Study the Behavior of Total Least Squares Technique in Adjusting GPS Field Data - A Case Study

摘要

The main research fields in mathematical and satellite geodesy are computations and adjustment to assess the magnitude of errors and to study their distributions in terms of when they are within the adequate tolerance. In order to achieve this study’s objective, a GPS field direct results were adjusted using Least Squares (LS) and Total Least Squares (TLS) techniques. The difference between the LS and TLS, is that the first recognizes errors only in the observation matrix, adjusting observations in order to get the sum of their squared residuals minimum, whereas the latter acknowledge errors in both the observation matrix and design matrix, which minimizes the noise in both matrices. We used two case studies in this research, the first case study deals with baselines up to 30 km; and second one deals with baselines up to 4 km. The applied two solutions demonstrate that the result from LS technique is approximately the same of TLS on GPS network adjustment in some cases. This study main purpose is to compare the efficiency of the LS and TLS, assessing their individual accuracy and selecting the most effective method in adjusting GPS baselines. Based on statistical indicators of mean and root mean square error each model was assessed. After applying the LS and TLS techniques individually for the same data sets, it is noticed that, LS and TLS in the first case study gave root mean square error equal to 5.01mm and 5.12mm respectively. Again, in the second case study, both techniques gave the same results. Accordingly, this study highlights the efficiency of LS and TLS in solving different problems in satellite geodesy.