On consensus-based distributed blind calibration of sensor networks

This work was partially supported by Fundacao para a Ciencia e a Tecnologia under Grant CEECIND/02902/2017, Project UID/EEA/00066/2013, Project foRESTER PCIF/SSI/0102/2017, and Program Investigador FCT under Grant IF/00325/2015. The work by K. H. Johansson was supported in part by the Knut and Alice Wallenberg Foundation, the Swedish Research Council, and the Swedish Foundation for Strategic Research.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.publishersversionpublishe