Deformation analysis with Total Least Squares

Abstract

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.

The contribution of engineering surveys by means of GPS to the determination of crustal movements in Istanbul

“…Then the network was minimally constrained by fixing the ITRF96, epoch 1998.0, coordinates of ANKR only in order to avoid any datum effects within the internal geometry of the network. For deformation analysis, a conventional similarity-transformation based deformation analysis procedure was applied as described by Acar et al (2006). The movements of stations estimated with a confidence level of 0.95.…”

Performance evaluation of the Ordinary Least Square (OLS) and Total Least Square (TLS) in adjusting field data: an empirical study on a DGPS data

“…In the classical least square techniques, adjustment of the observation equations where only the observations are considered as stochastic (Acar et al, 2006). In some instances, the design matrix elements contain errors which are usually ignored in the classical least techniques and this ignorance remains as an uncertainty in the solution results (Acar et al, 2006).…”

“…The errors remain in the data could be adjusted. Several adjustment methods exist such as ordinary least squares (Annan et al, 2016a;Okwuashi and Eyoh, 2012a), Total least squares (Acar et al, 2006;Annan et al, 2016b;Okwuashi and Eyoh, 2012b), robust estimation (Wieser and Brunner, 2001), least square collocation (LSC) (Moritz, 1972). Conversely, there is a common belief that data obtain from the GPS instrument are very precise and accurate due to less interference of humans in the collection process and can be used to execute any given task without further adjustments.…”

“…Usually, adjustment is done using classical approach such as ordinary least approach (Annan et al, 2016a;Okwuashi & Eyoh, 2012b), but the ordinary least square which is based on regression analysis considers only the observations to be stochastic (Acar et al, 2006) and thus account for errors only in the observation vector. Conversely, there exist errors in both the design and observation matrices which ought to be modelled out (Annan et al, 2016a).…”

“…The total least squares (TLS) was invented to resolve the working efficiency of the OLS (Annan et al, 2016a). The TLS have the ability to adjust the errors in both the observation matrix and design matrix (Acar et al, 2006) in order to yield a better estimate. The limited availability of technical papers in geodesy on TLS have called for the need to undergone this study.…”