Closed-form Solution for Joint Localization and Synchronization in Wireless Sensor Networks With and Without Beacon Uncertainties



In Wireless Sensor Networks (WSNs), the use of the same set of measurement data for simultaneous localization and synchronization is potentially useful for achieving higher estimation accuracy, and lower communication overhead and power consumption. In this paper, we first analyze the impact of asynchronous sensor nodes (SNs) on the accuracy of time-based localization schemes, and the impact of inaccurate SN location information on the accuracy of synchronization based on packet delay measurement, to illustrate the necessity and significance of simultaneous localization and synchronization of SNs. We then consider the joint localization and synchronization problem for two cases. In the first case, we assume that the beacon information is perfectly known. The Maximum Likelihood (ML) estimator is first formulated, which is computationally expensive. A new closed-form Joint Localization and Synchronization I (JLS-I) estimator is then proposed to provide a computationally efficient solution. In the second case, we assume that the beacon locations and timings are known inaccurately, and develop the ML and JLS-II estimators accordingly. JLS-II is based on Weighted Least Square and Generalized Total Least Square, and is of low complexity. The Cramer-Rao Lower Bounds (CRLBs) and the analytical Mean Square Errors of the proposed estimators are derived, and we also analytically show that JLS-I can achieve the corresponding CRLB. Simulation results demonstrate the effectiveness of the proposed estimators compared to other approaches. With only a three-way message exchange, JLS-I can attain the CRLB and JLS-II can provide close to optimal performance in their respective scenarios. They are also robust against the Geometric Dilution of Precision problem, and outperform existing algorithms in NLOS scenarios. Our results demonstrate the advantages of JLS-I and JLS-II in reduced computational complexity with lower power consumption and communication cost while achieving high estimation accuracy. They are therefore attractive solutions to the simultaneous localization and synchronization problem in WSNs where energy and network resources are the most important considerations.


Cramer-Rao lower bound (CRLB) Localization Synchronization Wireless sensor network (WSN) 



We would like to thank Hong Kong RGC (Project Number: 620410) for supporting this work, and we also like to thank the anonymous reviewers for their valuable comments and suggestions.


