{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:45:50Z","timestamp":1760229950786,"version":"build-2065373602"},"reference-count":62,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T00:00:00Z","timestamp":1656547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Polish Air Force University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The paper presents an approach to the simultaneous use of SDCM and EGNOS corrections for two GNSS receivers placed at a constant distance. The SDCM and EGNOS corrections were applied for two GPS code measurements on L1 frequency: C1C and C1W. The approach is based mainly on the constrained least squares adjustment, but for the horizontal and vertical coordinates, the Kalman Filter was applied in order to reduce pseudo-range noises. It allows for obtaining a higher autonomous accuracy of GPS\/(SDCM+EGNOS) positioning than when using only the GPS\/EGNOS or GPS\/SDCM system. The final dual-redundant solution, in which two SBAS systems were used (EGNOS+SDCM) and two GPS pseudo-ranges (C1C+C1W) were present, yielded RMS errors of 0.11 m for the horizontal coordinates and 0.25 m for the vertical coordinates. Moreover, the accuracy analysis in the developed mathematical model for the determined 3D coordinates with simultaneous use of EGNOS and SDCM systems proved to be much more reliable than using only a single EGNOS or SDCM system. The presented approach can be used not only for precise navigation, but also for some geoscience applications and remote sensing where the reliable accuracy of autonomous GPS positioning is required.<\/jats:p>","DOI":"10.3390\/rs14133152","type":"journal-article","created":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T01:40:36Z","timestamp":1656639636000},"page":"3152","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Dual Receiver EGNOS+SDCM Positioning with C1C and C1W Pseudo-Range Measurements"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7180-8483","authenticated-orcid":false,"given":"Mieczys\u0142aw","family":"Baku\u0142a","sequence":"first","affiliation":[{"name":"Institute of Navigation, Polish Air Force University, 08-521 D\u0119blin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9821-4450","authenticated-orcid":false,"given":"Kamil","family":"Krasuski","sequence":"additional","affiliation":[{"name":"Institute of Navigation, Polish Air Force University, 08-521 D\u0119blin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8837-700X","authenticated-orcid":false,"given":"Karol","family":"Dawidowicz","sequence":"additional","affiliation":[{"name":"Institute of Geodesy and Civil Engineering, University of Warmia and Mazury, 10-724 Olsztyn, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,30]]},"reference":[{"key":"ref_1","unstructured":"Wubbena, G., Bagge, A., Seeber, G., Boder, V., and Hankemeier, P. (1996, January 17\u201320). Reducing Distance Dependent Errors for Real-Time Precise DGPS Applications by Establishing Reference Station Networks. Proceedings of the 9th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1996), Kansas City, MO, USA."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Weng, D., Ji, S., Lu, Y., Chen, W., and Li, L. (2021). Improving DGNSS Performance through the Use of Network RTK Corrections. Remote Sens., 13.","DOI":"10.3390\/rs13091621"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"23","DOI":"10.2478\/v10018-012-011-0","article-title":"Reliable and redundant RTK positioning for applications in hard observational conditions","volume":"47","author":"Walawski","year":"2012","journal-title":"Artif. Satell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1109\/TGRS.2014.2332372","article-title":"Reliable Technology of Centimeter GPS\/GLONASS Surveying in Forest Environments","volume":"53","author":"Przestrzelski","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2283","DOI":"10.1109\/TGRS.2005.855625","article-title":"EGNOS test bed ionospheric corrections under the October and November 2003 storms","volume":"43","author":"Zornoza","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5802614","DOI":"10.1109\/TGRS.2022.3149635","article-title":"Towards a reliable ionospheric polar patch climatology with ground-based GNSS","volume":"60","author":"Sieradzki","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","first-page":"447","article-title":"Integration of GPS with remote sensing and GIS: Reality and prospect","volume":"68","author":"Gao","year":"2002","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lin, Y.C., Manish, R., Bullock, D., and Habib, A. (2021). Comparative