Skip to main content
  • Research Article
  • Open access
  • Published:

Positioning Based on Factor Graphs


This paper covers location determination in wireless cellular networks based on time difference of arrival (TDoA) measurements in a factor graphs framework. The resulting nonlinear estimation problem of the localization process for the mobile station cannot be solved analytically. The well-known iterative Gauss-Newton method as standard solution fails to converge for certain geometric constellations and bad initial values, and thus, it is not suitable for a general solution in cellular networks. Therefore, we propose a TDoA positioning algorithm based on factor graphs. Simulation results in terms of root-mean-square errors and cumulative density functions show that this approach achieves very accurate positioning estimates by moderate computational complexity.


  1. Caffery JJ: Wireless Location in CDMA Cellular Radio Systems. Kluwer Academic Publishers, Boston, Mass, USA; 2000.

    Google Scholar 

  2. Sayed AH, Tarighat A, Khajehnouri N: Network-based wireless location: challenges faced in developing techniques for accurate wireless location information. IEEE Signal Processing Magazine 2005,22(4):24-40.

    Article  Google Scholar 

  3. Gustafsson F, Gunnarsson F: Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements. IEEE Signal Processing Magazine 2005,22(4):41-53.

    Article  Google Scholar 

  4. Federal Communications Commission (FCC) FCC 99-245: Third Report and Order. October 1999,

  5. Coordination Group on Access to Location Information for Emergency Services (CGALIES) Final Report: Report on Implementation Issues Related to Access to Location Information by Emergency Services (E112) in the European Union. February 2002,

  6. Parkinson BW, Spilker JJ Jr.: Global Positioning System: Theory and Applications, Volume 1, Progress in Astronautics and Aeronautics. Volume 163. American Institute of Aeronautics & Astronautics, Reston, Va, USA; 1996.

    Google Scholar 

  7. Misra P, Enge P: Global Positioning System: Signals, Measurements and Performance. Ganga-Jamuna Press, Lincoln, Mass, USA; 2004.

    Google Scholar 

  8. Ercek R, De Doncker P, Grenez F: Study of pseudo-range error due to non-line-of-sight-multipath in urban canyons. Proceedings of the 18th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS '05), September 2005, Long Beach, Calif, USA 1083–1094.

    Google Scholar 

  9. Zhao Y: Standardization of mobile phone positioning for 3G systems. IEEE Communications Magazine 2002,40(7):108-116. 10.1109/MCOM.2002.1018015

    Article  Google Scholar 

  10. IST-2003-507581 WINNER Project.

  11. IST-2003-507581 WINNER Deliverable D4.8.1: WINNER II Intramode and Intermode Cooperation Schemes Definition. June 2006,

  12. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Upper Saddle River, NJ, USA; 1993.

    MATH  Google Scholar 

  13. Mensing C, Plass S: Positioning algorithms for cellular networks using TDoA. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '06), May 2006, Toulouse, France 4: 513–516.

    Google Scholar 

  14. Chen J-C, Maa C-S, Wang Y-C, Chen J-T: Mobile position location using factor graphs. IEEE Communications Letters 2003,7(9):431-433. 10.1109/LCOMM.2003.817337

    Article  Google Scholar 

  15. Chen J-C, Wang Y-C, Maa C-S, Chen J-T: Network-side mobile position location using factor graphs. IEEE Transactions on Wireless Communications 2006,5(10):2696-2704.

    Article  Google Scholar 

  16. Chen J-C, Ting P, Maa C-S, Chen J-T: Wireless geolocation with TOA/AOA measurements using factor graph and sum-product algorithm. Proceedings of the 60th IEEE Vehicular Technology Conference (VTC '04), September 2004, Los Angeles, Calif, USA 5: 3526–3529.

    Google Scholar 

  17. Chan YT, Ho KC: A simple and efficient estimator for hyperbolic location. IEEE Transactions on Signal Processing 1994,42(8):1905-1915. 10.1109/78.301830

    Article  Google Scholar 

  18. Foy WH: Position-location solutions by Taylor-series estimation. IEEE Transactions on Aerospace and Electronic Systems 1976,12(2):187-194.

    Article  Google Scholar 

  19. Kschischang FR, Frey BJ, Loeliger H-A: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 2001,47(2):498-519. 10.1109/18.910572

    Article  MathSciNet  Google Scholar 

  20. Smith JO, Abel JS: The spherical interpolation method of source localization. IEEE Journal of Oceanic Engineering 1987,12(1):246-252. 10.1109/JOE.1987.1145217

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Christian Mensing.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Mensing, C., Plass, S. Positioning Based on Factor Graphs. EURASIP J. Adv. Signal Process. 2007, 041348 (2007).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: