ACCURACY ASSESSMENT OF HEIGHTS OBTAINED FROM TOTAL STATION AND LEVEL INSTRUMENT USING TOTAL LEAST SQUARES AND ORDINARY LEAST SQUARES METHODS

Abstract

Spirit levelling has been the traditional means of determining Reduced Levels (RL’s) of points by most surveyors. The assertion that the level instrument is the best instrument for determining elevations of points needs to be reviewed; this is because technological advancement is making the total station a very reliable tool for determining reduced levels of points. In order to achieve the objective of this research, reduced levels of stations were determined by a spirit level and a total station instrument. Ordinary Least Squares (OLS) and Total Least Squares (TLS) techniques were then applied to adjust the level network. Unlike OLS which considers errors only in the observation matrix, and adjusts observations in order to make the sum of its residuals minimum, TLS considers errors in both the observation matrix and the data matrix, thereby minimising the errors in both matrices. This was evident from the results obtained in this study such that OLS approximated the adjusted reduced levels, which compromises accuracy, whereas the opposite happened in the TLS adjustment results. Therefore, TLS was preferred to OLS and Analysis of Variance (ANOVA) was performed on the preferred TLS solution and the RL’s from the total station in order to ascertain how accurate the total station can be relative to the spirit level.

Keywords

• Levelling
• Least Squares
• Analysis of Variance