{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:12:01Z","timestamp":1760238721360,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T00:00:00Z","timestamp":1598918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Satellite geodetic networks are commonly used in surveying tasks, but they can also be used in mobile surveys. Mobile satellite surveys can be used for trackage inventory, diagnostics and design. The combination of modern technological solutions with the adaptation of research methods known in other fields of science offers an opportunity to acquire highly accurate solutions for railway track inventory. This article presents the effects of work carried out using a mobile surveying platform on which Global Navigation Satellite System (GNSS) receivers were mounted. The satellite observations (surveys) obtained were aligned using one of the methods known from classical land surveying. The records obtained during the surveying campaign on a 246th km railway track section were subjected to alignment. This article provides a description of the surveying campaign necessary to obtain measurement data and a theoretical description of the method employed to align observation results as well as their visualisation.<\/jats:p>","DOI":"10.3390\/s20174948","type":"journal-article","created":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T08:53:43Z","timestamp":1598950423000},"page":"4948","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Application of Least Squares with Conditional Equations Method for Railway Track Inventory Using GNSS Observations"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3595-347X","authenticated-orcid":false,"given":"Krzysztof","family":"Czaplewski","sequence":"first","affiliation":[{"name":"Department of Geodesy and Oceanography, Faculty of Navigation, Gdynia Maritime University, 81-374 Gdynia, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7069-7670","authenticated-orcid":false,"given":"Zbigniew","family":"Wisniewski","sequence":"additional","affiliation":[{"name":"Department of Geodesy, Faculty of Geoengineering, University of Warmia and Mazury, 10-719 Olsztyn, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5631-6969","authenticated-orcid":false,"given":"Cezary","family":"Specht","sequence":"additional","affiliation":[{"name":"Department of Geodesy and Oceanography, Faculty of Navigation, Gdynia Maritime University, 81-374 Gdynia, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5265-6189","authenticated-orcid":false,"given":"Andrzej","family":"Wilk","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Faculty of Electrical and Control Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"given":"Wladyslaw","family":"Koc","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Faculty of Electrical and Control Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1662-6051","authenticated-orcid":false,"given":"Krzysztof","family":"Karwowski","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Faculty of Electrical and Control Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1373-0961","authenticated-orcid":false,"given":"Jacek","family":"Skibicki","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Faculty of Electrical and Control Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6177-0493","authenticated-orcid":false,"given":"Pawe\u0142","family":"Dabrowski","sequence":"additional","affiliation":[{"name":"Department of Geodesy and Oceanography, Faculty of Navigation, Gdynia Maritime University, 81-374 Gdynia, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7904-5567","authenticated-orcid":false,"given":"Bartosz","family":"Czaplewski","sequence":"additional","affiliation":[{"name":"Department of Teleinformation Networks, Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6026-306X","authenticated-orcid":false,"given":"Mariusz","family":"Specht","sequence":"additional","affiliation":[{"name":"Department of Transport and Logistics, Faculty of Navigation, Gdynia Maritime University, 81-225 Gdynia, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5454-026X","authenticated-orcid":false,"given":"Piotr","family":"Chrostowski","sequence":"additional","affiliation":[{"name":"Department of Rail Transportation and Bridges, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8380-0374","authenticated-orcid":false,"given":"Jacek","family":"Szmaglinski","sequence":"additional","affiliation":[{"name":"Department of Rail Transportation and Bridges, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4620-8416","authenticated-orcid":false,"given":"Slawomir","family":"Judek","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Faculty of Electrical