Robust Geodetic Parameter Estimation Under Least Squares Through Weighting on the Basis of the Mean Square Error

  • Francis W. O. Aduol


A technique for the robust estimation of geodetic parameters under the least squares method when weights are specified through the use of the mean square error is presented. The mean square error is considered in the specification of observational weights instead of the conventional approach based on the observational variance. The practical application of the proposed approach is demonstrated through computational examples based on a geodetic network. The results indicate that the least squares estimation with observational weights based on the mean square error is relatively robust against outliers in the observational set, provided the network (or the system) under consideration has a good level of reliability, as to make the network (or system) stable under estimation.


Robust Estimation Outlier Detection Observational Error Geodetic Network Outlying Observation 
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  1. 1.
    Aduol, F.W.O., 1994. Robust geodetic parameter estimation through iterative weighting. Survey Review, 32, 252: 359–367.CrossRefGoogle Scholar
  2. 2.
    Baarda, W., 1967. Statistical concepts in geodesy. Netherlands Geodetic Commission, publications on Geodesy, New Series, Vol. 2, No. 4, Delft.Google Scholar
  3. 3.
    Baarda, W., 1968a. Statistics — a compass for the land surveyor. Computing Centre of the Delft Geodetic Institute. Google Scholar
  4. 4.
    Baarda, W., 1968b. A testing procedure for use in geodetic networks. Netherlands Geodetic Commission, publications on Geodesy, New Series, Vol. 2, No. 5, Delft.Google Scholar
  5. 5.
    Borutta, H. 1988. Robuste Schätzverfahren für geodätische Anwendungen. Schriftenreihe Studiengang Vermessungswesen Universität der Bundeswehr München, Heft 33. München.Google Scholar
  6. 6.
    Grafarend, E.W., Schaffrin, B., 1993. Ausgleichungsrechnung in linearen Modellen. Wissenschaftsverlag, Mannheim. Pp. 116–117.Google Scholar
  7. 7.
    Hampel, RR., Ronchetti, E.M., Rousseeuw, R, and Stahel, W.A., 1986. Robust Statistics — the Approach based on Influence Functions. John Wiley & Sons, New York.Google Scholar
  8. 8.
    Huber, P.J., 1964. Robust estimation of a location parameter. Annals of Mathematical Statistics, 35: 73–101.CrossRefGoogle Scholar
  9. 9.
    Huber, P.J., 1972. Robust statistics — A review. Annals of Mathematical Statistics, 43: 1041–1067.CrossRefGoogle Scholar
  10. 10.
    Huber, P.J., 1981. Robust Statistics. John Wiley & Sons, New York.CrossRefGoogle Scholar
  11. 11.
    Toutenburg, H., 1992. Lineare Modelle. Physica Verlag, Heidelberg. Pp 35–36.CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2003

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  • Francis W. O. Aduol

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