Outlier Detection with Robust Exact and Fast Least Trimmed Squares Methods in Coordinate Transformation

Abstract

Different terrestrial reference systems have been defined and used because of some practical and historical events in geodesy domain. The transition from one system to another requires the coordinate transformation. Helmert transformation is the most commonly used model for 2D networks. 2D Helmert transformation are defined by four transformation parameters and two common points in both coordinate systems provides a unique solution. To increase the reliability of the transformation parameters, redundant observations are generally used. In this case, the Least Squares (LS) is the most common method used to obtain the unique solution from redundant observations. However, outliers occur often in dataset and affect severely the results of LS. There are generally two approaches applied for outlier detection: classical outlier tests and robust methods. The most common robust methods are Least Absolute Deviation (L<inf>1</inf> ), M-estimators, the Total Least Squares (TLS), Generalised M-estimators, the Least Median of Squares (LMS) and the Least Trimmed Squares (LTS). For the solution of the LTS method, there are exact and approximate solutions. In this study, 2D Helmert transformation parameters between ED50 and ITRF coordinates are esti-mated with the LS method including classical outlier test, exact LTS solution and Fast-LTS solution which is an approximate solution to compare outlier detection performances of the methods. © 2023, Croatian Geodetic Society. All rights reserved.