Diagnosis of metrological characteristics of highprecision GNSS observations by methods of non-classical error theory of measurements

Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University

The aim of the research is to diagnose the metrological characteristics of high-precision GNSS-observations by methods of non-classical error theory of measurements (NETM) based on Ukrainian reference stations. Methodology. We selected 72 GNSS reference stations, downloaded daily observation files from the LPI analysis center server, and created time series in the topocentric coordinate system. The duration of the time series is almost two years (March 24, 2019 - January 2, 2021). Using a specialized software package, the time series have been cleaned of offsets and breaks, seasonal effects, and the trend component has been removed. Verification of empirical distributions of errors was provided by the procedure of NETM on the recommendations offered by G. Jeffries and on the principles of hypothesis tests the theory according to Pearson's criterion. The main result of the research. It is established that the obtained time series of coordinates of reference GNSS stations do not confirm the hypothesis of their conformity to the normal Gaussian distribution law. NETM diagnostics of the accuracy of high-precision GNSS measurements, which is based on the use of confidence intervals for assessing the asymmetry and kurtosis of a significant sample, followed by the Pearson test, confirms the presence of weak, not removed from GNSS-processing, sources of systematic errors. Scientific novelty. The authors use the possibility of NETM to improve the processing of high-precision GNSS measurements and the need to take into account the sources of systematic errors. Failure to take into account certain factors creates the effect of shifting the time coordinate series, which, in turn, leads to subjective estimates of station velocity, i.e. their geodynamic interpretation. Practical significance. Research of the reasons for deviations of errors distribution from the established norms provides metrological literacy of carrying out high-precision GNSS measurements of large samples.

1. Blewitt, G., & Lavallée, D. (2002). Effect of annual signals on geodetic velocity.J. Geophys. Res. Solid Earth, vol. 107, no. B7, pp. ETG 9-11.
2. Dvulit, P. D., & Dzhun, I. V. (2017). Application of methods of the non-classical error theory in absolute measurements of galilean acceleration. Geodynamics, 1(22), 7-15. (in Ukrainian). 
3. Dzhun, I. V. (2015). Nonclassical errors theory of measurements. Publishing house: "Estero", Rivne. 168 p. (in Russian).
4. Dvulit, P., & Dzhun, J. (2019). Diagnostics of the high-precise ballistic measured gravity acceleration by methods of non-classical errors theory. Geodynamics, 1(26), 5-16. 
5. Dvulit, P., Savchuk, S., & Sosonka, I. (2020). The processing of GNSS observation by non-classical error theory of measurements, Geodynamics, 1(28) 19-28. 
6. Karaim, M., Elsheikh, M., Noureldin, A., & Rustamov, R. B. (2018). GNSS error sources. Multifunctional Operation and Application of GPS; Rustamov, RB, Hashimov, AM, Eds, 69-85. 
7. Herring, T. (2003). MATLAB Tools for viewing GPS velocities and time series. GPS Solut., 7, 194-199. 
8. Jiang, W, He, X., Montillet, J.-P., Fernandes, R., Bos, M., Hua, X., Yu, K., et al. (2017). Review of current GPS methodologies for producing accurate time series and their error sources. Journal of Geodynamics, 106, 12-29. 
9. Maciuk, K., Vārna, I., & Xu, C. (2020).Characteristics of seasonal variations and noises of the daily double-difference and PPP solutions. Journal of Applied Geodesy, 2021; 15(1): 61-73. 
10. Ostini, L., Dach, R., Meindl, M., Schaer, S., Hugentobler, U.( 2008). FODITS: A New Tool of the Bernese GPS Software. In Proceedings of the 2008 European Reference Frame (EUREF), Brussels, Belgium, 18-21 June 2008; Torres, J.A., Hornik, H., Eds.
11. Tian Y.( 2011). iGPS: IDL tool package for GPS position time series analysis. GPS Solutions., 15(3),299-303. 
12. Van Dam, T., J. Wahr, P. C. D. Milly, A. B. Shmakin, G. Blewitt, D. Lavallee, K. M. Larson, (2001). Crustal displacements due to continental water loading, Geophys. Res. Lett., 28, 651- 654.
13. Wdowinski, S., Y. Bock, J. Zhang, P. Fang, J. Gengrich. (1997). Southern California Permament GPS Geodetic Array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake, J. Geophys. Res., 102, 18,057- 18,070.
14. Williams, S.D.P.(2008). CATS: GPS coordinate time series analysis software. GPS Solut., 12, 147-153.