Relative Localization for Small Wireless Sensor Networks

  • Yifeng ZhouEmail author
  • Franklin Wong
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 184)


In this paper, we investigate relative localization techniques based on internode distance measurements for small wireless networks. High precision ranging is assumed, which is achieved by using technologies such as ultra-wide band (UWB) ranging. A number of approaches are formulated and compared for relative location estimation, which include the Linear Least Squares (LLS) approach, the Maximum Likelihood Estimation (MLE) approach, the Map Registration Approach (MAP), the Multidimensional Scaling (MDS) approach and the enhanced MDS approaches. Finally, computer simulations are used to compare the performances and effectiveness of these techniques, and conclusions are drawn on the suitability of the relative localization techniques for small networks.


Wireless sensor networks Localization Ranging Ultra-wide band (UWB) Least squares (LS) Maximum likelihood method (MLE) Multidimensional scaling (MDS) 


  1. 1.
    Savvides, A., Han, C.C., Srivastava, M.B.: Dynamic fine-grained localization in ad hoc networks of sensors. In: Proceedings of the 7th Annual ACM/IEEE International Conference on Mobile Computing and Networking (MobiCom 2001), Rome, Italy, pp. 166–179, July 2001Google Scholar
  2. 2.
    Mao, G., Fidan, B., Anderson, B.D.O.: Wireless sensor network localization techniques. Comput. Netw. 51(10), 2529–2553 (2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    Savvides, A., Park, H., Srivastava, M.B.: The bits and flops of the \(N\)-hop multilateration primitive for node localization problems. In: Proceedings of the First ACM International Workshop on Wireless Sensor Networks and Applications, Atlanta, Georgia, USA, pp. 112–121, September 2002Google Scholar
  4. 4.
    Shang, Y., Ruml, W.: Improved MDS-based localization. In: Proceedings of the IEEE INFOCOM 2004, The 23rd Annual Joint Conference of the IEEE Computer and Communications Societies, Hong Kong, China, March 2004Google Scholar
  5. 5.
    Zhou, Y., Lamont, L.: An optimal local map registration technique for wireless sensor network localization problems. In: Proceedings of the 11th International Conference on Information Fusion (FUSION 2008), Cologne, Germany, 30 June–03 July 2008Google Scholar
  6. 6.
    Zhou, Y., Lamont, L.: A mobile beacon based localization approach for wireless sensor network applications. In: Proceedings of the Fifth International Conference on Sensor Technologies and Applications (SENSORCOMM), Nice, France, August 2011Google Scholar
  7. 7.
    Savarese, C., Rabaey, J.M., Beutel, J.: Location in distributed ad-hoc wireless sensor networks. In: Proceedings of the 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, UT, vol. 4, pp. 2037–2040, May 2001Google Scholar
  8. 8.
    Mendel, J.M.: Lessons in Digital Estimation Theory. Prentice Hall, Englewood Cliffs (1987)Google Scholar
  9. 9.
    Golub, G.H., Van Loan, C.F.: Matrix Computation, 3rd edn. The Johns Hopkins University Press, London (1996)zbMATHGoogle Scholar
  10. 10.
    Shang, Y., Ruml, W., Zhang, Y., Fromherz, M.: Localization from connectivity in sensor networks. IEEE Trans. Parallel Distrib. Syst. 15(11), 961–974 (2004)CrossRefGoogle Scholar
  11. 11.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling, Theory and Applications. Springer, New York (1997)CrossRefzbMATHGoogle Scholar
  12. 12.
    Ji, X., Zha, H.: Sensor positioning in wireless ad hoc networks using multidimensional scaling. In: Proceedings of the IEEE 23rd Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2004), Hong Kong, China, vol. 4, pp. 2652–2661, March 2004Google Scholar
  13. 13.
    Dijkstra, E.W.: A note on two problems in connection with graphs. Numer. Math. 1, 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Warshall, S.: A theorem on Boolean matrices. J. ACM 9(1), 11–12 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Zhou, Y., Lamont, L.: Optimal local map registration technique for wireless sensor network localization problems. In: Mukhopadhyay, S.C., Leung, H. (eds.) Advances in Wireless Sensors and Sensors Networks. LNEE, vol. 64, pp. 177–198. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Jennrich, R.I.: A simple general procedure for orthogonal rotation. Psychometrika 66(2), 289–306 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Jennrich, R.I.: A simple general method for oblique rotation. Psychometrika 67(1), 7–19 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Dennisand, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization, Nonlinear Equations. Prentice-Hall, Englewood Cliffs (1983)Google Scholar
  19. 19.
    Chung, F.R.K.: Spectra Graph Theory. American Mathematical Society, Providence (1997)Google Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2017

Authors and Affiliations

  1. 1.Communications Research Centre CanadaNepeanCanada
  2. 2.Defence Research and Development CanadaOttawaCanada

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