GNSS Vector Networks in a Local Conventional Reference Frame
Source abstract
Abstract
The paper presents a proposal for a simple method of transforming initial GNSS vectors into a spatial local conventional reference frame. This transformation can serve as an alternative to the complex traditional procedure, which involves projecting coordinates onto a reference ellipsoid, mapping them onto a plane of an official local reference frame, and converting ellipsoidal heights into a system of orthometric heights. Local vectors (increments in horizontal coordinates and height differences) are often used in land surveying to analyse relative ground displacement, for example. The article offers a detailed definition of a local conventional reference frame and discusses its potential value for surveying practice. The proposed computation procedure was verified using a control network established to monitor displacement in a mining area. The calculated values of vector components in the local conventional reference frame were compared with the results of the traditional method for transforming GNSS vectors into official local reference frames (the PL-2000 coordinate system and the PL-EVRF2007-NH vertical reference frame). The results of both methods were verified against reference values from typical terrestrial surveys (electronic distance measurement and high-precision geometric levelling). The analysis demonstrates that the proposed numerical procedure is appropriate for control networks with certain areal limitations (up to about 300 m).
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Geodetic Measurements and Engineering Structures · GNSS positioning and interference · Geophysics and Gravity Measurements
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Geodesy, Faculty of Environmental Engineering and Land Surveying, University of Agriculture in Krakow, 253a Balicka Street, 30-149 Krakow, Poland
Funding
Ministry of Science and Higher Education
References (43)
Show source-provided references
1. Analysis of Coordinates Time Series Obtained Using the NAWGEO Service of the ASG-EUPOS System
2. Routing corners of building structures—By the method of vector addition—Surveyed with RTN GNSS technology using indirect methods of measurement
3. Satellite leveling as an alternative to classic height measurements for typical engineering problems
4. Modelling the Velocity Field in a Regular Grid in the Area of Poland on the Basis of the Velocities of European Permanent Stations10.1007/s00024-013-0645-2 ↗
5. Operation of ASG-EUPOS POZGEO sub-service in the event of failure of reference stations used in the standard solution—Case study
6. Head Office of Geodesy and Cartography in Poland (2008). Technical Guidelines G-1.12. Satellite Measurements Based on the ASGEUPOS Precise Positioning System—Draft Dated March 1, 2008, with Amendments, (In Polish).
7. Acosta, L.E., De Lacy, M.C., Ramos, M.I., Cano, J.P., Herrera, A.M., Avilés, M., and Gil, A.J. (2018). Displacements study of an earth fill dam based on high precision geodetic monitoring and numerical modeling. Sensors, 18.10.3390/s18051369 ↗
8. A concept of using static GPS measurements for determination of vertical and horizontal land deformations in the Main and Old City of Gdansk
9. A kinematic model of a modular network as applied for the determination of displacements
10. Gargula, T. (2011). Integrated Modular Networks in the Application for Determination of the Displacements, Zeszyty Naukowe Uniwersytetu Rolniczego. (In Polish).
11. Kadaj, R. (1998). Models, Methods and Computing Algorithms of Kinematic Networks in Geodetic Measurements of Movements and Deformation of Objects, Publishing House of Agricultural University of Krakow. (In Polish).
12. Preweda, E. (2002). Estymacja Parametrów Kinematycznego Modelu Przemieszczeń (Estimation of Parameters of the Kinematic Displacement Model), Wydawnictwo Naukowe i Dydaktyczne AGH. (In Polish).
13. Prószyński, W., and Kwaśniak, M. (2006). Basics of the Geodetic Assignation of Movements. Concepts and Elements of the Methodology, Publishing House of Warsaw University of Technology. (In Polish).
