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

Abstract

Survey measurements have become the traditional means of obtaining point positions by most surveyors over the centuries. The assertion that a post processed DGPS field data is precise, accurate and can be used to execute any engineering works due to its minimum human errors need to be reviewed; this is because the post processed field data still contains errors and needs to be adjust. Adjustments and computations is one of the main research field in mathematical and satellite geodesy to assess the magnitude of errors and to study their distributions whether they are within or not within the acceptable tolerance. In order to achieve the objective of this study, a DGPS field data was adjusted using the Ordinary Least Square (OLS) and Total Least Square (TLS) techniques. The OLS considers errors only in the observation matrix, and adjusts observations in order to make the sum of its residuals minimum. The TLS considers errors in both the observation matrix and the data matrix, thereby minimizing the errors in both matrices. The limited availability of information on OLS and TLS in adjusting DGPS field data and the uncertainty of which method is optimal, whether the OLS and TLS is the most appropriate technique has called for the need to undertake this study. This study aimed at comparing the working efficiency of the OLS and TLS, assessing their individual accuracy and selecting the most effective method in adjusting DGPS field data. Each model was assessed based on statistical indicators of mean horizontal error (MHE), mean bias error (MBE), mean absolute error (MAE), root mean square error (RMSE), and standard deviation (SD). After applying the OLS and TLS methods independently for the same datasets, it was ascertained that, the OLS method was better in adjusting DGPS field data than the TLS with a MHE and SD of +1.203079 m and +1.663134 m as compared to TLS with MHE and SD of +7.0985507 m  and +2.594045 m respectively. This study will therefore create opportunity for geospatial professionals to know the efficiency of OLS and TLS in solving some of the problems in mathematical and satellite geodesy.

Keywords: Differential Global Positioning, System, Total Least Square, Ordinary Least Square, Survey Adjustments, Horizontal Position Displacement