and Control Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3352-624X","authenticated-orcid":false,"given":"Slawomir","family":"Grulkowski","sequence":"additional","affiliation":[{"name":"Department of Rail Transportation and Bridges, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"given":"Roksana","family":"Licow","sequence":"additional","affiliation":[{"name":"Department of Rail Transportation and Bridges, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/S0191-2615(99)00004-1","article-title":"Railway traffic control and train scheduling based oninter-train conflict management","volume":"33","author":"Sahin","year":"1999","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.omega.2015.11.003","article-title":"Collaborative optimization for train scheduling and train stop planning on high-speed rail ways","volume":"64","author":"Yang","year":"2016","journal-title":"Omega"},{"key":"ref_3","first-page":"4247","article-title":"Anastasiadis, Probabilistic Slope Stability Evaluation for the New Railway Embankment in Ethiopia","volume":"21","author":"Assefa","year":"2016","journal-title":"Elect. J. Geotech. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.measurement.2018.07.079","article-title":"Acceleration measurements inside vehicles: Passengers\u2019 comfort mapping on railways","volume":"129","author":"Zoccali","year":"2018","journal-title":"Measurement"},{"key":"ref_5","unstructured":"Strach, M. (2009). Surveying of Railroads and Related Facilities and Developing Results for the Conventional Railway Modernization. Archiwum Fotogrametrii, Kartografii i Teledetekcji, Polish Society of Photogrammetry and Remote Sensing. (In Polish)."},{"key":"ref_6","first-page":"65","article-title":"Geodezyjne i diagnostyczne techniki pomiaru geometrii tor\u00f3w kolejowych","volume":"1","author":"Grabias","year":"2017","journal-title":"Res. Tech. Pap. Pol. Assoc. Trans. Eng. Crac."},{"key":"ref_7","first-page":"229","article-title":"Global Positioning System: Political Support, Directions of Development, and Expectations","volume":"9","author":"Czaplewski","year":"2015","journal-title":"TransNav Int. J. Marine Navig. Saf. Sea Transp."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/978-3-319-97955-7_35","article-title":"Does Poland Need eLoran?","volume":"Volume 897","author":"Mikulski","year":"2018","journal-title":"Management Perspective for Transport Telematics: 18th International Conference on Transport System Telematics, TST 2018, Krakow, Poland, 20\u201323 March 2018"},{"key":"ref_9","first-page":"74","article-title":"Applications of Global Navigation Satellite Systems in Maritime Navigation","volume":"2016","author":"Januszewski","year":"2016","journal-title":"Sci. J. Marit. Univ. Szczec."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bia\u0142y, J., Ciecko, A., Cwiklak, J., Grzegorzewski, M., Koscielniak, P., Ombach, J., and Oszczak, S. (2011, January 19\u201323). Aircraft Landing System Utilizing a GPS Receiver with Position Prediction Functionality. Proceedings of the 24th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS), Portland, OR, USA.","DOI":"10.1201\/b11344-33"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Urbanski, J., Morgas, W., and Specht, C. (2008, January 18\u201321). Perfecting the Maritime Navigation Information Services of the European Union. Proceedings of the 2008 1st International Conference on Information Technology, Gdansk, Poland. (In Polish).","DOI":"10.1109\/INFTECH.2008.4621631"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1017\/S0373463316000230","article-title":"A Vessel\u2019s Mathematical Model and Its Real Counterpart: A Comparative Methodology Based on a Real-world Study","volume":"69","author":"Czaplewski","year":"2016","journal-title":"J. Navig."},{"key":"ref_13","first-page":"58","article-title":"Wyniki pomiar\u00f3w satelitarnych toru kolejowego","volume":"15","author":"Koc","year":"2009","journal-title":"Tech. Transp. Szyn."},{"key":"ref_14","unstructured":"Koc, W., Specht, C., Jurkowska, A., Chrostowski, P., Nowak, A., Lewi\u0144ski, L., and Bornowski, M. (2009, January 22\u201324). Okre\u015blanie przebiegu trasy kolejowej na drodze pomiar\u00f3w satelitarnych. Proceedings of the II Scientific and Technical Conference Design, Construction and Maintenance of Infrastructure in Rail Transport INFRASZYN 2009, Zakopane, Poland. (In Polish)."},{"key":"ref_15","unstructured":"Weintrit, A., and Neumann, T. (2011). Application of the Polish Active Geodetic Network for Railway Track Determination. Transport Systems and Processes: Marine Navigation and Safety of Sea Transportation, CRC Press\/Balkema. [1st ed.]."