Deformation analysis with Total Least Squares

Abstract

Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS) technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS) that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS) and the Total Least Squares (TLS), respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.