Abstract
Wireless sensor networks are networks of devices which collaborate to perform distributed sensing, processing, and possibly even actuation tasks. In this chapter we consider the problem of the synchronizing clocks in wireless sensor networks. We analyze an approach to clock synchronization, called spatial smoothing, that generally synchronizes clocks in a network more accurately than alternative tree-based methods. This approach leads to a distributed least-squares vector estimation problem whose goal is to smooth out the noisy estimates of clock differences of pairs of nodes that can directly exchange packets. We point out connections between the error variance of such a least squares-based clock synchronization and resistance in electrical networks. We determine the limiting clock synchronization accuracy for several types of networks of interest and quantify the improvement over the tree-based method. For random connected wireless sensor networks we show that the clock synchronization error can remain bounded even as the number of nodes in the network increases. This lends support for the feasibility of time-based computation in large networks. We further analyze the convergence time of a distributed iterative algorithm to compute the optimally spatial smoothed estimates. We also propose ways of exploiting the network connectivity graph structure in order to speed up computation.
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References
K. Plarre and P. Kumar. Object tracking by directional sensors. In Proceedings of IEEE Conference on Decision and Control (CDC), Seville, Spain, pages 3123–3128, 2006.
A. Mainwaring, D. Culler, J. Polastre, R. Szewczyk, and J. Anderson. Wireless sensor networks for habitat monitoring. In WSNA ’02: Proceedings of the 1st ACM International Workshop on Wireless Sensor Networks and Applications, pages 88–97, 2002.
S. Ganeriwal, R. Kumar, and M. B. Srivastava. Timing-sync protocol for sensor networks. In SenSys ’03: Proceedings of the 1st International Conference on Embedded Networked Sensor Systems, New York, NY, pages 138–149, 2003.
M. Sichitiu and C. Veerarittiphan. Simple, accurate time synchronization for wireless sensor networks. In IEEE Wireless Communications and Networking Conference(WCNC), New Orleans, LA, pages 1266–1273, 2003.
R. Karp, J. Elson, D. Estrin, and S. Shenker. Optimal and global time synchronization in sensornets, Center for Embedded Networked Sensing, Technical Reports, University of California, Los Angeles, April 2003.
R. Solis, V. Borkar, and P. R. Kumar. A new distributed time synchronization protocol for multihop wireless networks. Technical Report, University of Illinois, April 2005.
A. Giridhar and P. R. Kumar. Distributed clock synchronization over wireless networks: algorithms and analysis. Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, pages 4915–4920, December 13–15, 2006.
A. Giridhar. In-Network computation in wireless sensor networks. Ph. D. Thesis, Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign. April 2006.
B. Sundararaman, U. Buy, and A. Kshemkalyani. Clock synchronization for wireless sensor networks: a survey. Ad-Hoc Networks, 3(3): 281–323, May 2005.
S. Graham and P. R. Kumar. Time in general-purpose control systems: the control time protocol and an experimental evaluation. In Proceedings of the 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, pages 4004–4009, December 14–17, 2004.
N. M. Freris and P. R. Kumar. Fundamental limits on synchronization of affine clocks in networks. In Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, pages 921–926, December 12–14, 2007.
O. Gurewitz, I. Cidon, and M. Sidi. One-way delay estimation using network-wide measurements. IEEE/ACM Transactions on Networking, 14:2710–2724, June 2006.
N. M. Freris, V. S. Borkar, and P. R. Kumar. A model-based approach to clock synchronization. In Proceedings of 48th IEEE Conference on Decision and Control, Shanghai, December 16–18, 2009.
P. Gupta and P. R. Kumar. Critical power for asymptotic connectivity in wireless networks. In W. McEneaney, G. Yin, and Q. Zhang, Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, editors pages 547–566, Birkhauser, Boston, MA, 1998.
H. Poor. An Introduction to Signal Detection and Estimation, 2nd ed., Springer-Verlag, UK, 1995.
L. Chua, C. Desoer, and E. Kuh. Linear and Nonlinear Circuits. McGraw Hill Book Company, New York, NY, 1987.
A. Jadbabaie. On geographical routing without location information. In Proceedings of IEEE Conference on Decision and Control (CDC), Nassau, Bahamas, pages 4764–4769, 2004.
F. Y. Wu. Theory of resistor networks: The two-point resistance, Journal of Physics A, 37:6653, 2004.
F. Xue and P. R. Kumar. The number of neighbors needed for connectivity of wireless networks. Wireless Networks, 10(2):169–181, 2004.
D. P. Bertsekas and J. N. Tsitsiklis. Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, Englewood Cliffs, NJ, 1989.
C. D. Meyer. Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia, PA, 2000.
P. Diaconis and D. Stroock. Geometric bounds for eigenvalues of Markov chains. Annals of Applied Probability, 1(1):36–61, 1991.
R. Horn and C. R. Johnson. Matrix Analysis. Cambridge University Press, Cambridge, UK, 1990.
M. Penrose. Random geometric graphs. Oxford University Press, Oxford, UK, 2003.
J. Tsitsiklis. Problems in decentralized decision making and computation. Ph.D. Dissertation, Massachusetts Institute of Technology, 1984.
Acknowledgements
This material is based upon work partially supported by NSF under contract nos. CNS-07-21992 and CNS-0626584, the USARO under contract no. W-911-NF-0710287, and AFOSR under contract no. FA9550-09-0121.
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Giridhar, A., Kumar, P. (2011). The Spatial Smoothing Method of Clock Synchronization in Wireless Networks. In: Nikoletseas, S., Rolim, J. (eds) Theoretical Aspects of Distributed Computing in Sensor Networks. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14849-1_8
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