Analytical investigation of intersection based range-free localization

  • Michel SortaisEmail author
  • Sven D. Hermann
  • Adam Wolisz
Original Paper


The localization of mobile devices is essential for the provisioning of location-based services, e.g., to locate people facing an accident or to provide relevant information to device users, depending on their current whereabouts. Several localization mechanisms have been developed using estimates of absolute distances or angles between the devices and the base stations of the networks. These mechanisms often require expensive enhancements of the existing base stations or mobile devices. In recent years, so-called range-free approaches have been proposed, which limit the possible positions of a device to the coverage areas of radio network cells, without relying on precise distances or angles. The accuracy of the corresponding information can be refined by computing the intersection area of all cells that cover the current position of the device. However, the computation of this intersection area, e.g., by the location server of a network carrier, can be a complex task. To avoid unnecessary workload, one would like to preestimate the possible reduction of location uncertainty, i.e., the information gain that can be achieved. The contribution of this paper is an analytical and numerical investigation of the problem. Several approaches are presented for the computation of the information gain, based on stochastic geometry and on a Monte-Carlo method. We show that simple scaling arguments can be used to estimate the order of magnitude of the average information gain, while more complex approximations based on Voronoi cells lead to relatively good results.


Range-free localization Location information gain Stochastic geometry Poisson point processes Voronoi tessellations 


  1. 1.
    Schiller J, Voisard A (2004) Location-based services, ser. Morgan Kaufmann series in data management systems. Morgan Kaufmann, San FranciscoGoogle Scholar
  2. 2.
    He T, Huang C, Blum BM, Stankovic JA, Abdelzaher T (2003) Range-free localization schemes for large scale sensor networks. In: International conference on mobile computing and networking, San Diego, 14–19 September 2003Google Scholar
  3. 3.
    Trevisani E, Vitaletti A (2004) Cell-id location technique, limits and benefits: an experimental study. In: Sixth IEEE workshop on mobile computing systems and applications (WMCSA). IEEE, Piscataway, pp 51–60, DecCrossRefGoogle Scholar
  4. 4.
    Lück S, Scharf M, Gil J (2005) An architecture for acquisition and provision of hotspot coverage information. In: 11th European wireless 2005 (EW 2005), Nicosia, 10–13 April 2005, pp 287–293Google Scholar
  5. 5.
    Koch T (2004) Rapid mathematical programming. Ph.D. dissertation, Technische Universität BerlinGoogle Scholar
  6. 6.
    Bulusu N, Heidemann J, Estrin D (2000) Gps-less low cost outdoor localization for very small devices. IEEE Wirel Commun 7(5):27–34, OctGoogle Scholar
  7. 7.
    Simic S, Sastry S (2002) Distributed localization in wireless ad hoc networks. UC Berkeley, Tech. Rep. UCB/ERL M02/26Google Scholar
  8. 8.
    Stupp G, Sidi M (2005) The expected uncertainty of range-free localization protocols in sensor networks. Theor Comp Sci 344:86–99zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chu H-C, Jan R-H (2003) A cell-based location-sensing method for wireless networks. Wirel Commun Mob Comput 3(4):455–463CrossRefGoogle Scholar
  10. 10.
    Baccelli F, Gloaguen C, Zuyev S (2000) Superposition of planar voronoi tessellations. Commun Stat Stoch Models 16:69–98zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Rappaport T (1999) Wireless communications. Prentice Hall, Englewood CliffsGoogle Scholar
  12. 12.
    Gupta P, Kumar PR (2000) The capacity of wireless networks. IEEE Trans Inform Theory 46(2):388–404, MarchzbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Aguiar A, Gross J (2003) Wireless channel models. Telecommunication Networks Group, Technische Universität Berlin. Tech. Rep. TKN-03-007, AprGoogle Scholar
  14. 14.
    Baccelli F, Zuyev S (1997) Stochastic geometry models of mobile communication networks. In: Frontiers in queueing: models and applications in science and engineering. CRC, Boca Raton, pp 227–243Google Scholar
  15. 15.
    Okabe A, Boots B, Sugihara K, Chiu SN (2000) Spatial tessellations: concepts and applications of Voronoi diagrams, 2nd edn., ser. Probability and statistics. Wiley, New York, JulyzbMATHGoogle Scholar
  16. 16.
    Cover TM, Thomas JA (1991) Elements of information theory, ser. telecommunications. Wiley, New YorkGoogle Scholar
  17. 17.
    Calka P (2003) Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson–Voronoi tessellation and a poisson line process. Adv Appl Probab 35(3):551–562zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Moller J (1994) Lectures on random Voronoi tessellations. Springer, Berlin Heidelberg New YorkGoogle Scholar
  19. 19.
    Hermann SD, Sortais M, Wolisz A (2007) Enhancing the accuracy of position information through superposition of location server data. In: Proc. of IEEE international con ference on communications (ICC), Glasgow, JuneGoogle Scholar
  20. 20.
    Wiener N (1939) The ergodic theorem. Duke Math J 5(1):1–18zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Cowan R (1978) The use of the ergodic theorems in random geometry. Adv Appl Probab 10:47–57zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Cowan R (1980) Properties of ergodic random mosaic processes. Math Nachr 97:89–102zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Stoyan D, Kendall WS, Mecke J (1995) Stochastic geometry and its applications. Wiley, New YorkzbMATHGoogle Scholar
  24. 24.
    Mecke J (1981) Formulas for stationary planar fibre processes III—intersections with fibre systems. Math Oper Forsch Stat Ser Stat 12(2):201–210zbMATHMathSciNetGoogle Scholar

Copyright information

© Institut TELECOM and Springer-Verlag France 2008

Authors and Affiliations

  1. 1.MAP5, UMR CNRS 8145Université Paris DescartesParisFrance
  2. 2.Telecommunications Networks GroupTechnische Universität BerlinBerlinGermany

Personalised recommendations