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On Consensus-Based Distributed Blind Calibration of Sensor Networks

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Innovation Center, School of Electrical Engineering, University of Belgrade, 11120 Belgrade, Serbia
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Vlatacom Institute, 11070 Belgrade, Serbia
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School of Technical Sciences, Singidunum University, 11000 Belgrade, Serbia
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School of Electrical Engineering, University of Belgrade, 11120 Belgrade, Serbia
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ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
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COPELABS, Universidade Lusófona de Humanidades e Tecnologias, Campo Grande 376, 1749-024 Lisboa, Portugal
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CTS/UNINOVA , Monte de Caparica, 2829-516 Caparica, Portugal
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Faculty of Sciences and Technology, NOVA University of Lisbon, 2825-149 Caparica, Portugal
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Author to whom correspondence should be addressed.
Sensors 2018, 18(11), 4027; https://doi.org/10.3390/s18114027
Received: 25 September 2018 / Revised: 29 October 2018 / Accepted: 5 November 2018 / Published: 19 November 2018
(This article belongs to the Special Issue Signal and Information Processing in Wireless Sensor Networks)
This paper deals with recently proposed algorithms for real-time distributed blind macro-calibration of sensor networks based on consensus (synchronization). The algorithms are completely decentralized and do not require a fusion center. The goal is to consolidate all of the existing results on the subject, present them in a unified way, and provide additional important analysis of theoretical and practical issues that one can encounter when designing and applying the methodology. We first present the basic algorithm which estimates local calibration parameters by enforcing asymptotic consensus, in the mean-square sense and with probability one (w.p.1), on calibrated sensor gains and calibrated sensor offsets. For the more realistic case in which additive measurement noise, communication dropouts and additive communication noise are present, two algorithm modifications are discussed: one that uses a simple compensation term, and a more robust one based on an instrumental variable. The modified algorithms also achieve asymptotic agreement for calibrated sensor gains and offsets, in the mean-square sense and w.p.1. The convergence rate can be determined in terms of an upper bound on the mean-square error. The case when the communications between nodes is completely asynchronous, which is of substantial importance for real-world applications, is also presented. Suggestions for design of a priori adjustable weights are given. We also present the results for the case in which the underlying sensor network has a subset of (precalibrated) reference sensors with fixed calibration parameters. Wide applicability and efficacy of these algorithms are illustrated on several simulation examples. Finally, important open questions and future research directions are discussed. View Full-Text
Keywords: blind calibration; macro calibration; distributed estimation; sensor networks; consensus; synchronization; stochastic approximation blind calibration; macro calibration; distributed estimation; sensor networks; consensus; synchronization; stochastic approximation
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MDPI and ACS Style

Stanković, M.S.; Stanković, S.S.; Johansson, K.H.; Beko, M.; Camarinha-Matos, L.M. On Consensus-Based Distributed Blind Calibration of Sensor Networks. Sensors 2018, 18, 4027. https://doi.org/10.3390/s18114027

AMA Style

Stanković MS, Stanković SS, Johansson KH, Beko M, Camarinha-Matos LM. On Consensus-Based Distributed Blind Calibration of Sensor Networks. Sensors. 2018; 18(11):4027. https://doi.org/10.3390/s18114027

Chicago/Turabian Style

Stanković, Miloš S., Srdjan S. Stanković, Karl H. Johansson, Marko Beko, and Luis M. Camarinha-Matos 2018. "On Consensus-Based Distributed Blind Calibration of Sensor Networks" Sensors 18, no. 11: 4027. https://doi.org/10.3390/s18114027

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