  1. 1.
    D. S. Ray, A. Trachtenberg and R. Ungrangsi, Robust location detection with sensor networks, IEEE Journal on Selected Areas in Communications, Vol. 22, pp. 1016–1025, 2004.CrossRefGoogle Scholar
  2. 2.
    N. Bulusu, J. Heidemann and D. Estrin, GPS-less low-cost outdoor localization for very small devices, IEEE Personal Communications, Vol. 7, pp. 28–34, 2000.CrossRefGoogle Scholar
  3. 3.
    M. Kanaan and K. Pahlavan, A comparison of wireless geolocation algorithms in the indoor environment, in Wireless Communications and Networking Conference, 2004. WCNC. IEEE, Vol. 1, pp. 177–182, 2004.Google Scholar
  4. 4.
    F. K. W. Chan, H. C. So, J. Zheng and K. W. K. Lui, Best linear unbiased estimator approach for time-of-arrival based localisation, IET Signal Processing, Vol. 2, pp. 156–162, 2008.CrossRefGoogle Scholar
  5. 5.
    Y. T. Chan and K. C. Ho, A simple and efficient estimator for hyperbolic location, IEEE Transactions on Signal Processing, Vol. 42, pp. 1905–1915, 1994.CrossRefGoogle Scholar
  6. 6.
    X. Cheng, A. Thaeler, G. Xue and D. Chen, TPS: a time-based positioning scheme for outdoor wireless sensor networks, in INFOCOM 2004. Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies, Vol. 4, pp. 2685–2696, 2004.Google Scholar
  7. 7.
    D. Niculescu and B. Nath, Ad hoc positioning system (APS) using AOA, in INFOCOM 2003. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies. IEEE, Vol. 3, pp. 1734–1743, 2003.Google Scholar
  8. 8.
    S. Sakagami, S. Aoyama, K. Kuboi, S. Shirota and A. Akeyama, Vehicle position estimates by multibeam antennas in multipath environments, IEEE Transactions on Vehicular Technology, Vol. 41, pp. 63–68, 1992.CrossRefGoogle Scholar
  9. 9.
    G. Mao, B. Fidan and B. D. O. Anderson, Wireless sensor network localization techniques, Computer Networks, Vol. 51, pp. 2529–2553, 2007.MATHCrossRefGoogle Scholar
  10. 10.
    V. Y. Zhang and A. K. Wong, Combined AOA and TOA NLOS localization with nonlinear programming in severe multipath environments, in Wireless Communications and Networking Conference, 2009. WCNC 2009. IEEE, pp. 1–6, 2009.Google Scholar
  11. 11.
    S. Y. Park, H.-S. Ahn, and W. Yu, A simple object tracking system using ITDOA without time synchronization, in Advanced Communication Technology, the 9th International Conference on, Vol. 3, pp. 2026–2028, 2007.Google Scholar
  12. 12.
    T. Li, A. Ekpenyong and Y.-F. Huang, Source localization and tracking using distributed asynchronous sensors, IEEE Transactions on Signal Processing, Vol. 54, pp. 3991–4003, 2006.CrossRefGoogle Scholar
  13. 13.
    E. Nakamura and A. Loureiro, Information fusion in wireless sensor networks, in SBBD ‘08: Proceedings of the 23rd Brazilian Symposium on Databases, pp. 317–318, 2008.Google Scholar
  14. 14.
    D. L. Mills, Network time protocol version 4 reference and implementation guide, Department of Electrical and Computer Engineering, University of Delaware, Tech. Rep. 06-06-1, 2006.Google Scholar
  15. 15.
    F. Sivrikaya and B. Yener, Time synchronization in sensor networks: a survey, IEEE Network, Vol. 18, pp. 45–50, 2004.CrossRefGoogle Scholar
  16. 16.
    J. Elson, L. Girod and D. Estrin, Fine-grained network time synchronization using reference broadcasts, SIGOPS Operating System Review, Vol. 36, pp. 147–163, 2002.CrossRefGoogle Scholar
  17. 17.
    M. Maroti, B. Kusy, G. Simon, and A. Ledeczi, The flooding time synchronization protocol, in SenSys ‘04: Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems, pp. 39–49, 2004.Google Scholar
  18. 18.
    S. Ping, Delay measurement time synchronization for wireless sensor networks, Technical Report IRB-TR-03-013, Intel Research, June, 2003.Google Scholar
  19. 19.
    K. Römer and F. Mattern, Towards a unified view on space and time in sensor networks, Computer Communications, vol. 28, no. 13, pp. 1484–1497, Aug. 2005.Google Scholar
  20. 20.
    H. A. B. F. de Oliveira, E. F. Nakamura, A. A. F. Loureiro, and A. Boukerche, Localization in time and space for sensor networks, in AINA ‘07: Proceedings of the 21st International Conference on Advanced Networking and Applications, pp. 539–546, 2007.Google Scholar
  21. 21.
    A. Boukerche, H. A. B. F. Oliveira, E. F. Nakamura, and A. A. F. Loureiro, A novel lightweight algorithm for time-space localization in wireless sensor networks, in MSWiM ‘07: Proceedings of the 10th ACM Symposium on Modeling, Analysis, and Simulation of Wireless and Mobile Systems, pp. 336–343, 2007.Google Scholar
  22. 22.
    A. Boukerche, H. A. B. Oliveira, E. F. Nakamura, and A. A. F. Loureiro, Localization in time and space for wireless sensor networks: A Mobile Beacon approach, in World of Wireless, Mobile and Multimedia Networks, 2008. WoWMoM 2008. 2008 International Symposium on a, pp. 1–8, 2008.Google Scholar
  23. 23.
    J. Zheng and Y.-C. Wu, Localization and time synchronization in wireless sensor networks: a unified approach, in IEEE Asia Pacific Conference on Circuits and Systems, 2008. APCCAS 2008, pp. 594–597, 2008.Google Scholar
  24. 24.
    J. Zheng and Y.-C. Wu, Joint localization and time synchronization in wireless sensor networks with anchor uncertainties, in IEEE Wireless Communications and Networking Conference, 2009. WCNC 2009, pp. 1–5, 2009.Google Scholar
  25. 25.
    K.-L. Noh, Q. M. Chaudhari, E. Serpedin and B. W. Suter, Novel clock phase offset and skew estimation using two-way timing message exchanges for wireless sensor networks, IEEE Transactions on Communications, Vol. 55, pp. 766–777, 2007.CrossRefGoogle Scholar
  26. 26.
    S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University PressCambridge, UK, 2004.MATHGoogle Scholar
  27. 27.
    S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-HallEnglewood Cliffs, NJ, 1993.MATHGoogle Scholar
  28. 28.
    J. Albowicz, A. Chen, and Lixia Zhang, Recursive position estimation in sensor networks, in Ninth International Conference on Network Protocols, 2001, pp. 35–41, 2001.Google Scholar
  29. 29.
    S. Van Huffel and J. Vandewalle, Analysis and properties of the generalized total least squares problem AX ≈ B when some or all columns in A are subject to error, SIAM Journal on Matrix Analysis and Applications, Vol. 10, No. 3, pp. 294–315, 1989.MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    L. L. Scharf, Statistical Signal Process: Detection, Estimation and Time Series Analysis, Addison-WesleyReading, MA, 1991.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Electronic and Computer EngineeringThe Hong Kong University of Science and TechnologyKowloonHong Kong

Personalised recommendations