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arXiv · 1303.2830

Almost sure convergence of a randomized algorithm for relative localization in sensor networks

Chiara Ravazzi·Paolo Frasca·Roberto Tempo·Hideaki Ishii
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Abstract

This paper regards the relative localization problem in sensor networks. We study a randomized algorithm, which is based on input-driven consensus dynamics and involves pairwise "gossip" communications and updates. Due to the randomness of the updates, the state of this algorithm ergodically oscillates around a limit value. Exploiting the ergodicity of the dynamics, we show that the time-average of the state almost surely converges to the least-squares solution of the localization problem. Remarkably, the computation of the time-average does not require the sensors to share any common clock. Hence, the proposed algorithm is fully distributed and asynchronous.

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Chiara Ravazzi, Paolo Frasca, Roberto Tempo, Hideaki Ishii. 2013-03-12. Almost sure convergence of a randomized algorithm for relative localization in sensor networks. https://arxiv.org/abs/1303.2830

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