Analysis of Different Mobile LiDAR Mapping Systems for Ditch Line Characterization. Remote Sens., 13.","DOI":"10.3390\/rs13132485"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, T., Zhang, H., Gao, Z., Niu, X., and El-Sheimy, N. (2019). Tight fusion of a monocular camera, MEMS-IMU, and single-frequency multi-GNSS RTK for precise navigation in GNSS-challenged environments. Remote Sens., 11.","DOI":"10.3390\/rs11060610"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"044007","DOI":"10.1088\/1361-6501\/ab0271","article-title":"Consumer GNSS chipsets-based, dual-frequency receivers as enablers of precise navigation and dense networks","volume":"30","author":"Bar","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1111\/phor.12259","article-title":"GPS precise point positioning for UAV photogrammetry","volume":"33","author":"Grayson","year":"2018","journal-title":"Photogramm. Rec."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"015015","DOI":"10.1088\/1361-6501\/abac27","article-title":"A new algorithm for a multi-baseline solution based on the equivalence principle","volume":"32","author":"Wang","year":"2022","journal-title":"Meas. Sci. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Krasuski, K., Cie\u0107ko, A., Baku\u0142a, M., and Wierzbicki, D. (2022). New strategy for improving the accuracy of aircraft positioning based on GPS SPP solution. Sensors, 20.","DOI":"10.3390\/s20174921"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Krasuski, K., and Wierzbicki, D. (2021). Application the SBAS\/EGNOS Corrections in UAV Positioning. Energies, 14.","DOI":"10.3390\/en14030739"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Cie\u0107ko, A., Baku\u0142a, M., Grunwald, G., and \u0106wiklak, J. (2020). Examination of Multi-Receiver GPS\/EGNOS Positioning with Kalman Filtering and Validation Based on CORS Stations. Sensors, 20.","DOI":"10.3390\/s20092732"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"035002","DOI":"10.1088\/0957-0233\/26\/3\/035002","article-title":"Precise GNSS single epoch positioning with multiple receiver configuration for medium-length baselines: Methodology and performance analysis","volume":"26","author":"Paziewski","year":"2015","journal-title":"Meas. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"109016","DOI":"10.1016\/j.measurement.2021.109016","article-title":"Innovative mobile method to determine railway track axis position in global coordinate system using position measurements performed with GNSS and fixed base of the measuring vehicle","volume":"175","author":"Wilk","year":"2021","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s10291-018-0747-5","article-title":"Robust adaptive filter for shipborne kinematic positioning and velocity determination during the Baltic Sea experiment","volume":"22","author":"Li","year":"2018","journal-title":"GPS Solut."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/s00190-020-01421-4","article-title":"A shipborne experiment using a dual-antenna reflectometry system for GPS\/BDS code delay measurements","volume":"94","author":"Gao","year":"2020","journal-title":"J. Geod."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"16895","DOI":"10.3390\/s150716895","article-title":"Medium to long range kinematic GPS positioning with position-velocity-acceleration model using multiple reference stations","volume":"15","author":"Hong","year":"2015","journal-title":"Sensors"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wang, J., Xu, T., Nie, W., and Xu, G. (2020). GPS\/BDS RTK Positioning Based on Equivalence Principle Using Multiple Reference Stations. Remote Sens., 12.","DOI":"10.3390\/rs12193178"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"109446","DOI":"10.1016\/j.measurement.2021.109446","article-title":"A simplified processing algorithm for multi-baseline RTK positioning in urban environments","volume":"179","author":"Wang","year":"2021","journal-title":"Measurement"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Baku\u0142a, M., and Ka\u017amierczak, R. (2017, January 22\u201325). Technology of rapid and ultrarapid static GPS\/GLONASS surveying in urban environments. Proceedings of the 2017 Baltic Geodetic Congress (BGC Geomatics) IEEE, Gdansk, Poland.","DOI":"10.1109\/BGC.Geomatics.2017.51"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1080\/00396265.2018.1547532","article-title":"Constrained and network multi-receiver single-epoch RTK positioning","volume":"52","year":"2020","journal-title":"Surv. Rev."