Error Propagation of the Hidden-Point Bar Method: Effect of Bar Geometry
The hidden-point bar method is useful in many
surveying applications. The method involves determining the
coordinates of a hidden point as a function of horizontal and vertical
angles measured to three fixed points on the bar. Using these
measurements, the procedure involves calculating the slant angles,
the distances from the station to the fixed points, the coordinates of
the fixed points, and then the coordinates of the hidden point. The
propagation of the measurement errors in this complex process has
not been fully investigated in the literature. This paper evaluates the
effect of the bar geometry on the position accuracy of the hidden
point which depends on the measurement errors of the horizontal and
vertical angles. The results are used to establish some guidelines
regarding the inclination angle of the bar and the location of the
observed points that provide the best accuracy.
[1] A. L. Allan, Practical surveying and computations. Butterworth-
Heinemann, Oxford, U.K, 1997.
[2] W. F. Teskey, R. J. Fox, and D. H. Adler, "Hidden point bar method for
precise heighting." J. Survey. Eng., vol. 130, no. 4, pp. 179-182, 2004.
[3] L. M. Sebert, "Resections revisited." Geomatica, vol. 50, no. 3, pp. 310-
311, 1996.
[4] W. F. Teskey, B. Paul, and W. J. Teskey, 2005. "Hidden point bar
method for high-precision industrial surveys." J. Survey. Eng., vol. 131,
no. 4, pp. 103-106, 2005.
[5] A. Antonopoulos, "Fixation by Hidden Points Bar from One
Theodolite." J. Survey. Eng., vol. 131, no. 4, pp. 113-117, 2005.
[6] M. Recoskie, L. Le, and M. Berber, Current technology and new
techniques for total station surveys of inaccessible points. CD-Rom
Proceedings, Annual Conference of the Canadian Society for Civil
Engineering, Quebec, QC, 2008.
[7] J. M. Anderson, and E. M. Mikhail, Surveying: Theory and practice.
McGraw Hill, New York, ch. 2, 1998.
[8] Ghilani, C.D., and P.R. Wolf, Adjustment computations: Spatial data
analysis. John Wiley & Sons , New York, ch. 6, 2006.
[9] P. Venkataraman, Applied optimization with MATLAB® programming.
John Wiley, New York, U.S.A., 2002.
[10] A. Antonopoulos, Personal notes on industrial surveying practicals.
University College London, London, 1994.
[11] S. M. Easa, "Direct distance-based positioning without redundancy - In
land surveying." J. Survey. and Land Info. Science, vol. 67, no. 2, pp.
69-74, 2007.
[12] E. El-Hasan, "Analysis of the three-point resection accuracy." The
Australian Surveyor, vol. 34, no. 7, pp. 716-727, 1989.
[1] A. L. Allan, Practical surveying and computations. Butterworth-
Heinemann, Oxford, U.K, 1997.
[2] W. F. Teskey, R. J. Fox, and D. H. Adler, "Hidden point bar method for
precise heighting." J. Survey. Eng., vol. 130, no. 4, pp. 179-182, 2004.
[3] L. M. Sebert, "Resections revisited." Geomatica, vol. 50, no. 3, pp. 310-
311, 1996.
[4] W. F. Teskey, B. Paul, and W. J. Teskey, 2005. "Hidden point bar
method for high-precision industrial surveys." J. Survey. Eng., vol. 131,
no. 4, pp. 103-106, 2005.
[5] A. Antonopoulos, "Fixation by Hidden Points Bar from One
Theodolite." J. Survey. Eng., vol. 131, no. 4, pp. 113-117, 2005.
[6] M. Recoskie, L. Le, and M. Berber, Current technology and new
techniques for total station surveys of inaccessible points. CD-Rom
Proceedings, Annual Conference of the Canadian Society for Civil
Engineering, Quebec, QC, 2008.
[7] J. M. Anderson, and E. M. Mikhail, Surveying: Theory and practice.
McGraw Hill, New York, ch. 2, 1998.
[8] Ghilani, C.D., and P.R. Wolf, Adjustment computations: Spatial data
analysis. John Wiley & Sons , New York, ch. 6, 2006.
[9] P. Venkataraman, Applied optimization with MATLAB® programming.
John Wiley, New York, U.S.A., 2002.
[10] A. Antonopoulos, Personal notes on industrial surveying practicals.
University College London, London, 1994.
[11] S. M. Easa, "Direct distance-based positioning without redundancy - In
land surveying." J. Survey. and Land Info. Science, vol. 67, no. 2, pp.
69-74, 2007.
[12] E. El-Hasan, "Analysis of the three-point resection accuracy." The
Australian Surveyor, vol. 34, no. 7, pp. 716-727, 1989.
@article{"International Journal of Architectural, Civil and Construction Sciences:63228", author = "Said M. Easa and Ahmed Shaker", title = "Error Propagation of the Hidden-Point Bar Method: Effect of Bar Geometry", abstract = "The hidden-point bar method is useful in many
surveying applications. The method involves determining the
coordinates of a hidden point as a function of horizontal and vertical
angles measured to three fixed points on the bar. Using these
measurements, the procedure involves calculating the slant angles,
the distances from the station to the fixed points, the coordinates of
the fixed points, and then the coordinates of the hidden point. The
propagation of the measurement errors in this complex process has
not been fully investigated in the literature. This paper evaluates the
effect of the bar geometry on the position accuracy of the hidden
point which depends on the measurement errors of the horizontal and
vertical angles. The results are used to establish some guidelines
regarding the inclination angle of the bar and the location of the
observed points that provide the best accuracy.", keywords = "Hidden point, accuracy, error propagation,surveying, evaluation, simulation, geometry.", volume = "4", number = "8", pages = "272-7", }