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Specht, C., Specht, M., and D\u0105browski, P. (July, January 29). Comparative Analysis of Active Geodetic Networks in Poland. Proceedings of the 17th International Multidisciplinary Scientific GeoConference SGEM 2017, Albena, Bulgaria.","DOI":"10.5593\/sgem2017\/22\/S09.021"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1515\/pomr-2015-0012","article-title":"Accuracy of the GPS Positioning System in the Context of Increasing the Number of Satellites in the Constellation","volume":"22","author":"Specht","year":"2015","journal-title":"Pol. Marit. Res."},{"key":"ref_18","first-page":"3076","article-title":"Diagnostics of the Tram Track Shape with the use of the Global Positioning Satellite Systems (GPS\/Glonass) Measurements with a 20 Hz Frequency Sampling","volume":"16","author":"Specht","year":"2014","journal-title":"J. Vibroeng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1016\/j.trpro.2016.05.310","article-title":"Mobile Satellite Measurements in Designing and Exploitation of Rail Roads","volume":"14","author":"Specht","year":"2016","journal-title":"Transp. Res. Procedia"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"309","DOI":"10.24425\/mms.2019.128359","article-title":"Accuracy Assessment of Mobile Satellite Measurements Relation to the Geometrical Layout of Rail Tracks","volume":"26","author":"Specht","year":"2019","journal-title":"Metrol. Measur. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1061\/(ASCE)TE.1943-5436.0000303","article-title":"Design of Rail-Track Geometric Systems by Satellite Measurement","volume":"138","author":"Koc","year":"2012","journal-title":"J. Transp. Eng. ASCE"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"04013017","DOI":"10.1061\/(ASCE)TE.1943-5436.0000643","article-title":"Computer-Aided Design of Railroad Horizontal Arc Areas in Adapting to Satellite Measurements","volume":"140","author":"Koc","year":"2014","journal-title":"J. Transp. Eng. ASCE"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Koc, W. (2016). The analytical design method of railway route\u2019s main directions intersection area. Open Eng., 1.","DOI":"10.1515\/eng-2016-0001"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"11004","DOI":"10.1051\/matecconf\/201926211004","article-title":"Analysis of the possibilities in railways shape assessing using GNSS mobile measurements","volume":"262","author":"Koc","year":"2019","journal-title":"MATEC Web Conf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1515\/eng-2016-0017","article-title":"Computer-aided evaluation of the railway track geometry on the basis of satellite measurements","volume":"6","author":"Specht","year":"2016","journal-title":"Open Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1179\/003962608X325448","article-title":"Determining Rail Track Axis Geometry Using Satellite and Terrestrial Geodetic Data","volume":"40","author":"Gikas","year":"2008","journal-title":"Surv. Rev."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1002\/navi.78","article-title":"Railway track irregularity measuring by GNSS\/INS integration","volume":"62","author":"Chen","year":"2015","journal-title":"Navigation"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Chen, Q., Niu, X., Zuo, L., Zhang, T., Xiao, F., Liu, Y., and Liu, J. (2018). A Railway Track Geometry Measuring Trolley System Based on Aided INS. Sensors, 18.","DOI":"10.3390\/s18020538"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Lou, Y., Zhang, T., Tang, J., Song, W., Zhang, Y., and Chen, L. (2018). A Fast Algorithm for Rail Extraction Using Mobile Laser Scanning Data. Remote Sens., 10.","DOI":"10.3390\/rs10121998"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2127","DOI":"10.1016\/j.measurement.2013.03.006","article-title":"Review of mobile mapping and surveying technologies","volume":"46","author":"Puente","year":"2013","journal-title":"Measurement"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.measurement.2016.01.012","article-title":"Axlebox accelerations: Their acquisition and time-frequency characterization for railway track monitoring purposes","volume":"82","author":"Salvador","year":"2016","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Pham, N.T., Timofeev, A.N., and Nekrylov, I.S. (2019, January 24\u201327). Study of the errors of stereoscopic optical-electronic system for railroad track position. Proceedings of the Optical Measurement Systems for Industrial Inspection XI, SPIE 11056, Munich, Germany.","DOI":"10.1117\/12.2526081"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1007\/s00190-019-01270-w","article-title":"Attitude variometric approach using DGNSS\/INS integration to detect deformation in railway track irregularity measuring","volume":"93","author":"Zhu","year":"2019","journal-title":"J. Geod."