{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:41:57Z","timestamp":1760233317435,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T00:00:00Z","timestamp":1672099200000},"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>Positioning error components related to tropospheric and ionospheric delays are caused by the atmosphere in positioning determined by global navigation satellite systems (GNSS). Depending on the user\u2019s requirements, the position error caused by tropospheric influences, which is commonly referred to as zenith tropospheric delay (ZTD), must be estimated during position determination or determined later by external tropospheric corrections. In this study, a new approach was adopted based on the reduction of residual tropospheric error (RTE), i.e., the unmodeled part of the tropospheric error that remains included in the total geodetic position error, along with other unmodeled systematic and random errors. The study was performed based on Global Navigation Satellite System (GLONASS) positioning solutions and accompanying meteorological parameters in a defined and harmonized temporal-spatial frame of three locations in the Republic of Croatia. A multidisciplinary approach-based analysis from a navigational science aspect was applied. The residual amount of satellite positioning signal tropospheric delay was quantitatively reduced by employing statistical analysis methods. The result of statistical regression is a model which correlates surface meteorological parameters with RTE. Considering the input data, the model has a regional character, and it is based on the Saastamoinen model of zenith tropospheric delay. The verification results show that the model reduces the RTE and thus increases the geodetic accuracy of the observed GNSS stations (with horizontal components of position accuracy of up to 3.8% and vertical components of position of up to 4.37%, respectively). To obtain these results, the Root Mean Square Error (RMSE) was used as the fundamental parameter for position accuracy evaluation. Although developed based on GLONASS data, the proposed model also shows a considerable degree of success in the verification of geodetic positions based on Global Positioning System (GPS). The purpose of the research, and one of its scientific contributions, is that the proposed method can be used to quantitatively monitor the dynamics of changes in deviations of X, Y, and Z coordinate values along coordinate axes. The results show that there is a distinct interdependence of the dynamics of Y and Z coordinate changes (with almost mirror symmetry), which has not been investigated and published so far. The resultant position of the coordinates is created by deviations of the coordinates along the Y and Z axes\u2014in the vertical plane of space, the deviations of the coordinate X (horizontal plane) are mostly uniform and independent of deviations along the Y and Z axes. The proposed model shows the realized state of the statistical position equilibrium of the selected GNSS stations which were observed using RTE values. Although of regional character, the model is suitable for application in larger areas with similar climatological profiles and for users who do not require a maximum level of geodetic accuracy achieved by using Satellite-Based Augmentation Systems (SBAS) or other more advanced, time-consuming, and equipment-consuming positioning techniques.<\/jats:p>","DOI":"10.3390\/rs15010162","type":"journal-article","created":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T05:30:27Z","timestamp":1672205427000},"page":"162","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New Approach for Improving GNSS Geodetic Position by Reducing Residual Tropospheric Error (RTE) Based on Surface Meteorological Data"],"prefix":"10.3390","volume":"15","author":[{"given":"Mario","family":"Bakota","sequence":"first","affiliation":[{"name":"Faculty of Maritime Studies, University of Split, Ru\u0111era Bo\u0161kovi\u0107a 37, 21000 Split, Croatia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0067-6150","authenticated-orcid":false,"given":"Serdjo","family":"Kos","sequence":"additional","affiliation":[{"name":"Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000 Rijeka, Croatia"}]},{"given":"Zoran","family":"Mrak","sequence":"additional","affiliation":[{"name":"Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000 