{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:46:18Z","timestamp":1760143578292,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T00:00:00Z","timestamp":1708473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The time series of GNSS coordinates contain signals caused by the age-related movement of tectonic plates, the deformation of the Earth\u2019s surface, as well as errors at different time scales from sub-daily tidal deformation to the long-term deformation of the surface load. Depending on the nature of the signal, specific approaches are used for both the visual interpretation and pre-processing of time series and their statistical analysis. However, none of the present software analyzes the nature of the residual errors but assumes their random nature and obedience to the classical normal distribution. One of the methods for analyzing the time series of coordinates with residual, unaccounted-for systematic errors is the non-classical error theory of measurements. The result of this work is a developed software solution for analyzing the time series of GNSS coordinates to test their normality, or in other words, to test whether a particular GNSS station is subject to the influence of small, unaccounted-for errors. Conclusions: After testing our software on four reference stations in Europe, we concluded that none of the chosen stations followed the normal law of distribution; thus, it is vital to perform such tests before conducting any experiments on the time series from reference stations.<\/jats:p>","DOI":"10.3390\/rs16050757","type":"journal-article","created":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T10:52:00Z","timestamp":1708512720000},"page":"757","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Python Software Tool for Diagnostics of the Global Navigation Satellite System Station (PS-NETM)\u2013Reviewing the New Global Navigation Satellite System Time Series Analysis Tool"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2475-9666","authenticated-orcid":false,"given":"Stepan","family":"Savchuk","sequence":"first","affiliation":[{"name":"Institute of Navigation, Military University of Aviation, 08-521 Deblin, Poland"}]},{"given":"Petro","family":"Dvulit","sequence":"additional","affiliation":[{"name":"Department of Geodesy and Astronomy, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"given":"Vladyslav","family":"Kerker","sequence":"additional","affiliation":[{"name":"Department of Geodesy and Astronomy, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"given":"Daniel","family":"Michalski","sequence":"additional","affiliation":[{"name":"Security Studies Department, Military University of Aviation, 08-521 Deblin, Poland"}]},{"given":"Anna","family":"Michalska","sequence":"additional","affiliation":[{"name":"Logistic and Transport Institute, Military University of Aviation, 08-521 Deblin, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,21]]},"reference":[{"key":"ref_1","unstructured":"Bock, Y., and Wdowinski, S. (2020). Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, IEEE."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.jog.2017.01.004","article-title":"Review of current GPS methodologies for producing accurate time series and their error sources","volume":"106","author":"He","year":"2017","journal-title":"J. Geodyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"B03405","DOI":"10.1029\/2005JB003806","article-title":"Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis","volume":"111","author":"Dong","year":"2006","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s00190-016-0973-y","article-title":"Spatiotemporal filtering for regional GPS network in China using independent component analysis","volume":"91","author":"Ming","year":"2017","journal-title":"J. Geod."},{"key":"ref_5","first-page":"4383","article-title":"Extraction of common mode errors of GNSS coordinate time series based on multi-channel singular spectrum analysis","volume":"61","author":"Zhou","year":"2018","journal-title":"Chin. J. Geophys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1002\/2015JB012253","article-title":"Extracting the regional common-mode component of GPS station position time series from dense continuous network","volume":"121","author":"Tian","year":"2016","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bos, M.S., Montillet, J.P., Williams, S.D.P., and Fernandes, R.M.S. (2019). Introduction to Geodetic Time Series Analysis, Springer.","DOI":"10.1007\/978-3-030-21718-1"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2500","DOI":"10.1029\/2009JB006543","article-title":"Long GPS coordinate time series: Multipath and geometry effects","volume":"115","author":"King","year":"2010","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1007\/s10291-017-0637-2","article-title":"TSAnalyzer, a GNSS time series analysis software","volume":"21","author":"Wu","year":"2017","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/s10291-019-0846-y","article-title":"SARI: Interactive GNSS position time series analysis software","volume":"23","year":"2019","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"He, X., Yu, K., Montillet, J.