{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:27:51Z","timestamp":1772252871493,"version":"3.50.1"},"reference-count":77,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,19]],"date-time":"2018-11-19T00:00:00Z","timestamp":1542585600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/EEA\/00066\/2013, foRESTER PCIF\/SSI\/0102\/2017"],"award-info":[{"award-number":["UID\/EEA\/00066\/2013, foRESTER PCIF\/SSI\/0102\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program Investigador FCT","award":["IF\/00325\/2015"],"award-info":[{"award-number":["IF\/00325\/2015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/s18114027","type":"journal-article","created":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T09:18:25Z","timestamp":1542878305000},"page":"4027","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["On Consensus-Based Distributed Blind Calibration of Sensor Networks"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9064-7059","authenticated-orcid":false,"given":"Milo\u0161 S.","family":"Stankovi\u0107","sequence":"first","affiliation":[{"name":"Innovation Center, School of Electrical Engineering, University of Belgrade, 11120 Belgrade, Serbia"},{"name":"Vlatacom Institute, 11070 Belgrade, Serbia"},{"name":"School of Technical Sciences, Singidunum University, 11000 Belgrade, Serbia"}]},{"given":"Srdjan S.","family":"Stankovi\u0107","sequence":"additional","affiliation":[{"name":"Vlatacom Institute, 11070 Belgrade, Serbia"},{"name":"School of Electrical Engineering, University of Belgrade, 11120 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9940-5929","authenticated-orcid":false,"given":"Karl Henrik","family":"Johansson","sequence":"additional","affiliation":[{"name":"ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7315-8739","authenticated-orcid":false,"given":"Marko","family":"Beko","sequence":"additional","affiliation":[{"name":"COPELABS, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Campo Grande 376, 1749-024 Lisboa, Portugal"},{"name":"CTS\/UNINOVA , Monte de Caparica, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0594-1961","authenticated-orcid":false,"given":"Luis M.","family":"Camarinha-Matos","sequence":"additional","affiliation":[{"name":"CTS\/UNINOVA , Monte de Caparica, 2829-516 Caparica, Portugal"},{"name":"Faculty of Sciences and Technology, NOVA University of Lisbon, 2825-149 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1109\/JPROC.2012.2189792","article-title":"Cyber\u2013physical systems: A perspective at the centennial","volume":"100","author":"Kim","year":"2012","journal-title":"Proc. IEEE"},{"key":"ref_2","unstructured":"Holler, J., Tsiatsis, V., Mulligan, C., Avesand, S., Karnouskos, S., and Boyle, D. (2014). From Machine-to-Machine to the Internet of Things: Introduction to a New Age of Intelligence, Academic Press."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Akyildiz, I.F., and Vuran, M.C. (2010). Wireless Sensor Networks, John Wiley & Sons.","DOI":"10.1002\/9780470515181"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1109\/JPROC.2003.814925","article-title":"Special issue on sensor networks and applications","volume":"91","author":"Gharavi","year":"2003","journal-title":"Proc. IEEE"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/S1389-1286(01)00302-4","article-title":"Wireless sensor networks: A survey","volume":"38","author":"Akyildiz","year":"2002","journal-title":"Comput. Netw."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Speranzon, A., Fischione, C., and Johansson, K.H. (2006, January 13\u201315). Distributed and collaborative estimation over wireless sensor networks. Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, USA.","DOI":"10.1109\/CDC.2006.377101"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1109\/LWC.2016.2567394","article-title":"Distributed RSS-AoA Based Localization with Unknown Transmit Powers","volume":"5","author":"Tomic","year":"2016","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.pmcj.2016.09.013","article-title":"Distributed algorithm for target localization in wireless sensor networks using RSS and AoA measurements","volume":"37","author":"Tomic","year":"2017","journal-title":"Pervasive Mob. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"18410","DOI":"10.3390\/s141018410","article-title":"Distributed RSS-Based Localization in Wireless Sensor Networks Based on Second-Order Cone Programming","volume":"14","author":"Tomic","year":"2014","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Whitehouse, K., and Culler, D. (2002, January 28). Calibration as parameter estimation in sensor networks. Proceedings of the 1st ACM International Workshop on Wireless sensor networks and applications, Atlanta, GA, USA.","DOI":"10.1145\/570738.570747"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1023\/A:1024548100497","article-title":"Macro-calibration in sensor\/actuator networks","volume":"8","author":"Whitehouse","year":"2003","journal-title":"Mob. Netw. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Balzano, L., and Nowak, R. (2007, January 25\u201327). Blind calibration of sensor networks. Proceedings of the 6th International Conference on Information Processing in Sensor Networks, Cambridge, MA, USA.","DOI":"10.1109\/IPSN.2007.4379667"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3257","DOI":"10.1109\/TAC.2015.2426272","article-title":"Distributed Blind Calibration in Lossy Sensor Networks via Output Synchronization","volume":"60","author":"Johansson","year":"2015","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1109\/TCNS.2016.2633788","article-title":"Asynchronous Distributed Blind Calibration of Sensor Networks under Noisy Measurements","volume":"5","author":"Johansson","year":"2018","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, M.S., Stankovi\u0107, S.S., and Johansson, K.H. (2012, January 3\u20136). Distributed Macro Calibration in Sensor Networks. Proceedings of the 20th Mediterranean Conference on Control & Automation (MED), Barcelona, Spain.","DOI":"10.1109\/MED.2012.6265777"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, M.S., Stankovi\u0107, S.S., and Johansson, K.H. (2012, January 10\u201313). Distributed Calibration for Sensor Networks under Communication Errors and Measurement Noise. Proceedings of the IEEE 51st IEEE Conference on Decision and Control (CDC), Maui, HI, USA.","DOI":"10.1109\/CDC.2012.6426180"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"111","DOI":"10.2298\/SJEE1601111S","article-title":"A consensus-based distributed calibration algorithm for sensor networks","volume":"13","author":"Johansson","year":"2016","journal-title":"Serb. J. Electr. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1109\/JPROC.2006.887293","article-title":"Consensus and cooperation in networked multi-agent systems","volume":"95","author":"Fax","year":"2007","journal-title":"Proc. IEEE"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/0022-247X(85)90250-1","article-title":"Overlapping block diagonal dominance and existence of Lyapunov functions","volume":"112","author":"Ohta","year":"1985","journal-title":"J. Math. Anal. Appl."},{"key":"ref_20","unstructured":"\u0160iljak, D.D. (1991). Decentralized Control of Complex Systems, Academic Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0022-0531(74)90064-7","article-title":"Matrices with dominating diagonal blocks","volume":"9","author":"Pierce","year":"1974","journal-title":"J. Econ. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Levin, A., Weiss, Y., Durand, F., and Freeman, W. (2009, January 20\u201325). Understanding and evaluating blind deconvolution algorithms. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, USA.","DOI":"10.1109\/CVPRW.2009.5206815"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1109\/TSP.2014.2376884","article-title":"On Recursive Blind Equalization in Sensor Networks","volume":"63","author":"Yu","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Nandi, A. (1999). Blind Estimation Using Higher-Order Statistics, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4757-2985-6"},{"key":"ref_25","unstructured":"Balzano, L., and Nowak, R. (2007). Blind Calibration, Networked and Embedded Systems Laboratory, UCLA. Technical Report TR-UCLA-NESL-200702-01."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lipor, J., and Balzano, L. (2014, January 4\u20139). Robust blind calibration via total least squares. Proceedings of the 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Florence, Italy.","DOI":"10.1109\/ICASSP.2014.6854402"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4847","DOI":"10.1109\/TSP.2014.2342651","article-title":"Convex Optimization Approaches for Blind Sensor Calibration Using Sparsity","volume":"62","author":"Bilen","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Bychkovskiy, V., Megerian, S., Estrin, D., and Potkonjak, M. (2003, January 22\u201323). A Collaborative Approach to In-Place Sensor Calibration. Proceedings of the International Conference on Information Processing in Sensor Networks, Palo Alto, CA, USA.","DOI":"10.1007\/3-540-36978-3_20"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wang, C., Ramanathan, P., and Saluja, K.K. (2008, January 19\u201323). Moments Based Blind Calibration in Mobile Sensor Networks. Proceedings of the 2008 IEEE International Conference on Communications, Beijing, China.","DOI":"10.1109\/ICC.2008.176"},{"key":"ref_30","unstructured":"Takruri, M., Challa, S., and Yunis, R. (2009, January 6\u20139). Data Fusion Techniques for Auto Calibration in Wireless Sensor Networks. Proceedings of the International Conference on Information Fusion, Seattle, WA, USA."},{"key":"ref_31","unstructured":"Wang, Y., Yang, A., Li, Z., Wang, P., and Yang, H. (2015, January 7\u20139). Blind drift calibration of sensor networks using signal space projection and Kalman filter. Proceedings of the 2015 IEEE Tenth International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Singapore."},{"key":"ref_32","first-page":"6249","article-title":"Blind Drift Calibration of Sensor Networks Using Sparse Bayesian Learning","volume":"16","author":"Wang","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4158","DOI":"10.1109\/JSEN.2017.2703885","article-title":"A Deep Learning Approach for Blind Drift Calibration of Sensor Networks","volume":"17","author":"Wang","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Yang, J., Tay, W.P., and Zhong, X. (2017, January 5\u20139). A dynamic Bayesian nonparametric model for blind calibration of sensor networks. Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA.","DOI":"10.1109\/ICASSP.2017.7952949"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.1109\/JSEN.2013.2297714","article-title":"A Blind Calibration Scheme Exploiting Mutual Calibration Relationships for a Dense Mobile Sensor Network","volume":"14","author":"Lee","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Vincent, E., Yeredor, A., Koldovsk\u00fd, Z., and Tichavsk\u00fd, P. (2015). Blind Calibration of Mobile Sensors Using Informed Nonnegative Matrix Factorization. Latent Variable Analysis and Signal Separation, Springer International Publishing.","DOI":"10.1007\/978-3-319-22482-4"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Dorffer, C., Puigt, M., Delmaire, G., and Roussel, G. (2016, January 20\u201325). Blind mobile sensor calibration using an informed nonnegative matrix factorization with a relaxed rendezvous model. Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7472216"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Schulke, C., Caltagirone, F., and Zdeborova, L. (2015). Blind sensor calibration using approximate message passing. J. Stat. Mech. Theory Exp., 2015.","DOI":"10.1088\/1742-5468\/2015\/11\/P11013"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1145\/2736697","article-title":"Geospatial Estimation-Based Auto Drift Correction in Wireless Sensor Networks","volume":"11","author":"Kumar","year":"2015","journal-title":"ACM Trans. Sens. Netw."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, M.S., Stankovi\u0107, S.S., and Johansson, K.H. (2016, January 21\u201324). Distributed drift estimation for time synchronization in lossy networks. Proceedings of the 24th Mediterranean Conference on Control and Automation (MED), Athens, Greece.","DOI":"10.1109\/MED.2016.7535942"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.automatica.2018.03.054","article-title":"Distributed time synchronization for networks with random delays and measurement noise","volume":"93","author":"Johansson","year":"2018","journal-title":"Automatica"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Giridhar, D., and Kumar, P.R. (2006, January 13\u201315). Distributed clock synchronization over wireless networks: Algorithms and analysis. Proceedings of the IEEE Conference on Decision and Control, San Diego, CA, USA.","DOI":"10.1109\/CDC.2006.377325"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Sommer, P., and Wattenhofer, R. (2009, January 13\u201316). Gradient clock synchronization in wireless sensor networks. Proceedings of the 2009 International Conference on Information Processing in Sensor Networks, San Francisco, CA, USA.","DOI":"10.1145\/1435473.1435477"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1016\/j.automatica.2011.06.012","article-title":"Average TimeSynch: A consensus-based protocol for time synchronization in wireless sensor networks","volume":"47","author":"Schenato","year":"2011","journal-title":"Automatica"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1146","DOI":"10.1109\/TAC.2011.2107051","article-title":"Optimal Synchronization for Networks of Noisy Double Integrators","volume":"56","author":"Carli","year":"2008","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3015","DOI":"10.1016\/j.automatica.2013.07.015","article-title":"Distributed clock skew and offset estimation from relative measurements in mobile networks with Markovian switching topologies","volume":"49","author":"Liao","year":"2013","journal-title":"Automatica"},{"key":"ref_47","unstructured":"Stankovi\u0107, M.S., Stankovi\u0107, S.S., and Johansson, K.H. (2012, January 13\u201314). Distributed time synchronization in lossy wireless sensor networks. Proceedings of the 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems, Santa Barbara, CA, USA."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/TCNS.2014.2367571","article-title":"Ergodic randomized algorithms and dynamics over networks","volume":"2","author":"Ravazzi","year":"2015","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1109\/TCNS.2014.2353512","article-title":"An asynchrnous consensus-based algorithm for estimation from noisy relative measurements","volume":"1","author":"Carron","year":"2014","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1002\/rnc.1452","article-title":"Consensus-based distributed sensor calibration and least-square parameter identification in WSNs","volume":"20","author":"Bolognani","year":"2010","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_51","unstructured":"Miluzzo, E., Lane, N.D., Campbell, A.T., and Olfati-Saber, R. (2008, January 11\u201314). CaliBree: A Self-calibration System for Mobile Sensor Networks. Proceedings of the 4th IEEE International Conference on Distributed Computing in Sensor Systems, Santorini Island, Greece."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/JSTSP.2011.2119291","article-title":"Gossip-Based Algorithm for Joint Signature Estimation and Node Calibration in Sensor Networks","volume":"5","author":"Ramakrishnan","year":"2011","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Buadhachain, S.O., and Provan, G. (2013, January 17\u201319). A model-based control method for decentralized calibration of wireless sensor networks. Proceedings of the 2013 American Control Conference, Washington, DC, USA.","DOI":"10.1109\/ACC.2013.6580870"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1109\/TAC.2005.846556","article-title":"Consensus seeking in multi-agent systems under dynamically changing interaction topologies","volume":"50","author":"Ren","year":"2005","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Ljung, L., and S\u00f6derstr\u00f6m, T. (1983). Theory and Pracice of Recursive Identification, MIT Press.","DOI":"10.1007\/978-1-4612-5612-0_14"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Xiong, Z., Niyato, D., and Han, Z. (2015, January 14\u201316). Distortion minimization via adaptive digital and analog transmission for energy harvesting-based wireless sensor networks. Proceedings of the IEEE Global Conference on Signal and Information Processing (GlobalSIP), Orlando, FL, USA.","DOI":"10.1109\/GlobalSIP.2015.7418249"},{"key":"ref_57","unstructured":"Chen, H.F. (2002). Stochastic Approximation and Its Applications, Kluwer Academic."