14. Geodetic monitoring of a landslide using conventional surveys and GPS techniques10.1179/175227007X197165 ↗
15. Wiśniewski, Z., and Kamiński, W. (2020). Estimation and Prediction of Vertical Deformations of Random Surfaces, Applying the Total Least Squares Collocation Method. Sensors, 20.10.3390/s20143913 ↗
16. GPS postprocessing module in GEONET system
17. Validation of the number of tie vectors in post-processing using the method of frequency in a centric cube10.1515/geo-2020-0057 ↗
18. Czarnecki, K. (2010). Contemporary Geodesy, Gall. (In Polish).
19. Leick, A. (2004). GPS Satellite Surveying, John Wiley & Sons. Inc.
20. Seeber, G. (2003). Satellite Geodesy, Walter de Gruyter.10.1515/9783110200089 ↗
21. Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J. (2001). Global Positioning System: Theory and Practice, Springer. Available online: https://link.springer.com/book/10.1007/978-3-7091-6199-9.10.1007/978-3-7091-6199-9 ↗
22. Head Office of Geodesy and Cartography in Poland (2001). Technical Guidelines G-1.10. Cartographic Projection Formulas and Coordinate System Parameters, (In Polish).
23. Łyszkowicz, A. (2024). Geodetic Systems and Reference Frames, (In Polish).
24. Direct determination of local coordinates from GPS without transformation10.1179/003962609X390076 ↗
25. GPS Vector Network Adjustment in a Local System of Coordinates Based on Linear-Angular Spatial Pseudo-Observations10.1061/(ASCE)SU.1943-5428.0000042 ↗
26. Global, Regional and National Geodetic Reference Frames for Geodesy and Geodynamics10.1007/s00024-013-0676-8 ↗
27. Hlibowicki, R., Krzywicka-Blum, E., Galas, R., Borkowski, A., Osada, E., and Cacoń, S. (1988). Advanced Geodesy and Geodetic Astronomy, PWN. (In Polish).
28. Transformations between the height reference frames: Kronsztadt’60, PL-KRON86-NH, PL-EVRF2007-NH
29. Study on choice of global geopotential model for quasi-geoid determination in Poland
30. Geoid in the area of Poland in the author’s investigations
31. Head Office of Geodesy and Cartography in Poland (2025, October 07). Model of the Valid Quasi-Geoid PL-Geoid2021 in the PL-EVRF2007-NH System, (In Polish).
32. Beluch, J. (1981). Detailed Situational and Height Geodetic Networks Determined in a Conventional Spatial System, Zeszyty Naukowe Akademii Górniczo-Hutniczej. (In Polish).
33. Lazzarini, T., Hermanowski, A., Gaździcki, J., Dobrzycka, M., and Laudyn, I. (1990). Geodesy—Detailed Geodetic Control Network, PPWK. (In Polish).
34. (2025, October 07). Regulation of the Council of Ministers in Poland of 15 October 2012 on the National Spatial Reference System, (In Polish).
35. Wiśniewski, Z. (2005). Adjustment Calculus in Geodesy, Publications of University of Warmia and Mazury in Olsztyn. (In Polish).
36. Ghilani, C.D. (2018). Adjustment Computations: Spatial Data Analysis, John Wiley & Sons. Inc.10.1002/9781119390664 ↗
37. Gargula, T. (2021). Adjustment of an Integrated Geodetic Network Composed of GNSS Vectors and Classical Terrestrial Linear Pseudo-Observations. Appl. Sci., 11.10.3390/app11104352 ↗
38. Point position accuracy in a vector GNSS Network and the way it is linked to reference stations
39. GeoNet Geodetic System (2025, October 07). AlgoRes-Soft. (In Polish).
40. Head Office of Geodesy and Cartography in Poland (2025, October 07). Transpol v.20.6, A Computer Program for Transforming Coordinates and Heights in the National Spatial Reference System, (In Polish).
41. The Helmert transformation: A proposal for the problem of post-transformation corrections
42. Geodetic reference frames transformations10.1179/sre.2006.38.301.608 ↗
43. A generalized method for determination of point displacements in control networks, based on the modified method of observation differences