M_splittransformation of coordinates

Abstract

The transformation of coordinates allows for the conversion of coordinates from one geodetic system to another. Usually, the determination of transformation parameters is performed by the means of a least squares method. Unfortunately, the least squares method is not immune to outliers. It means that if, for any reason, some reference points are disturbed with gross errors or they belong to two different archival coordinate systems, transformation parameters will be estimated with those errors. Therefore, it is very important to identify incorrect data and remove them from the estimation process or decrease their influence on the estimated parameters. This problem can be solved by applying the M split estimation to calculate transformation parameters. The method of estimation adopted in the paper allows the determination of two competitive vectors of transformation parameters and two competitive residual vectors. The suitability of using the M split estimation method in the process of coordinate transformation was tested on a real geodetic network. In the 'M split estimation' section the authors presents the idea of M split estimation, along with its application to estimation of transformation parameters. The authors performed the calculations in three scenarios: with different number, value and distribution of gross errors respectively. The results of the transformations compared with the catalogue value of coordinates, as well as the differences between coordinates after Helmert transformation, the M split transformation (for the vector of parameters V a ), the M split transformation (for the vector of parameters V b ) and the catalogue coordinates are presented in the 'Numerical example' section.

Outliers Detection by Ransac Algorithm in the Transformation of 2d Coordinate Frames

“…The application of robust estimation methods in the process of coordinate transformation has been tested. The obtained results confirmed the effectiveness of these methods (JANICKA & RAPINSKI, 2013). The biggest problem occurs when the dataset has many points with gross errors in their coordinates.…”

The circle object detection with the use of Msplit estimation

“…It is worth to notice that among the existing applications of Msplit [23] there is lack of practical implementation of using this application for more than 2 spited sets (q>2). As the industrial application of the presented algorithm, the measurements of space with a highly structured form, but unknown objects parameters with circle shapes can be indicated.…”

Verification of a GNSS Time Series Discontinuity Detection Approach in Support of the Estimation of Vertical Crustal Movements

“…In such a situation, a more sophisticated method of model parameters estimation than LS should be used. For example, M split estimation can be used to fit multiple functional models into single data set [22][23][24].…”