Rijeka, Croatia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0643-841X","authenticated-orcid":false,"given":"David","family":"Br\u010di\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000 Rijeka, Croatia"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3513504","DOI":"10.1109\/LGRS.2022.3204323","article-title":"Effect of Weighted PDOP on Performance of Linear Kalman Filter for RTK Drone Data","volume":"19","author":"Ansari","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"unstructured":"Kaplan, E.D., and Hegarty, C.J. (2006). Understanding GPS: Principles and Application, Artech House. [2nd ed.].","key":"ref_2"},{"key":"ref_3","first-page":"349","article-title":"Reconstruction of Geomagnetic Event as Observed in Northern Adriatic Region and Its Correlation with GPS Single-frequency Positioning Deviations","volume":"14","year":"2020","journal-title":"Int. J. Mar. Navig. Saf. Sea Transp."},{"unstructured":"Subirana, J.S., Zornoza, J.M.J., and Hern\u00e1ndez-Pajares, M. (2013). GNSS DATA PROCESSING Volume I: Fundamentals and Algorithms Acknowledgements, ESA Communications ESTE.","key":"ref_4"},{"unstructured":"Elektronika, Ure\u0111aji (1998). \u0160irenje Valova. Tehni\u010dka Enciklopedija, LZMIK.","key":"ref_5"},{"unstructured":"Ustinov, U.M., Afanasev, V.V., Pripotnyuk, A.V., and Marinich, A.N. (2009). \u0421\u0443\u0434o\u0432\u044b\u0435 \u0420\u0430\u0434\u0438o\u043bo\u043a\u0430\u0446\u0438o\u043d\u043d\u044b\u0435 \u0421\u0438\u0441\u0442\u0435\u043c\u044b, \u0412\u0435\u043b\u0435\u043d\u0430\u0440\u0430. [3rd ed.].","key":"ref_6"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/978-94-007-7482-7_2","article-title":"GNSS Atmospheric and Multipath Delays","volume":"Volume 19","author":"Jin","year":"2014","journal-title":"GNSS Remote Sensing"},{"unstructured":"El-Arini, M.B. (2018, January 14\u201316). Tropospheric Effects on GNSS Bertram Arbesser-Rastburg. Proceedings of the Atmosphere and its Effect on GNSS Systems, Santiago, Chile.","key":"ref_8"},{"key":"ref_9","first-page":"88","article-title":"Determination of the best-fit Tropospheric Delay Model on the Nigerian Permanent GNSS Network","volume":"3","author":"Dodo","year":"2015","journal-title":"J. Geosci. Geomat."},{"unstructured":"Katsougiannopoulos, S., Pikridas, C., Rossikopoulos, D., Ifadis, I.M., and Fotiou, A. (2006, January 8\u201313). Tropospheric Refraction Estimation Using Various Models, Radiosonde Measurements and Permanent GPS Data. Proceedings of the XXIII FIG Congress, Munich, Germany.","key":"ref_10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4487","DOI":"10.1029\/JC074i018p04487","article-title":"Two-quartic tropospheric refractivity profile for correcting satellite data","volume":"74","author":"Hopfield","year":"1969","journal-title":"J. Geophys. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02521844","article-title":"Contributions to the theory of atmospheric refraction","volume":"105","author":"Saastamoinen","year":"1972","journal-title":"Bull. G\u00e9od\u00e9sique"},{"key":"ref_13","first-page":"84","article-title":"Comparative analysis of tropospheric delay models in precise point positioning in satellite navigation systems GLONASS\/GPS","volume":"7","author":"Pershin","year":"2009","journal-title":"\u0412\u0435\u0441\u0442\u043d\u0438\u043a \u041do\u0432o\u0441\u0438\u0431\u0438\u0440\u0441\u043ao\u0433o \u0413o\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043do\u0433o \u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430. \u0421\u0435\u0440\u0438\u044f: \u0418\u043d\u0444o\u0440\u043c\u0430\u0446\u0438o\u043d\u043d\u044b\u0435 \u0422\u0435\u0445\u043do\u043bo\u0433\u0438\u0438"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1029\/RS007i002p00223","article-title":"Correction of Satellite Tracking Data for an Arbitrary Tropospheric Profile","volume":"7","author":"Marini","year":"1972","journal-title":"Radio Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1029\/RS020i006p01593","article-title":"Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length","volume":"20","author":"Davis","year":"1985","journal-title":"Radio Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1179\/sre.1992.31.243.289","article-title":"The excess propagation path of radio waves: Study of the influence of the atmospheric parameters on its elevation dependence","volume":"31","author":"Ifadis","year":"2013","journal-title":"Surv. Rev."