Robust and Efficient Weighted Least Squares Adjustment of Relative Gravity Data

  • F. TouatiEmail author
  • S. Kahlouche
  • M. Idres
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 135)


When gravimetric data observations have outliers, using standard least squares (LS) estimation will likely give poor accuracies and unreliable parameter estimates. One of the typical approaches to overcome this problem consists of using the robust estimation techniques. In this paper, we modified the robust estimator of Gervini and Yohai (2002) called REWLSE (Robust and Efficient Weighted Least Squares Estimator), which combines simultaneously high statistical efficiency and high breakdown point by replacing the weight function by a new weight function. This method allows reducing the outlier impacts and makes more use of the information provided by the data. In order to adapt this technique to the relative gravity data, weights are computed using the empirical distribution of the residuals obtained initially by the LTS (Least Trimmed Squares) estimator and by minimizing the mean distances relatively to the LS estimator without outliers. The robustness of the initial estimator is maintained by an adapted cut-off values as suggested by the REWLSE method which allows also a reasonable statistical efficiency. Hereafter we give the advantage and the pertinence of REWLSE procedure on real and semi-simulated gravity data by comparing it with conventional LS and other robust approaches like M and MM estimators.


Relative gravity Weighted least squares Outlier Robust estimation Efficiency Breakdown point REWLSE 



The authors would like to first thank Prof C. Hwang from NCTU university of Taiwan for making available the data set used in this research. They also would like to thank Dr D. Gervini from university of Zurich for his help.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Geodetic LaboratoryCenter of Space TechniquesArzewAlgeria
  2. 2.Department of GeophysicsUniversity of Science and Technology H.B.AlgiersAlgeria

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