Skip to main content


We're creating a new version of this page. See preview

  • Research Article
  • Open Access

Systematic Errors and Location Accuracy in Wireless Networks

EURASIP Journal on Advances in Signal Processing20062006:081787

  • Received: 13 May 2005
  • Accepted: 23 March 2006
  • Published:


Wireless systems already provide time delay and signal strength measurements and the future may see antenna arrays that provide directional information. All these may be used for positioning. Although the statistical accuracy of different positioning methods is well studied, the systematic error effects, which arise, for example, from errors in sensor (node) location, network synchronization, or the path loss model, are not. This study fills this gap providing a unified error-propagation-law-based tool to analyze measurement and systematic error effects. The considered positioning systems, which are compared based on the developed framework, are the hyperbolic (time-delay-based), direction finding (DF), received signal strength (RSS), and relative RSS (RRSS) location systems. The obtained analytical results verify our intuitive expectations; the hyperbolic methods are sensitive to errors in network synchronization, RRRS methods to channel modelling errors, whereas DF methods are rather insensitive to systematic errors. However, the bias of DF methods is at its largest if the sensor location error is perpendicular to the line joining the sensor and the source. If the methods are compared based on overall accuracy, hyperbolic methods may be preferred in large sized networks, whereas the DF and RRSS methods may provide better accuracy in small sized networks. However, RRSS systems require a dense network in order to provide reliable results.


  • Wireless Network
  • Location Error
  • Antenna Array
  • Path Loss
  • Direction Finding

Authors’ Affiliations

Centre for Wireless Communications, University of Oulu, P.O. Box 4500, Oulu, 90014, Finland


  1. IEEE Signal Processing Magazine : Location is everything: positioning in wireless networks (a special issue). IEEE Signal Processing Magazine 2005., 22(3):Google Scholar
  2. Sadler BM: Fundamentals of energy-constrained sensor network systems. IEEE Aerospace and Electronic Systems Magazine 2005, 20(8):17–35. part 2: tutorialsView ArticleGoogle Scholar
  3. Foy WH: Position-location solutions by Taylor-series estimation. IEEE Transactions on Aerospace and Electronic Systems 1976, 12(2):187–193.View ArticleGoogle Scholar
  4. Torrieri DJ: Statistical theory of passive location systems. IEEE Transactions on Aerospace and Electronic Systems 1984, 20(2):183–198.View ArticleGoogle Scholar
  5. Kaplan D: Understanding GPS Principles and Applications. Artech House, Boston, Mass, USA; 1996.Google Scholar
  6. Patwari N, Hero AO III, Perkins M, Correal NS, O'Dea RJ: Relative location estimation in wireless sensor networks. IEEE Transactions on Signal Processing 2003, 51(8):2137–2148. 10.1109/TSP.2003.814469View ArticleGoogle Scholar
  7. Weiss AJ: On the accuracy of a cellular location system based on RSS measurements. IEEE Transactions on Vehicular Technology 2003, 52(6):1508–1518. 10.1109/TVT.2003.819613View ArticleGoogle Scholar
  8. Slijepcevic S, Megerian S, Potkonjak M: Location errors in wireless embedded sensor networks: sources, models, and effect on applications. Mobile Computing and Communications Review 2002, 6(3):67–78. 10.1145/581291.581301View ArticleGoogle Scholar
  9. 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.View ArticleGoogle Scholar
  10. 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.View ArticleGoogle Scholar
  11. Patwari N, Ash JN, Kyperountas S, Hero AO III, Moses RL, Correal NS: Locating the nodes: cooperative localization in wireless sensor networks. IEEE Signal Processing Magazine 2005, 22(4):54–69.View ArticleGoogle Scholar
  12. Pham T, Sadler B, Papadopoulus H: Energy-based source localization via ad-hoc acoustic sensor network. Proceedings of IEEE Workshop on Statistical Signal Processing, September-October 2003, St. Louis, Mo, USA 387–390.Google Scholar
  13. Savvides A, Garber WL, Moses RL, Srivastava MB: An analysis of error inducing parameters in multihop sensor node localization. IEEE Transactions on Mobile Computing 2005, 4(6):567–577.View ArticleGoogle Scholar
  14. Wu NE, Fowler ML: Aperture error mitigation via local-state estimation for frequency-based emitter location. IEEE Transactions on Aerospace and Electronic Systems 2003, 39(2):414–429. 10.1109/TAES.2003.1207254View ArticleGoogle Scholar
  15. Taylor JR: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. 2nd edition. University Science Books, Sausalito, Calif, USA; 1997.Google Scholar
  16. Gezici S, Tian Z, Giannakis GB, et al.: Localization via ultra-wideband radios: a look at positioning aspects of future sensor networks. IEEE Signal Processing Magazine 2005, 22(4):70–84.View ArticleGoogle Scholar
  17. Khuri AE: Advanced Calculus with Applications in Statistics. John Wiley & Sons, New York, NY, USA; 1993.MATHGoogle Scholar
  18. Carter GC: Time delay estimation for passive sonar signal processing. IEEE Transactions on Acoustics, Speech, and Signal Processing 1981, 29(3):463–470. 10.1109/TASSP.1981.1163560View ArticleGoogle Scholar
  19. Wang X, Wang Z, O'Dea B: A TOA-based location algorithm reducing the errors due to non-line-of-sight (NLOS) propagation. IEEE Transactions on Vehicular Technology 2003, 52(1):112–116. 10.1109/TVT.2002.807158View ArticleGoogle Scholar
  20. Kay SM: Fundamendals of Statistical Signal Prosessing: Estimation Theory. PTR Prentice Hall, Englewood Cliffs, NJ, USA; 1993.Google Scholar
  21. Xia HH: Simplified analytical model for predicting path loss in urban and suburban environments. IEEE Transactions on Vehicular Technology 1997, 46(4):1040–1046. 10.1109/25.653077View ArticleGoogle Scholar
  22. Sarkar TK, Ji Z, Kim K, Medouri A, Salazar-Palma M: A survey of various propagation models for mobile communication. IEEE Antennas and Propagation Magazine 2003, 45(3):51–82. 10.1109/MAP.2003.1232163View ArticleGoogle Scholar
  23. Figel WG, Shepherd NH, Trammell WF: Vehicle location by a signal attenuation method. IEEE Transactions on Vehicular Technology 1969, 18(3):105–109.View ArticleGoogle Scholar
  24. Horn RA, Johnson CR: Topics in Matrix Analysis. Cambridge University Press, Cambridge, UK; 1991.View ArticleGoogle Scholar


© H. Saarnisaari and T. Bräysy 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.