unknown static vector parameter θ) in a streaming fashion over discrete time instances t. The goal for each agent is to continuously generate an estimate of θ over time instances t in a recursive fashion, where the estimate update of an agent involves simultaneous assimilation of the newly acquired local observations, and the received information through messages with agents in its immediate neighborhood. Real-world applications such as large-scale deployment of CPS or IoT typically involve entities or agents with limited on board energy resources. In addition to the limited on board power, the energy requirement per unit communication is usually significantly higher than the energy
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