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1002\/j.2161-4296.1995.tb01900.x","article-title":"The US Wide-Area Augmentation System (WAAS)","volume":"42","author":"Loh","year":"1995","journal-title":"Navigation"},{"key":"ref_26","unstructured":"Walter, T., Kee, C., Chao, Y.C., Tsai, Y.J., Peled, U., Ceva, J., Barrows, A.K., Abbott, E., Powell, D., and Enge, P. (1994, January 20\u201323). Flight Trials of the Wide Area Augmentation System (WAAS). Proceedings of the ION GPS-94 7th International Technical Meeting of the Satellite Division of the Institute of Navigation, Salt Palace Convention Center, Salt Lake City, UT, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1093\/njaf\/22.1.5","article-title":"A comparison of autonomous, WAAS, real-time, and post-processed global positioning systems (GPS) accuracies in northern forests","volume":"22","author":"Bolstad","year":"2005","journal-title":"North J. Appl. For."},{"key":"ref_28","unstructured":"Radio Technical Committee for Aeronautics (RTCA) (2006). Minimum Operational Performance Standards for Airborne Equipment Using Global Positioning System\/Wide Area Augmentation System, Radio Technical Committee for Aeronautics (RTCA). Doc. DO-229D, with Change 1, 2013."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/S1290-0958(99)80016-1","article-title":"MSAS (MTSAT satellite-based augmentation system) project status","volume":"2","author":"Shimamura","year":"1999","journal-title":"Air Space Eur."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Liu, Y., Cao, Y., Tang, C., Chen, J., Zhao, L., Zhou, S., Hu, X., Tian, Q., and Yang, Y. (2021). Pseudorange Bias Analysis and Preliminary Service Performance Evaluation of BDSBA. Remote Sens., 13.","DOI":"10.3390\/rs13234815"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1007\/s10291-016-0569-2","article-title":"GNSS satellite-based augmentation systems for Australia","volume":"21","author":"Choy","year":"2017","journal-title":"GPS Solut."},{"key":"ref_32","unstructured":"European GNSS Agency (GSA) (2017). EGNOS Open Service (OS) Service Definition Document (v. 2.3)."},{"key":"ref_33","unstructured":"Averin, S., Dvorkin, V., Karutin, S., Kurshin, V., Urlichich, U., and Klimov, V. (2006, January 26\u201329). Russian System for Differential Correction and Monitoring: A Concept and Results of the First Phase of Development. Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), Fort Worth, TX, USA."},{"key":"ref_34","unstructured":"Averin, S.V., Dvorkin, V.V., Karutin, V.S.N., and Sergey, N. (2007, January 25\u201328). Russian System for Differential Correction and Monitoring: A Concept, Present Status, And Prospects For Future. Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, USA."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s10291-011-0253-5","article-title":"Measured performance of the application of EGNOS in the road traffic sector","volume":"16","author":"Ali","year":"2012","journal-title":"GPS Solut."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"821","DOI":"10.12693\/APhysPolA.122.821","article-title":"Analysis of EGNOS-augmented GPS receiver positioning accuracy","volume":"122","year":"2012","journal-title":"Acta Phys. Pol."},{"key":"ref_37","first-page":"50","article-title":"Extending the reach of SBAS. Some aspects of EGNOS performance in Ukraine","volume":"1","author":"Konin","year":"2015","journal-title":"Inside GNSS"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.1017\/aer.2016.66","article-title":"Study of EGNOS accuracy and integrity in eastern Poland","volume":"120","author":"Grunwald","year":"2016","journal-title":"Aeronaut. J."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1049\/iet-rsn.2015.0053","article-title":"Examination of GPS\/EGNOS integrity in north-eastern Poland","volume":"10","author":"Grunwald","year":"2016","journal-title":"IET Radar Sonar Navig."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1017\/S0373463318000838","article-title":"Assessment of the positioning accuracy of DGPS and EGNOS systems in the Bay of Gdansk using maritime dynamic measurements","volume":"72","author":"Specht","year":"2019","journal-title":"J. Navig."},{"key":"ref_41","unstructured":"GSA (2019). EGNOS Safety of Life (SoL) Service Definition Document (v. 3.3)."},{"key":"ref_42","first-page":"81","article-title":"Application of the GPS\/EGNOS solution for the precise positioning of an aircraft vehicle","volume":"96","author":"Krasuski","year":"2017","journal-title":"Sci. J. Sil. Univ. Technol. Ser. Transp."},{"key":"ref_43","first-page":"301","article-title":"Assessment of velocity accuracy of aircraft in the dynamic tests using GNSS sensors","volume":"18","author":"Krasuski","year":"2020","journal-title":"Facta Univ. Ser. Mech. Eng."