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1029\/RS022i003p00379","article-title":"Estimation of tropospheric delay for microwaves from surface weather data","volume":"22","author":"Askne","year":"1987","journal-title":"Radio Sci."},{"unstructured":"Shrestha, S.M. (2003). Investigations into the Estimation of Tropospheric Delay, University of Calgary.","key":"ref_18"},{"doi-asserted-by":"crossref","unstructured":"Kleijer, F. (2004). Troposphere Modeling and Filtering for Precise GPS Leveling, Delft University of Technology.","key":"ref_19","DOI":"10.54419\/qz77xn"},{"doi-asserted-by":"crossref","unstructured":"Xia, P., Xia, J., Ye, S., and Xu, C. (2020). A new method for estimating tropospheric zenith wet-component delay of gnss signals from surface meteorology data. Remote Sens., 12.","key":"ref_20","DOI":"10.3390\/rs12213497"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4389","DOI":"10.1002\/2014GL060271","article-title":"An improved model for calculating tropospheric wet delay","volume":"41","author":"Dousa","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2007RS003782","article-title":"Development of a regional tropospheric delay model for GPS-based navigation with emphasis to the Indian Region","volume":"43","author":"Parameswaran","year":"2008","journal-title":"Radio Sci."},{"unstructured":"Parameswaran, K., Raju, C.S., and Saha, K. (2007, January 5\u20137). Region-specific Tropospheric Delay Model for the Indian Subcontinent. Proceedings of the ICG-Meeting, Bangalore, India.","key":"ref_23"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"502","DOI":"10.4314\/sajg.v4i4.10","article-title":"Performance Evaluation of Blind Tropospheric Delay correction Models over Africa","volume":"4","author":"Isioye","year":"2015","journal-title":"S. Afr. J. Geomat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2857","DOI":"10.1016\/j.asr.2018.10.035","article-title":"A new method for vertical stratification of zenith tropospheric delay","volume":"63","author":"Hu","year":"2019","journal-title":"Adv. Sp. Res."},{"doi-asserted-by":"crossref","unstructured":"Yang, F., Guo, J., Zhang, C., Li, Y., and Li, J. (2021). A regional zenith tropospheric delay (Ztd) model based on Gpt3 and Ann. Remote Sens., 13.","key":"ref_26","DOI":"10.3390\/rs13050838"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.asr.2014.10.004","article-title":"Validity and behaviour of tropospheric gradients estimated by GPS in Corsica","volume":"55","author":"Morel","year":"2015","journal-title":"Adv. Sp. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6007","DOI":"10.1029\/2011RS004687","article-title":"Validation of tropospheric slant path delays derived from single and dual frequency GPS receivers","volume":"46","author":"Deng","year":"2011","journal-title":"Radio Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4157","DOI":"10.1016\/j.aej.2018.10.017","article-title":"Regional Egypt tropospheric mapping function model","volume":"57","author":"Mohammed","year":"2018","journal-title":"Alex. Eng. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"148","DOI":"10.3846\/20296991.2014.987465","article-title":"Accuracy improvement of tropospheric delay correction models in space geodetic data. Case study: Egypt","volume":"40","author":"Younes","year":"2014","journal-title":"Geod. Cartogr."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.5194\/isprs-archives-XLII-3-W10-1197-2020","article-title":"Research on zenith tropospheric delay modeling of regional cors network","volume":"XLII-3\/W10","author":"Yang","year":"2020","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_32","first-page":"201","article-title":"Evaluation of Five Tropospheric Delay Models on Global Navigation Satellite System Measurements in Southern Nigeria","volume":"7","author":"Dodo","year":"2019","journal-title":"J. Geosci. Geomat."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"e2019RS006909","DOI":"10.1029\/2019RS006909","article-title":"Evaluation of Spatio-Temporal Characteristics of Different Zenith Tropospheric Delay Models in Antarctica","volume":"55","author":"Li","year":"2020","journal-title":"Radio Sci."