On Consensus-Based Distributed Blind Calibration of Sensor Networks.

Miloš Stanković,Karl Johansson,Srdjan Stanković,Marko Beko,Luis Camarinha-Matos

doi:10.3390/s18114027

Abstract

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.

Highlights

Emerged technologies dealing with networked systems, such as the Internet of Things (IoT), Networked Cyber-Physical Systems (CPS), and Sensor Networks (SN), still have many conceptual and practical challenges intriguing to both researchers and practitioners [1,2,3,4,5,6,7,8,9]
We present the results of extensive simulations, illustrating that the algorithms are applicable to real-world problems involving sensor networks with decentralized architectures
It is clear from the figure that the convergence to consensus, and, implicit asymptotic calibration is achieved with the asymptotic values close the desired

Summary

Introduction

Emerged technologies dealing with networked systems, such as the Internet of Things (IoT), Networked Cyber-Physical Systems (CPS), and Sensor Networks (SN), still have many conceptual and practical challenges intriguing to both researchers and practitioners [1,2,3,4,5,6,7,8,9]. Of significant interest are methods for automatic calibration of SNs which successfully perform even if there are no reference signals/sensors, or other sources of groundthruth information about the measured process. In these situations, the goal of the calibration is to achieve homogeneous behavior of all the nodes, possibly enforcing dominant influence of sensors that are a priori known to provide sufficently good (calibrated) measurements. In many applications of SNs, it is of essential importance that the network functions in a completely decentralized fashion, preforming calibration in real-time, without the requirement for any kind of centralized information fusion. Completely distributed and decentralized real-time calibration algorithms are of paramount importance

Results

Discussion

Conclusion