A Distributed Linear Least Squares Method for Precise Localization with Low Complexity in Wireless Sensor Networks

  • Frank Reichenbach
  • Alexander Born
  • Dirk Timmermann
  • Ralf Bill
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4026)


Localizing sensor nodes is essential due to their random distribution after deployment. To reach a long network lifetime, which strongly depends on the limited energy resources of every node, applied algorithms must be developed with an awareness of computation and communication cost. In this paper we present a new localization method, which places a minimum computational requirement on the nodes but achieves very low localization errors of less than 1%. To achieve this, we split the complex least squares method into a less central precalculation and a simple, distributed subcalculation. This allows precalculating the complex part on high-performance nodes, e.g. base stations. Next, sensor nodes estimate their own positions by simple subcalculation, which does not exhaust the limited resources. We analyzed our method with three commonly used numerical techniques – normal equations, qr-factorization, and singular-value decomposition. Simulation results showed that we reduced the complexity on every node by more than 47% for normal equations. In addition, the proposed algorithm is robust with respect to high input errors and has low communication and memory requirements.


Sensor Network Sensor Node Wireless Sensor Network Network Lifetime Normal Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless sensor networks: A survey. Computer Networks 38, 393–422 (2002)CrossRefGoogle Scholar
  2. 2.
    Bill, R., Cap, C., Kohfahl, M., Mund, T.: Indoor and outdoor positioning in mobile environments a review and some investigations on wlan positioning. Geographic Information Sciences 10, 91–98 (2004)Google Scholar
  3. 3.
    Gibson, J.: The mobile communications handbook. CRC Press, Boca Raton (1996)Google Scholar
  4. 4.
    Min, R., Bhardwaj, M., Cho, S., Sinha, A., Shih, E., Wang, A., Chandrakasan, A.: Low-power wireless sensor networks. In: International Conference on VLSI Design, pp. 205–210 (2001)Google Scholar
  5. 5.
    Savarese, C., Rabaey, J., Langendoen, K.: Robust positioning algorithms for distributed ad-hoc wireless sensor networks. In: USENIX Technical Annual Conference, pp. 317–327 (2002)Google Scholar
  6. 6.
    Bulusu, N.: Gps-less low cost outdoor localization for very small devices. IEEE Personal Communications Magazine 7, 28–34 (2000)CrossRefGoogle Scholar
  7. 7.
    Capkun, S., Hamdi, M., Hubaux, J.P.: Gps-free positioning in mobile ad hoc networks. Cluster Computing 5, 157–167 (2002)CrossRefGoogle Scholar
  8. 8.
    Tian, H., Chengdu, H., Brian, B.M., John, S.A., Tarek, A.: Range-free localization schemes for large scale sensor networks. In: 9th annual international conference on Mobile computing and networking, pp. 81–95 (2003)Google Scholar
  9. 9.
    Blumenthal, J., Reichenbach, F., Timmermann, D.: Precise positioning with a low complexity algorithm in ad hoc wireless sensor networks. PIK - Praxis der Informationsverarbeitung und Kommunikation 28, 80–85 (2005)CrossRefGoogle Scholar
  10. 10.
    Savvides, A., Han, C.-C., Srivastava, M.B.: Dynamic fine grained localization in ad-hoc networks of sensors. In: Seventh Annual ACM/IEEE International Conference on Mobile Computing and Networking, pp. 166–179 (2001)Google Scholar
  11. 11.
    Kwon, Y., Mechitov, K., Sundresh, S., Kim, W., Agha, G.: Resilient localization for sensor networks in outdoor environments. In: 25th IEEE International Conference on Distributed Computing Systems, pp. 643–652 (2005)Google Scholar
  12. 12.
    Ahmed, A.A., Shi, H., Shang, Y.: Sharp: A new approach to relative localization in wireless sensor networks. In: Second International Workshop on Wireless Ad Hoc Networking, pp. 892–898 (2005)Google Scholar
  13. 13.
    Karalar, T.C., Yamashita, S., Sheets, M., Rabaey, J.: An integrated, low power localization system for sensor networks. In: First Annual International Conference on Mobile and Ubiquitous Systems: Networking and Services, pp. 24–30 (2004) Google Scholar
  14. 14.
    Langendoen, K., Reijers, N.: Distributed localization in wireless sensor networks: A quantitative comparison. Computer Networks (Elsevier) 43, 499–518 (2003) (special issue on Wireless Sensor Networks)MATHGoogle Scholar
  15. 15.
    Niemeier, W.: Ausgleichsrechnung. de Gruyter (2002)Google Scholar
  16. 16.
    Murphy, W.S., Hereman, W.: Determination of a position in three dimensions using trilateration and approximate distances (1999)Google Scholar
  17. 17.
    Gramlich, G.: Numerische Mathematik mit Matlab - Eine Einführung für Naturwissenschaftler und Ingenieure. dpunkt.verlag (2000)Google Scholar
  18. 18.
    Lawson, C.L., Hanson, R.: Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs (1974)MATHGoogle Scholar
  19. 19.
    Golub, G.H., Reinsch, C.: Singular Value Decomposition and Least Square Solutions, Linear Algebra. Handbook for Automatic Computations, vol. II. Springer Verlag, Heidelberg (1971)Google Scholar
  20. 20.
    Golub, G.H., Van Loan, C.F.: Matrix Computations. The Johns Hopkins University Press (1996)Google Scholar
  21. 21.
    Niculescu, D., Nath, B.: Ad hoc positioning system (aps) using aoa. In: Proceedings of the IEEE Annu. Joint Conf. IEEE Computer and Communications Societies., pp. 1734–1743 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Frank Reichenbach
    • 1
  • Alexander Born
    • 2
  • Dirk Timmermann
    • 1
  • Ralf Bill
    • 2
  1. 1.Institute of Applied Microelectronics and Computer EngineeringUniversity of RostockGermany
  2. 2.Institute for Geodesy and GeoinformaticsUniversity of RostockGermany

Personalised recommendations