},{"key":"ref_44","first-page":"73","article-title":"Methods of precise aircraft positioning in the GPS system with an application of the troposphere correction","volume":"109","author":"Kirschenstein","year":"2020","journal-title":"Sci. J. Sil. Univ. Technol."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Krasuski, K., and Wierzbicki, D. (2020). Monitoring aircraft position using EGNOS data for the SBAS APV approach to the landing procedure. Sensors, 20.","DOI":"10.3390\/s20071945"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"181","DOI":"10.11003\/JPNT.2016.5.4.181","article-title":"Analysis on the multi-constellation SBAS performance of SDCM in Korea","volume":"5","author":"Lim","year":"2016","journal-title":"J. Position. Navig. Timing"},{"key":"ref_47","first-page":"245","article-title":"An efficient positioning method for multi-GNSS with multi-SBAS","volume":"7","author":"Park","year":"2018","journal-title":"J. Position. Navig. Timing"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Park, K.W., Park, J.I., and Park, C. (2020). Efficient methods of utilizing multi-SBAS corrections in multi-GNSS positioning. Sensors, 20.","DOI":"10.3390\/s20010256"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Krasuski, K., Wierzbicki, D., and Baku\u0142a, M. (2021). Improvement of UAV Positioning Performance Based on EGNOS+SDCM Solution. Remote Sens., 13.","DOI":"10.3390\/rs13132597"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/s10291-018-0804-0","article-title":"SBAS enhancement using an independent monitor station in a local area","volume":"23","author":"Weng","year":"2019","journal-title":"GPS Solut."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"105178","DOI":"10.1016\/j.jastp.2019.105178","article-title":"SBAS performance improvement with a new under sampled ionosphere threat model based on relative coverage metric","volume":"198","author":"Zhang","year":"2020","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_52","unstructured":"Romero, I. (2022, May 01). RINEX The Receiver Independent Exchange Format Version 3.05. ESA\/ESOC\/Navigation Support Office. Available online: https:\/\/files.igs.org\/pub\/data\/format\/rinex305.pdf."},{"key":"ref_53","unstructured":"Kaplan, E. (2006). Understanding GPS\/GNSS: Principles and Applications, Artech House. [2nd ed.]."},{"key":"ref_54","unstructured":"Takasu, T. (2022, February 10). RTKLIB ver. 2.4.2 Manual, RTKLIB: An Open Source Program, Package for GNSS Positioning. Available online: http:\/\/www.rtklib.com\/prog\/manual_2.4.2.pdf."},{"key":"ref_55","unstructured":"Minkler, G., and Minkler, J. (1993). Theory and Applications of Kalman Filtering, Magellan Book Company."},{"key":"ref_56","unstructured":"Brown, R.G., and Hwang, P.Y. (1997). Introduction to Random Signals and Applied Kalman Filtering: With MATLAB Exercises and Solutions, Wiley."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Kayton, M., and Fried, W.R. (1997). Avionics Navigation Systems, John Wiley & Sons.","DOI":"10.1002\/9780470172704"},{"key":"ref_58","unstructured":"Baran, L.W. (1999). Teoretyczne Podstawy Opracowania Wynik\u00f3w Pomiar\u00f3w Geodezyjnych, Wydawnictwo Naukowe PWN."},{"key":"ref_59","unstructured":"Wi\u015bniewski, Z. (2005). Rachunek Wyr\u00f3wnawczy w Geodezji (Z Przyk\u0142adami), Wydawnictwo UWM."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1002\/navi.64","article-title":"Differential code bias estimation using multi-GNSS observations and global ionosphere maps","volume":"61","author":"Montenbruck","year":"2014","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s00190-015-0867-4","article-title":"Determination of differential code biases with multi-GNSS observations","volume":"90","author":"Wang","year":"2016","journal-title":"J. Geod."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1186\/s43020-021-00040-4","article-title":"Functional model modification of precise point positioning considering the time-varying code biases of a receiver","volume":"2","author":"Zhang","year":"2021","journal-title":"Satell. Navig."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/13\/3152\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:41:22Z","timestamp":1760139682000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/13\/3152"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,30]]},"references-count":62,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["rs14133152"],"URL":"https:\/\/doi.org\/10.3390\/rs14133152","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,6,30]]}}}