Acta Geodaetica et Geophysica Hungarica

, Volume 46, Issue 3, pp 291–308 | Cite as

Increasing the efficacy of the tests for outliers for geodetic networks

  • S. Hekimoglu
  • B. Erdogan
  • R. C. Erenoglu
  • R. G. Hosbas


Outliers in geodetic networks badly affect all parameters and their variances estimated by least-squares. Tests for outliers (e.g. Baarda’s and Pope’s tests) are frequently used to detect outliers in geodetic networks. To measure the ability of these tests, the mean success rate (MSR) is proposed. Studies have shown that the MSRs of these tests in geodetic networks are low due to the smearing effect of the least-squares estimation even if there is only one outlier in the data set. In this paper, a new approach, for small outliers, is presented to increase the MSRs of the tests for outliers in geodetic networks. The main idea is that if the weight of one observation is increased, the corresponding studentized or normalized residuals are increased, too. This thesis is proved. Hence, the ability of the tests to detect outliers can be increased by appropriately increasing the weight of one observation at a time and repeating this for all observations. This approach is applied to three simulated geodetic networks. We show that the MSRs of the outlier tests are improved by approximately 5% if there is one small outlier in the data set. However, the improvements in the MSRs for more than one outlier are low.


efficacy geodetic networks outliers tests for outliers weight 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Amiri-Simkooei A R 2003: J. Surv. Eng., 129, 37–43.CrossRefGoogle Scholar
  2. Baarda W 1968: A testing procedure for use in geodetic Networks. Publication on Geodesy, New Series 2, No. 5., Netherlands Geodetic Commission, DelftGoogle Scholar
  3. Baselga S 2007: J. Surv. Eng., 133, 52–55.CrossRefGoogle Scholar
  4. Benning W 1995: zfv, 12, 606–617.Google Scholar
  5. Erenoglu R C, Hekimoglu S 2010: Acta Geod. Geoph. Hung., 45, 426–439.CrossRefGoogle Scholar
  6. Even-Tzur G 1999: zfv, 124, 128–134.Google Scholar
  7. Fuchs H 1982: Manuscr. Geod., 7, 151–207.Google Scholar
  8. Hadi A S, Siminoff J S 1993: J. American Statistical Ass., 88, 65–72.Google Scholar
  9. Hampel F, Ronchetti E, Rousseeuw P, Stahel W 1986: Robust statistics: the approach based on influence functions. John Wiley and Sons, New YorkGoogle Scholar
  10. Harvey P R 1993: Aust. J. Geod. Photogram. Surv. Google Scholar
  11. Hekimoglu S 2005a: zfv, 3, 174–180.Google Scholar
  12. Hekimoglu S 2005b: AVN, 112, 7–12.Google Scholar
  13. Hekimoglu S 2005c: Survey Review, 38, 274–285. 59, 39–52.Google Scholar
  14. Hekimoglu S, Erenoglu R C 2007: J. Geodesy, 81, 137–148.CrossRefGoogle Scholar
  15. Hekimoglu S, Erenoglu R C 2009: J. Surv. Eng., 135, 1–5.CrossRefGoogle Scholar
  16. Hekimoglu S, Koch K R 1999: In: Proc. Third Turkish-German Joint Geodetic Days. M O Altan, L Gründig eds, Istanbul, 1, 179–196.Google Scholar
  17. Hekimoglu S, Koch K R 2000: AVN, 107, 247–254.Google Scholar
  18. Hekimoglu S, Sanli D U 2003: zfv, 128, Heft 4, 271.Google Scholar
  19. Huber P J 1981: Robust statistics. John Wiley and Sons. Inc., New YorkCrossRefGoogle Scholar
  20. Koch K R 1996: AVN, 103, 1–18.Google Scholar
  21. Koch K R 1999: Parameter estimation and hypothesis testing in linear models. 2nd Ed. Springer-Verlag, BerlinCrossRefGoogle Scholar
  22. Pelzer H 1985: Überprüfung von Ausgleichungsmodellen. Geodätische Netze in Landesund Ingenieurvermessung II. Verlag Konrad Witter, StuttgartGoogle Scholar
  23. Pope A J 1976: The statistics of residuals and the outlier detection of outliers. NOAA Technical Report, NOS 65, NGS 1, Rockville, MDGoogle Scholar
  24. Rousseeuw P J, Leroy A M 1987: Robust regression and outlier detection. John Wiley and Sons, Inc., New York.CrossRefGoogle Scholar
  25. Schwarz C R, Kok J J 1993: J. Surv. Eng., 119, 128–136.CrossRefGoogle Scholar
  26. Snow K, Schaffrin B 2003: GPS Solutions, 7, 130–139.CrossRefGoogle Scholar
  27. Teunissen P J G 2006: Testing theory, an introduction. 2nd edition, Delft University Press, DelftGoogle Scholar
  28. Wicki F 1999: Robuste Schätzverfahren für die Parameterschätzung in geodätischen Netzen. Institut für Geodäsie und Photogrammetrie an der ETH, Zürich, Mitt. No. 67.Google Scholar
  29. Wilcox R R 1997: Introduction to robust estimation and hypothesis testing, Academic Press. San DiegoGoogle Scholar
  30. Xu P L 2005: J. Geodesy, 79, 146–159.CrossRefGoogle Scholar
  31. Yang Y, Cheng M K, Shum C K, Tapley B D 1999: J. Geodesy, 73, 345–349.CrossRefGoogle Scholar
  32. Yang Y, He H, Xu G 2001: J. Geodesy, 75, 109–116.CrossRefGoogle Scholar
  33. Yang Y, Song L, Xu T 2002: J. Geodesy, 76, 353–358.CrossRefGoogle Scholar
  34. Youcai H 1995: Bull. Geod., 69, 292–299.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 2011

Authors and Affiliations

  • S. Hekimoglu
    • 1
  • B. Erdogan
    • 1
  • R. C. Erenoglu
    • 1
  • R. G. Hosbas
    • 1
  1. 1.Department of Geomatic EngineeringYildiz Technical UniversityIstanbulTurkey

Personalised recommendations