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2043","DOI":"10.1109\/TAC.2010.2042982","article-title":"Consensus conditions of multi agent systems with time varying topologies","volume":"55","author":"Li","year":"2010","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/TAC.2009.2036291","article-title":"Stochastic consensus seeking with noisy and directed inter-agent communications: Fixed and randomly varying topologies","volume":"55","author":"Huang","year":"2010","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_60","unstructured":"Ljung, L. (1989). System Identification\u2014Theory for the User, Prentice Hall International."},{"key":"ref_61","unstructured":"S\u00f6derstr\u00f6m, T., and Stoica, P. (1989). System Identification, Prentice Hall International."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2748","DOI":"10.1109\/TSP.2009.2016247","article-title":"Broadcast gossip algorithms for consensus","volume":"57","author":"Aysal","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1109\/TAC.2010.2079650","article-title":"Asynchronous broadcast-based convex optimization over a network","volume":"56","year":"2011","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1214\/154957805100000104","article-title":"Basic Properties of Strong Mixing Conditions a Survey and Some Open Questions","volume":"2","author":"Bradley","year":"2005","journal-title":"Probab. Surv."},{"key":"ref_65","first-page":"711","article-title":"Some limit theorems for stochastic processes stationary in the strict sense","volume":"125","author":"Ibragimov","year":"1959","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1073\/pnas.42.1.43","article-title":"A central limit theorem and a strong mixing condition","volume":"42","author":"Rosenblatt","year":"1956","journal-title":"Proc. Natl. acad. Sci. USA"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Godsil, C., and Royle, G. (2001). Algebraic Graph Theory, Springer.","DOI":"10.1007\/978-1-4613-0163-9"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1137\/S0363012997331639","article-title":"The ODE method for convergence of stochastic approximation and reinforcement learning","volume":"38","author":"Borkar","year":"2000","journal-title":"SIAM J. Control Optim."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, M.S., Stankovi\u0107, S.S., and Johansson, K.H. (2018, January 12\u201315). Distributed Offset Correction for Time Synchronization in Networks with Random Delays. Proceedings of the European Control Conference, Limassol, Cyprus.","DOI":"10.1016\/j.automatica.2018.03.054"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.automatica.2015.11.034","article-title":"Structural modeling and convergence analysis of consensus-based time synchronization algorithms over networks: Non-topological conditions","volume":"65","author":"Tian","year":"2016","journal-title":"Automatica"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"2963","DOI":"10.1109\/TVT.2010.2049869","article-title":"Feedback-Based Clock Synchronization in Wireless Sensor Networks: A Control Theoretic Approach","volume":"59","author":"Chen","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"2287","DOI":"10.1049\/iet-cta.2018.5417","article-title":"Distributed Asynchronous Consensus-based Algorithm for Blind Calibration of Sensor Networks with Autonomous Gain Correction","volume":"12","year":"2018","journal-title":"IET Control Theory Appl."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1109\/TAC.2008.2009583","article-title":"Consensus based overlapping decentralized estimator","volume":"54","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1397","DOI":"10.1016\/j.automatica.2009.02.014","article-title":"Consensus Based Overlapping Decentralized Estimation with Missing Observations and Communication Faults","volume":"45","year":"2009","journal-title":"Automatica"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.automatica.2015.07.018","article-title":"Consensus-based decentralized real-time identification of large-scale systems","volume":"60","year":"2015","journal-title":"Automatica"},{"key":"ref_76","first-page":"816","article-title":"Model abstraction and inclusion principle: A comparison","volume":"8","year":"2001","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Seyboth, G., Schmidt, G., and Allg\u00f6wer, F. (2012, January 10\u201313). Output synchronization of linear parameter-varying systems via dynamic couplings. Proceedings of the IEEE 51st IEEE Conference on Decision and Control (CDC), Maui, HI, USA.","DOI":"10.1109\/CDC.2012.6426752"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/11\/4027\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:30:35Z","timestamp":1760196635000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/11\/4027"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,19]]},"references-count":77,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["s18114027"],"URL":"https:\/\/doi.org\/10.3390\/s18114027","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201809.0488.v1","asserted-by":"object"}]},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,19]]}}}