MEASUREMENT ERRORS IN GEODESY
Keywords:
Geodesy; measurement error; random error; systematic error; gross error; error propagation; least-squares adjustment; GNSS; EDM; levelling.Abstract
Errors accompany every geodetic observation, whether the observation is a zenith angle read with a theodolite, a carrier-phase measurement on a GNSS receiver, or a gravity reading with a spring gravimeter. Their presence does not mean a survey is unreliable; it simply means that uncertainty must be quantified and minimised by careful instrument design, thoughtful field procedure and rigorous adjustment computation. This paper classifies measurement errors in geodesy into random, systematic and gross varieties, reviews their physical origins, outlines statistical tools for their propagation, and demonstrates practical mitigation strategies. A comparative experiment using electronic total-station distance observations, dual-frequency GNSS baselines and differential levelling loops illustrates how error characteristics differ across techniques.
References
Wolf, P. R., & Ghilani, C. D. (2012). Elementary Surveying (14th ed.). New York: Pearson. [Wolf & Ghilani, 2012, 103]
Vaníček, P., & Krakiwsky, E. J. (1986). Geodesy: The Concepts (2nd ed.). Amsterdam: North-Holland. [Vaníček & Krakiwsky, 1986, 34]
Gauss, C. F. (1823). Theoria Combinationis Observationum Erroribus Minimis Obnoxiae. Göttingen. [Gauss, 1823, 8]
Helmert, F. R. (1907). Die Ausgleichungsrechnung. Leipzig: Teubner. [Helmert, 1907, 52]
Hofmann-Wellenhof, B., Lichtenegger, H., & Wasle, E. (2008). GNSS – Global Navigation Satellite Systems: GPS, GLONASS, Galileo & more. Vienna: Springer. [Hofmann-Wellenhof et al., 2008, 147]
Leick, A. (2015). GPS Satellite Surveying (4th ed.). Hoboken: Wiley. [Leick, 2015, 212]
Teunissen, P. J. G. (2006). Testing theory—An overview. Integrated Geospatial Technologies, 112–164. [Teunissen, 2006, 117]
Kukkamäki, T. J. (1938). The influence of refraction in precise levelling. Fennia, 61, 1–56. [Kukkamäki, 1938, 19]
Nassar, S., & Wang, J. (2019). Calibration of reflectorless EDM. Survey Review, 51(364), 202-214. [Nassar & Wang, 2019, 203]
Ritter, R., Jones, R., & Schaffrin, B. (2020). Robust M-estimators in deformation monitoring. Journal of Applied Geodesy, 14(2), 89-105. [Ritter et al., 2020, 92]
