The processing of GNSS observation by non-classical error theory of measurements
Received: April 14, 2020
Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University

The main goal of our research is to show the need to use modern methods of processing GNSS observations time series by non-classical error theory of measurements (NETM), which is characterized by large sample sizes n > 500. The errors of high-precision observations, for the most part, cannot be represented by the classical law of Gaussian distribution. With the increase in sample size, the empirical error distribution will increasingly deviate from the classical Gaussian error theory of measurements (CETM). Methods. For this research we pre-processed GNSS observation at five permanent stations in Ukraine (SULP, GLSV, POLV, MIKL and CRAO). After applying the "clean" procedures based on the iGPS software package, we obtained the GNSS observation time series for 2018-2020. The verification of empirical error distributions was ensured by the procedure of non-classical error theory of measurements, based on the recommendations offered by G. Jeffreys and on the principles of hypothesis testing according to Pearson criteria. Results. It has been established that the coordinate time series of permanent stations obtained from precision GNSS observations do not confirm the hypothesis of their conformity to normal Gaussian distribution law. NETM diagnostics of the accuracy of high-precision GNSS measurements, which is based on the use of confidence intervals for estimates of asymmetry and kurtosis of a large sample, followed by the Pearson test, confirms the presence of weak, non-GNSS-treated sources of systematic errors. Scientific novelty. The authors use the possibility of NETM to improve the method of processing high-precision GNSS measurements and necessity to take into account sources of systematic errors. The failure to account for individual factors creates the effect of shifting the coordinate time series, which, in turn, leads to subjective estimates of station movement velocities, their geodynamic interpretation. Practical significance is based on the application of NETM diagnostics of probabilistic form of permanent stations topocentric coordinates  distribution and improvement of the method of their determination. Research of the causes of the error distribution deviations from the established norms ensures the metrological literacy of large amount high-precision GNSS measurements.

  1. 1. Bogusz, J., & Klos, A. (2016). On the significance of periodic signals in noise analysis of GPS station coordinates time series. GPS Solutions, 20(4), 655-664.
    2. Bos, M.S., Fernandes, R.M.S., Williams, S.D.P., & Bastos, L. (2013). Fast error analysis of continuous GNSS observations with missing data. J. Geod., 87, 351-360.
    3. GIPSY X Software [Electronic resource]. - Access mode:
    4. GNSS Time Series [Electronic resource]. - Access mode:
    5. Dvulit, P., & Dzhun, J., (2017). Application of non-classical error theory methods for absolute measurements of Galilean acceleration. Geodynamics. (1 (22)), 7-15. [in Ukrainian]
    6. 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.
    7. Dzhun, J. (2015). Non-classical theory of measurement errors. Vydavnychyi dim: «Estero», Rivne. 168 p. [in Russian]
    8. Héroux, P., & Kouba, J. (1995). GPS precise point positioning with a difference. Natural Resources Canada, Geomatics Canada, Geodetic Survey Division.
    9. Herring, T. (2003). MATLAB Tools for viewing GPS velocities and time series. GPS Solut., 7, 194-199.
    10. Hofmann-Wellenhof, B., Lichtenegger, H., & Wasle, E. (2007). GNSS-global navigation satellite systems: GPS, GLONASS, Galileo, and more. Springer Science & Business Media.
    11. Jiang, W, He, X., Montillet, J. P., Fernandes, R., Bos, M., Yu, K., Hua, X., & Jiang, W. (2017). Review of current GPS methodologies for producing accurate time series and their error sources. Journal of Geodynamics, 106, 12-29.
    12. 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.
    13. Leandro, R. F., Santos, M. C., & Langley, R. B. (2011). Analyzing GNSS data in precise point positioning software. GPS solutions, 15(1), 1-13.
    14. Li, G., Wu, J., Zhao, C., & Tian, Y. (2017). Double differencing within GNSS constellations. GPS Solutions, 21(3), 1161-1177.
    15. 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.
    16. Ray, J., Griffiths, J., Collilieux, X., & Rebischung, P. (2013). Subseasonal GNSS positioning errors. Geophysical Research Letters, 40(22), 5854-5860.
    17. Savchuk, S., & Doskich, S. (2017). Monitoring of crustal movements in Ukraine using the network of reference GNSS-stations. Scientific journal" Geodynamics, 2(23), 7-13. DOI: 10.23939/jgd2017.02.007
    18. Tian Y.( 2011). iGPS: IDL tool package for GPS position time series analysis. GPS Solutions., 15(3), 299-303. DOI: 10.1007/s10291-011-0219-7
    19. Williams, S.D.P.( 2008). CATS: GPS coordinate time series analysis software. GPS Solut., 12, 147-153.