Analysis of Distributed Consensus Time Synchronization with Gaussian Delay over Wireless Sensor Networks

This paper presents theoretical results on the convergence of the distributed consensus timing synchronization (DCTS) algorithm for wireless sensor networks assuming general Gaussian delay between nodes. The asymptotic expectation and mean square of the global synchronization error are computed. The results lead to the definition of a time delay balanced network in which average timing consensus between nodes can be achieved despite random delays. Several structured network architectures are studied as examples, and their associated simulation results are used to validate analytical findings.

[1]  K. Dessouky,et al.  Network synchronization , 1985, Proceedings of the IEEE.

[2]  D. C. Dodder.  R-Matrix Analysis , 1976 .

[3]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[4]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[6]  Deborah Estrin,et al.  Proceedings of the 5th Symposium on Operating Systems Design and Implementation Fine-grained Network Time Synchronization Using Reference Broadcasts , 2022 .

[7]  J. Lasserre.  A trace inequality for matrix product , 1995, IEEE Trans. Autom. Control..

[8]  Mani Srivastava,et al.  Overview of sensor networks , 2004 .

[9]  Stephen P. Boyd,et al.  Distributed average consensus with least-mean-square deviation , 2007, J. Parallel Distributed Comput..

[10]  Umberto Spagnolini,et al.  Distributed Time Synchronization in Wireless Sensor Networks with Coupled Discrete-Time Oscillators , 2007, EURASIP J. Wirel. Commun. Netw..

[11]  Mark G. Terwilliger,et al.  Overview of Sensor Networks , 2004 .

[12]  B. Mohar.  Some applications of Laplace eigenvalues of graphs , 1997 .

[13]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[14]  Roberto Pagliari,et al.  Non-cooperative versus Cooperative Approaches for Distributed Network Synchronization , 2007, Fifth Annual IEEE International Conference on Pervasive Computing and Communications Workshops (PerComW'07).

[15]  Luca Schenato,et al.  A distributed consensus protocol for clock synchronization in wireless sensor network , 2007, 2007 46th IEEE Conference on Decision and Control.

[16]  Hisham Abdel-Ghaffar,et al.  Analysis of synchronization algorithms with time-out control over networks with exponentially symmetric delays , 2002, IEEE Trans. Commun..

[17]  Deborah Estrin,et al.  Guest Editors' Introduction: Overview of Sensor Networks , 2004, Computer.

[18]  Qingling Zhang,et al.  A trace bound for a general square matrix product , 2000, IEEE Trans. Autom. Control..

[19]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.