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Abstract

Summary

This study presents a comprehensive Monte Carlo simulation model developed to thoroughly investigate the behaviour and impact of systematic errors in geodetic angle-measuring instruments. The model is highly flexible and scalable, allowing for the simulation of a wide array of typical systematic errors, including collimation, zero-point, additive and multiplicative distance errors, horizontal axis tilt, and angular eccentricity. By directly simulating measurements and applying these errors, the model enables a detailed analysis of their propagation into X, Y, and Z coordinates across various measurement configurations. A key finding from the simulation results was the identification of a significant linear correlation between planar and vertical coordinate errors. This correlation was primarily attributed to the vertical circle zero-point error. While this error’s most pronounced effect is on the vertical coordinate, the study confirmed its consistent, albeit subtle (typically at the fourth decimal place), influence on planar coordinates. This planar manifestation was found to be dependent on the object’s orientation and the larger linear dimension of the surveyed area. The developed model serves as a powerful tool for quantitatively assessing individual systematic error contributions, understanding their complex interdependencies, and ultimately optimising geodetic measurement practices for enhanced accuracy and reliability.

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2025-10-06
2026-01-24
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References

  1. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML (2011) Supplement 2 to the Guide to the Expression of Uncertainty in Measurement-Extension to any number of output quantities. JCGM 102:2011
    [Google Scholar]
  2. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Evaluation of measurement data – Supplement 1 to the “Guide to the expression of uncertainty in measurement” – Propagation of distributions using a Monte Carlo method. Joint Committee for Guides in Metrology, JCGM 101:2008. doi:10.59161/JCGM101‑2008.
    https://doi.org/10.59161/JCGM101-2008 [Google Scholar]
  3. Bonimani, M. L. S., Rofatto, V. F., Matsuoka, M. T., & Klein, I. (2019). Aplicação de Números Aleatórios Artificiais e Método Monte Carlo na Análise de Confiabilidade de Redes Geodésicas [Application of Artificial Random Numbers and the Monte Carlo Method to Reliability Analysis of Geodetic Networks]. Revista Brasileira de Computação Aplicada, 11(2), 74–85. https://doi.org/10.5335/rbca.v11i2.8906
    [Google Scholar]
  4. DSTU 8955:2019 Metrolohiia. Teodolity i takheometry. Metrolohichni ta tekhnichni vymohy [Metrology. Theodolites and total stations. Metrological and technical requirements]. – Kyiv. DP «UkrNDNTs». – 2020
    [Google Scholar]
  5. Erenoğlu,R. Cüneyt (2018). A Novel Robust Scaling for EDM Calibration Baselines using Monte Carlo Study. Tehnicki vjesnik – Technical Gazette, 25(1). https://doi.org/10.17559/tv-20160407214150
    [Google Scholar]
  6. Niemeier, W., & Tengen, D. (2017). Uncertainty assessment in geodetic network adjustment by combining GUM and Monte-Carlo-simulations. Journal of Applied Geodesy, 11(2). https://doi.org/10.1515/jag-2016-0017
    [Google Scholar]
  7. Savchyn, I., Tretyak, K., Brusak, I., Lozynskyi, V., & Duma, M. (2023, October). Rapid Fixation and Digitization for Cultural Heritage Preservation in Conflict Zones. In International Conference of Young Professionals «GeoTerrace-2023» (Vol. 2023, No. 1, pp. 1–5). European Association of Geoscientists & Engineers. https://doi.org/10.3997/2214-4609.2023510030
    [Google Scholar]
  8. Shults, R. V., & Sossa, B. R. (2015). Systemne kalibruvannia nazemnykh lazernykh skaneriv: modeli ta metodyky [System calibration of terrestrial laser scanners: models and methodologies]. Visnyk heodezii ta kartohrafii, (2), 25–30.
    [Google Scholar]
  9. Sossa, B. & Havryshchuk, V. (2025). Vykorystannia metodu Monte-Karlo pry doslidzhenni pokhybok heodezychnykh pryladiv [Application of the Monte Carlo method in the study of errors of geodetic instruments]. Technical sciences and technologies. Scientific journal. 2(40), 472–484https://doi.org/10.25140/2411-5363-2025-2(40)-472-484
    [Google Scholar]
  10. Tomczyk, K. (2018). Influence of Monte Carlo generations applied for modelling of measuring instruments on maximum distance error. Transactions of the Institute of Measurement and Control, 41(1), 74–84. https://doi.org/10.1177/0142331217753062
    [Google Scholar]
  11. Wang, L., & Luo, X. (2021). Adaptive Quasi-Monte Carlo method for nonlinear function error propagation and its application in geodetic measurement. Measurement, 186, 110122. https://doi.org/10.1016/j.measurement.2021.110122
    [Google Scholar]
  12. Wyszkowska, P. (2017). Propagation of uncertainty by Monte Carlo simulations in case of basic geodetic computations. Geodesy and Cartography, 66(2), 333–346. https://doi.org/10.1515/geocart-2017-0022
    [Google Scholar]
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