},{"unstructured":"Krueger, E., Schueler, T., and Arbesser-rastburg, B. (,  2005). The Standard Tropospheric Correction Model for the European Satellite Navi\u2212Gation System Galileo. Proceedings of the General As-sembly URSI, New Delhi, India. Available online: https:\/\/www.researchgate.net\/profile\/Bertram_Arbesser\u2212Rastburg\/publication\/252717445_THE_STANDARD_TROPOSPHER-IC_CORRECTION_MODEL_FOR_THE_EUROPEAN_SATELLITE_NAVIGATION_SYSTEM_GALILEO\/links\/00b4952c318413b26d000000\/THE\u2212STANDARD\u2212TROPOSPHERIC\u2212CORRECTION\u2212MODEL\u2212FOR\u2212THE\u2212EUROPEAN\u2212SATELLITE\u2212NAVIGATION\u2212SYSTEM\u2212GALILEO.pdf.","key":"ref_34"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s00190-005-0010-z","article-title":"Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign","volume":"79","author":"Snajdrova","year":"2006","journal-title":"J. Geod."},{"unstructured":"Ajayi, G. (1989). Physics of the Tropospheric Radiopropagation, International Centre for Theoretical Physic.","key":"ref_36"},{"doi-asserted-by":"crossref","unstructured":"Grabner, M., and Kvicera, V. (2011). Atmospheric Refraction and Propagation in Lower Troposphere. Electromagnetic Waves, Prentice Hall.","key":"ref_37","DOI":"10.5772\/16379"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3-1","DOI":"10.1029\/2000RS002567","article-title":"A direction-sensitive model of atmospheric noise and its application to the analysis of HF receiving antennas","volume":"37","author":"Coleman","year":"2002","journal-title":"Radio Sci."},{"key":"ref_39","first-page":"21","article-title":"A Compression Format and Tools for GNSS Observation Data","volume":"55","author":"Hatanaka","year":"2008","journal-title":"Bull. Geogr. Surv. Inst."},{"unstructured":"(2021, November 28). DHMZ\u2014Dr\u017eavni Hidrometeorolo\u0161ki Zavod. Available online: http:\/\/meteo.hr\/index.php.","key":"ref_40"},{"key":"ref_41","first-page":"3","article-title":"Klimatska podjela Hrvatske prema zna\u010dajkama godi\u0161njeg hoda temperature zraka","volume":"19","author":"Lisac","year":"1984","journal-title":"Acta Geogr. Croat."},{"key":"ref_42","first-page":"31","article-title":"Drought Vulnerability in Croatia","volume":"79","year":"2014","journal-title":"Agric. Conspec. Sci."},{"unstructured":"(2021, August 16). EUREF Permanent GNSS Network. Available online: http:\/\/www.epncb.oma.be\/index.php.","key":"ref_43"},{"unstructured":"(2021, November 10). RTKLIB: Documents. Available online: http:\/\/www.rtklib.com\/rtklib_document.htm.","key":"ref_44"},{"doi-asserted-by":"crossref","unstructured":"Astudillo, M.J., Lau, L., Tang, Y.T., and Moore, T. (2018). Analysing the Zenith Tropospheric Delay Estimates in On-line Precise Point Positioning (PPP) Services and PPP Software Packages. Sensors, 18.","key":"ref_45","DOI":"10.3390\/s18020580"},{"unstructured":"(2021, November 29). RTKLIB: An Open Source Program Package for GNSS Positioning. Available online: http:\/\/www.rtklib.com.","key":"ref_46"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3227","DOI":"10.1029\/95JB03048","article-title":"Global mapping functions for the atmosphere delay at radio wavelengths","volume":"101","author":"Niell","year":"1996","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1186\/BF03352267","article-title":"Improved atmospheric mapping functions for VLBI and GPS","volume":"52","author":"Niell","year":"2000","journal-title":"Earth Planets Space"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/S1464-1895(01)00087-4","article-title":"Preliminary evaluation of atmospheric mapping functions based on numerical weather models","volume":"26","author":"Niell","year":"2001","journal-title":"Phys. Chem. Earth Part A Solid Earth Geod."},{"unstructured":"ICD GLONASS CDMA (2021, August 16). \u0418\u043d\u0444o\u0440\u043c\u0430\u0446\u0438o\u043d\u043do-\u0410\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0426\u0435\u043d\u0442\u0440 \u041ao\u043d\u0442\u0440o\u043b\u044f \u0413\u041b\u041e\u041d\u0410\u0421\u0421 \u0438 GPS. Available online: https:\/\/www.glonass-iac.ru\/.","key":"ref_50"},{"doi-asserted-by":"crossref","unstructured":"Plischke, M., and Bergersen, B. (2006). Equilibrium Statistical Physics, World Scientific Publishing Co. Pte. Ltd.. [3rd ed.].","key":"ref_51","DOI":"10.1142\/5660"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/1\/162\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:53:15Z","timestamp":1760147595000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/1\/162"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,27]]},"references-count":51,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["rs15010162"],"URL":"https:\/\/doi.org\/10.3390\/rs15010162","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,12,27]]}}}