-P., Xiong, C., Lu, T., Zhou, S., Ma, X., Cui, H., and Ming, F. (2020). GNSS-TS-NRS: An Open-Source MATLAB-Based GNSS Time Series Noise Reduction Software. Remote Sens., 12.","DOI":"10.3390\/rs12213532"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"101","DOI":"10.2478\/arsa-2021-0008","article-title":"First results of time series analysis of the permanent GNSS observations at polish EPN stations using GipsyX software","volume":"56","author":"Bernatowicz","year":"2021","journal-title":"Artif. Satell."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s10291-014-0386-4","article-title":"Systematic errors of mapping functions which are based on the VMF1 concept","volume":"19","author":"Zus","year":"2015","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1029\/2018JB016783","article-title":"Evaluation of temporally correlated noise in global navigation satellite system time series: Geodetic monument performance","volume":"124","author":"Langbein","year":"2019","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s10291-019-0888-1","article-title":"PRIDE PPP-AR: An open-source software for GPS PPP ambiguity resolution","volume":"23","author":"Geng","year":"2019","journal-title":"GPS Solut."},{"key":"ref_16","unstructured":"Bock, Y., Fang, P., Knox, A., Sullivan, A., Jiang, S., Guns, K., Golriz, D., Moore, A., Argus, D., and Liu, Z. (2023, June 12). Extended Solid Earth Science ESDR System: Algorithm Theoretical Basis Document. Available online: http:\/\/garner.ucsd.edu\/pub\/measuresESESES_products\/ATBD\/ESESES-ATBD.pdf."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Barba, P., Rosado, B., Ram\u00edrez-Zelaya, J., and Berrocoso, M. (2021). Comparative Analysis of Statistical and Analytical Techniques for the Study of GNSS Geodetic Time Series. Eng. Proc., 5.","DOI":"10.3390\/engproc2021005021"},{"key":"ref_18","unstructured":"(2023, June 12). Time Series in SOPAC Archive. Available online: http:\/\/garner.ucsd.edu\/pub\/measuresESESES_products\/Timeseries\/."},{"key":"ref_19","first-page":"231","article-title":"The law of error and the combination of observations","volume":"237","author":"Jeffreys","year":"1938","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci."},{"key":"ref_20","first-page":"7","article-title":"Application of methods of the non-classical error theory in absolute measurements of Galilean acceleration","volume":"1","author":"Dvulit","year":"2017","journal-title":"Geodynamics"},{"key":"ref_21","first-page":"417","article-title":"Software System for Simulation and Research of Probabilistic Regularities and Statistical Data Analysis in Reliability and Quality Control","volume":"Volume 114","author":"Chimitova","year":"2014","journal-title":"Mathematical and Statistical Models and Methods in Reliability: Applications to Medicine, Finance, and Quality Control"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"012082","DOI":"10.1088\/1742-6596\/1614\/1\/012082","article-title":"Statistical testing of hypotheses about the form of the factor law of influence by the Kolmogorov criterion","volume":"1614","author":"Tumanov","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.21105\/joss.01237","article-title":"PyWavelets: A Python package for wavelet analysis","volume":"4","author":"Lee","year":"2019","journal-title":"J. Open Source Softw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"key":"ref_25","unstructured":"Freymueller, J.T., and S\u00e1nchez, L. (2020). Beyond 100: The Next Century in Geodesy. International Association of Geodesy Symposia, Springer."},{"key":"ref_26","unstructured":"(2023, June 12). Time Series in CDDIS Archive, Available online: https:\/\/cddis.nasa.gov\/archive\/GPS_Explorer\/archive\/time_series\/."},{"key":"ref_27","unstructured":"(2023, June 12). Reference Stations Classification in EPN. Available online: http:\/\/www.epncb.oma.be\/_productsservices\/ReferenceFrame\/Station_Classification.php."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/5\/757\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:02:34Z","timestamp":1760104954000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/5\/757"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,21]]},"references-count":27,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["rs16050757"],"URL":"https:\/\/doi.org\/10.3390\/rs16050757","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,2,21]]}}}