Splitting the Linear Least Squares Problem for Precise Localization in Geosensor Networks

  • Frank Reichenbach
  • Alexander Born
  • Dirk Timmermann
  • Ralf Bill
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4197)


Large amounts of cheap and easily deployable wireless sensors enable area-wide monitoring of both urban environments and inhospitable terrain. Due to the random deployment of these sensor nodes, one of the key issues is their position determination. Noisy distance measurements and the highly limited resources of every sensor node, due to tiny hardware and small battery capacity, demand the development of robust, energy aware, and precise localization algorithms.

We believe this can be achieved by appropriately distributing the complex localization task between all participating nodes. Therefore, we use a linearization tool to linearize the arising non-linear system of equations into a linear form that can be solved by a distributed least squares method. It is shown in this paper that we can save with this new approach more than 47% of computation cost whilst maintaining a low network traffic. Additionally, we describe memory optimizations to process the complex matrix operations with only a few kilobyte of memory on the sensor node.


Sensor Network Sensor Node Wireless Sensor Network Localization Algorithm Receive Signal Strength Indicator 
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.


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  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.
    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 (2001)Google Scholar
  3. 3.
    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
  4. 4.
    Gibson, J.: The mobile communications handbook. CRC Press, Boca Raton (1996)Google Scholar
  5. 5.
    Alouini, M.: Global Positioning System: An Overview. California Institute of Technology (1996)Google Scholar
  6. 6.
    Stefanidis, A., Nittel, S.: GeoSensor Networks. CRC Press, Boca Raton (2004)CrossRefGoogle Scholar
  7. 7.
    Bulusu, N.: Gps-less low cost outdoor localization for very small devices. IEEE Personal Communications Magazine 7, 28–34 (2000)CrossRefGoogle Scholar
  8. 8.
    Delaunay, B.: Sur la sphere vide. In: Bulletin der Akademie der Wissenschaften der UdSSR, pp. 793–800 (1934)Google Scholar
  9. 9.
    Mirante, A., Weingarten, N.: The radial sweep algorithm for constructing triangulated irregular networks. In: IEEE Computer Graphics and Applications, pp. 11–21 (1982)Google Scholar
  10. 10.
    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 (2003)Google Scholar
  11. 11.
    Savarese, C., Rabaey, J., Langendoen, K.: Robust positioning algorithms for distributed ad-hoc wireless sensor networks. In: USENIX Annual Tech. Conf., Monterey, CA, June 2002, pp. 317–327 (2002)Google Scholar
  12. 12.
    Capkun, S., Hamdi, M., Hubaux, J.P.: Gps-free positioning in mobile ad hoc networks. Cluster Computing 5, 157–167 (2002)CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Savvides, A., Han, C.C., Srivastava, M.B.: Dynamic fine grained localization in ad-hoc networks of sensors. In: 7th ACM MobiCom, Rome, Italy, pp. 166–179 (2001)Google Scholar
  15. 15.
    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 (ICDCS 2005), pp. 643–652 (2005)Google Scholar
  16. 16.
    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 (WWAN) ICDCSW 2005, pp. 892–898 (2005)Google Scholar
  17. 17.
    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 (MobiQuitous 2004), pp. 24–30 (2004)Google Scholar
  18. 18.
    Langendoen, K., Reijers, N.: Distributed localization in wireless sensor networks: A quantitative comparison. Computer Networks (Elsevier), special issue on Wireless Sensor Networks 43, 499–518 (2003)MATHGoogle Scholar
  19. 19.
    Wolf, P.R., Ghilani, C.D.: Adjustment Computations: Statistics and Least Squares in Surveying and GIS (Surveying & Boundary Control). Wiley-Interscience, Chichester (1997)Google Scholar
  20. 20.
    Farebrother, R.: Fitting Linear Relationships. Springer, Heidelberg (1998)Google Scholar
  21. 21.
    Murphy, W.S., Hereman, W.: Determination of a position in three dimensions using trilateration and approximate distances (1999)Google Scholar
  22. 22.
    Lawson, C.L., Hanson, R.: Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs (1974)MATHGoogle Scholar
  23. 23.
    Golub, G.H., Loan, C.F.V.: Matrix Computations. The Johns Hopkins University Press (1996)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

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