Determination of Helmert transformation parameters for continuous GNSS networks: a case study of the Géoazur GNSS network

Abstract

In this paper, we propose an approach to determine seven parameters of the Helmert transformation by transforming the coordinates of a continuous GNSS network from the World Geodetic System 1984 (WGS84) to the International Terrestrial Reference Frame. This includes (1) converting the coordinates of common points from the global coordinate system to the local coordinate system, (2) identifying and eliminating outliers by the Dikin estimator, and (3) estimating seven parameters of the Helmert transformation by least squares (LS) estimation with the “clean” data (i.e. outliers removed). Herein, the local coordinate system provides a platform to separate points’ horizontal and vertical components. Then, the Dikin estimator identifies and eliminates outliers in the horizontal or vertical component separately. It is significant because common points in a continuous GNSS network may contain outliers. The proposed approach is tested with the Géoazur GNSS network with the results showing that the Dikin estimator detects outliers at 6 out of 18 common points, among which three points are found with outliers in the vertical component only. Thus, instead of eliminating all coordinate components of these six common points, we only eliminate all coordinate components of three common points and only the vertical component of another three common points. Finally, the classical LS estimation is applied to “clean” data to estimate seven parameters of the Helmert transformation with a significant accuracy improvement. The Dikin estimator’s results are compared to those of other robust estimators of Huber and Theil-Sen, which shows that the Dikin estimator performs better. Furthermore, the weighted total least-squares estimation is implemented to assess the accuracy of the LS estimation with the same data. The inter-comparison of the seven estimated parameters and their standard deviations shows a small difference at a few per million levels (E-6).