Preprint Review Version 1 This version is not peer-reviewed

On Consensus-based Distributed Blind Calibration of Sensor Networks

Version 1 : Received: 25 September 2018 / Approved: 25 September 2018 / Online: 25 September 2018 (14:30:23 CEST)

A peer-reviewed article of this Preprint also exists.

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. 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.

Journal reference: Sensors 2018, 18, 4027
DOI: 10.3390/s18114027

Abstract

This review paper deals with recently proposed algorithms for distributed blind macro-calibration of sensor networks based on consensus (synchronization), not requiring any fusion center. The basic algorithm, performing the estimation of the local calibration parameters, is derived commencing from appropriate local criteria, and developing the corresponding gradient descent scheme. It is shown that the estimated parameters of the calibration functions asymptotically converge, in the mean-square sense and with probability one (w.p.1), to such values that ensure consensus 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 introduced: one using a simple compensation term, and a more robust one based on an instrumental variable. By utilizing stochastic approximation arguments it is shown that the modified algorithms also achieve asymptotic agreement for calibrated sensor gains and offsets, in the mean-square sense and w.p.1. Convergence rate is analyzed in terms of an upper bound of the mean-square error. It is also shown that the communications between nodes can be completely asynchronous, which is of substantial importance for real-world applications. Suggestions for design of \textit{a priori} adjustable weights are given. Finally, it is shown that, if there is a subset of (precalibrated) reference sensors with fixed calibration parameters, the calibrated sensor gains and offsets of the rest of the sensors do not achieve consensus - they converge to different points dictated by the reference sensors and the network characteristics. Wide applicability and efficacy of these algorithms are illustrated on several simulation examples.

Subject Areas

Blind Calibration, Macro Calibration, Distributed Estimation, Sensor Networks, Consensus, Synchronization, Stochastic Approximation

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