Investigating efficacy of robust M-estimation of deformation from observation differences

Abstract

Generalized robust M-estimation of deformation from observation differences (GREDOD) is a robust method for deformation analysis of geodetic control networks. This method has been developed based on the well known robust Iterative weighted similarity transformation (IWST) method. Hence, in the GREDOD method, as in the IWST method, the L₁-norm weight function is the weight function for the displacement vector and the displacement vector components are the weight function variables. The L₁-norm weight function for variables in the form of the displacement vector components is the simplest and most natural solution, but it is not known whether this is the most efficacious solution for the GREDOD method. To assess this, the current study used different robust weight functions which were tested for variables in the widely used form of the displacement vector components and for variables in the form of displacement lengths. All solutions were tested on the basis of the simulated two-epoch observations of the absolute control network of the Montsalvens dam in Switzerland. The efficacy measure for individual solutions was the mean success rate (MSR).

Keywords:

• Robust M-estimation
• Median
• F-test
• Mean success rate
• Monte Carlo simulations

Acknowledgements

I am very grateful to the reviewers for their constructive comments. This research is supported by the project ‘RIM WIM – Regionalna Inwestycja w Młodych Naukowców Warmii i Mazur – wzrost potencjału wdrożeniowego wyników prac B+R doktorantów’ co-financed by the EU through the European Social Fund.