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

DOI: https://doi.org/10.14710/geoplanning.3.2.87-92
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Article Metrics: (Click on the Metric tab below to see the detail)

Article Info
Published: 25-10-2016
Section: Articles
Fulltext PDF Tell your colleagues Email the author

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

  1. Richard Fiifi Annan 
    University of Mines and Technology, Ghana
  2. Yao Yevenyo Ziggah 
    University of Mines and Technology, Ghana
  3. John Ayer 
    Kwame Nkrumah University of Science and Technology, Ghana
  4. Christian Amans Odutola 
    China University of Geosciences, Wuhan, China
  1. Acar, M., et al. (2006). Deformation analysis with total least squares. Natural Hazards and Earth System Science, 6(4), 663–669.
  2. Google Scholar [↗]
  3. Akyilmaz, O. (2007). Total least squares solution of coordinate transformation. Survey Review, 39(303), 68–80.
  4. CrossRef [↗] | Google Scholar [↗]
  5. Brown, L. C., & Berthouex, P. M. (2002). Statistics for Environmental Engineers. CRC press.
  6. Google Scholar [↗]
  7. Ghilani, C. D., & Wolf, P. R. (2014). Elementary Surveying (13th ed.). Pearson Education Inc., Upper Saddle River, New Jersey.
  8. Google Scholar [↗]
  9. Golub, G. H., & van Loan, C. F. (1980). An analysis of the total least squares problem. SIAM Journal on Numerical Analysis, 17(6), 883–893.
  10. CrossRef [↗] | Google Scholar [↗]
  11. Jackson, S. L. (2013). Statistics Plain and Simple. Cengage Learning, Boston.
  12. Google Scholar [↗]
  13. Jin, Y., Tong, X., & Li, L. (2011). Total least squares with application in geospatial data processing. In Geoinformatics, 2011 19th International Conference on (pp. 1–3).
  14. CrossRef [↗] | Google Scholar [↗]
  15. Lee, J., & Rho, T. (2001). Application to leveling using total station. In New Technology for a New Century International Conference FIG Working Week 2001. Seoul, Korea: FIG Conference Proceedings.
  16. Google Scholar [↗]
  17. Markovsky, I., & Van Huffel, S. (2007). Overview of total least-squares methods. Signal Processing, 87(10), 2283–2302.
  18. CrossRef [↗] | Google Scholar [↗]
  19. Okwuashi, O., & Eyoh, A. (2012a). 3D coordinate transformation using total least squares. Academic Research International, 3(1), 399–405.
  20. Google Scholar [↗]
  21. Okwuashi, O., & Eyoh, A. (2012b). Application of total least squares to a linear surveying network. Journal of Science and Arts, 4(21), 401–404.
  22. Google Scholar [↗]
  23. Rutherford, A. (2001). Introducing ANOVA and ANCOVA: a GLM approach. SAGE Publications Ltd., London.
  24. Google Scholar [↗]
  25. Schofield, W., & Breach, M. (2007). Engineering Surveying (6th ed.). Elsevier Ltd, Oxford, Great Britain.
  26. Google Scholar [↗]
  27. Uren, J., & Price, W. F. (2010). Surveying for engineers (4th ed.). Palgrave Macmillan, New York.
  28. Google Scholar [↗]