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s10291-018-0702-5","article-title":"Railway irregularity measuring using Rauch\u2013Tung\u2013Striebel smoothed multi-sensors fusion system: Quad-GNSS PPP, IMU, odometer, and track gauge","volume":"22","author":"Gao","year":"2018","journal-title":"GPS Solut."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"04017014","DOI":"10.1061\/(ASCE)SU.1943-5428.0000236","article-title":"Laser-Aided INS and Odometer Navigation System for Subway Track Irregularity Measurement","volume":"143","author":"Li","year":"2017","journal-title":"J. Surv. Eng."},{"key":"ref_36","first-page":"77","article-title":"Research of railway track parameters in the plan based on the different methods of survey","volume":"2","author":"Kurhan","year":"2018","journal-title":"Nauka Ta Prog. Transp."},{"key":"ref_37","unstructured":"Izvoltova, J., and Cesnek, T. (2017, January 10\u201313). Accuracy analysis of continual geodetic diagnostics of a railway line. Proceedings of the 10th International Scientific and Professional Conference on Geodesy, Cartography and Geoinformatics (GCG 2017), Low Tatras, Slovakia."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"05016008","DOI":"10.1061\/(ASCE)SU.1943-5428.0000197","article-title":"Estimating the Accuracy of Track-Surveying Trolley Measurements for Railway Maintenance Planning","volume":"143","author":"Sanchez","year":"2017","journal-title":"J. Surv. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1080\/01490419.2019.1645769","article-title":"A Novel Approach of Using Selected Unconventional Geodesic Methods of Estimation on VTS Areas","volume":"42","author":"Czaplewski","year":"2019","journal-title":"Mar. Geod."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1515\/pomr-2017-0044","article-title":"Application of Square M-Split Estimation in Determination of Vessel Position in Coastal Shipping","volume":"24","author":"Zienkiewicz","year":"2017","journal-title":"Pol. Marit. Res."},{"key":"ref_41","unstructured":"Wisniewski, Z. (2016). Rachunek Wyr\u00f3wnawczy w Geodezji z Przyk\u0142adami, Wydawnictwo UWM. (In Polish)."},{"key":"ref_42","unstructured":"Kub\u00e1\u010dkov\u00e1, L., Kub\u00e1\u010dek, L., and Kuku\u010da, J. (1987). Probability and Statistics in Geodesy and Geophysics, Elsevier."},{"key":"ref_43","unstructured":"Rao, C.R. (2001). Linear Statistical Inference and Its Applications, John Wiley and Sons."},{"key":"ref_44","first-page":"39","article-title":"Methods for solving a system of interdependent conditional equations","volume":"34","author":"Wisniewski","year":"1985","journal-title":"Geod. Kartogr."},{"key":"ref_45","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 Baltic Geodetic Congress (BGC Geomatics), Gdansk, Poland.","DOI":"10.1109\/BGC.Geomatics.2017.51"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"04019001","DOI":"10.1061\/(ASCE)SU.1943-5428.0000271","article-title":"Deformation Analysis of Geodetic Networks by Applying Msplit Estimation with Conditions Binding the Competitive Parameters","volume":"145","author":"Zienkiewicz","year":"2019","journal-title":"J. Surv. Eng."},{"key":"ref_47","first-page":"895","article-title":"Use of a Least Squares with Conditional Equations Method in Positioning a Tramway Track in the Gdansk Agglomeration","volume":"13","author":"Czaplewski","year":"2019","journal-title":"TransNav Int. J. Mar. Navig. Saf. Sea Transp."},{"key":"ref_48","unstructured":"(2020, July 03). Rozporz\u0105dzenie Rady Ministr\u00f3w z Dnia 15 Pa\u017adziernika 2012 r. w Sprawie Pa\u0144stwowego Systemu Odniesie\u0144 Przestrzennych, Available online: http:\/\/isap.sejm.gov.pl\/isap.nsf\/DocDetails.xsp?id=WDU20120001247."},{"key":"ref_49","unstructured":"HxGN SmartNet (2020, July 03). Network of Reference Stations. Available online: https:\/\/leica-geosystems.com\/pl-pl\/services-and-support\/hxgn-smartnet-satellite-positioning-service."},{"key":"ref_50","unstructured":"(2020, July 03). Geoportal360.pl: Geoportal Polski, Wszystkie Dzia\u0142ki na Mapie. Available online: https:\/\/geoportal360.pl."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/17\/4948\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:05:31Z","timestamp":1760177131000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/17\/4948"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,1]]},"references-count":50,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["s20174948"],"URL":"https:\/\/doi.org\/10.3390\/s20174948","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,9,1]]}}}