{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:06:23Z","timestamp":1760238383638,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2020,8,7]],"date-time":"2020-08-07T00:00:00Z","timestamp":1596758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NCBiR and PKP PLK SA","award":["InnoSatTrack (POIR.04.01.01-00-0017\/17)"],"award-info":[{"award-number":["InnoSatTrack (POIR.04.01.01-00-0017\/17)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We present the main assumptions about the algorithmization of the analysis of measurement data recorded in mobile satellite measurements. The research team from the Gda\u0144sk University of Technology and the Maritime University in Gdynia, as part of a research project conducted in cooperation with PKP PLK (Polish Railway Infrastructure Manager), developed algorithms supporting the identification and assessment of track axis layout. This article presents selected issues concerning the identification of a tramway line\u2019s axis system. For this purpose, the supporting algorithm was developed and measurement data recorded using Global Navigation Satellite System (GNSS) techniques was evaluated and analyzed. The discussed algorithm identifies main track directions from multi-device data and repeated position recordings. In order to observe the influence of crucial factors, the investigated route was carefully selected. The chosen tramway track was characterized by its location in various field conditions and a diversified and complex geometric layout. The analysis of the obtained results was focused on the assessment of the signal\u2019s dispersion and repeatability using residuals in relation to the estimated track\u2019s direction. The presented methodology is intended to support railway infrastructure management processes, mainly in planning and maintenance through an efficient inventory of the infrastructure in service.<\/jats:p>","DOI":"10.3390\/s20164408","type":"journal-article","created":{"date-parts":[[2020,8,7]],"date-time":"2020-08-07T09:30:54Z","timestamp":1596792654000},"page":"4408","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Evaluation of the Possibility of Identifying a Complex Polygonal Tram Track Layout Using Multiple Satellite Measurements"],"prefix":"10.3390","volume":"20","author":[{"given":"Andrzej","family":"Wilk","sequence":"first","affiliation":[{"name":"Department of Electrified Transportation, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5631-6969","authenticated-orcid":false,"given":"Cezary","family":"Specht","sequence":"additional","affiliation":[{"name":"Department of Geodesy and Oceanography, Gdynia Maritime University, Morska 81-87, 81-225 Gdynia, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wladyslaw","family":"Koc","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1662-6051","authenticated-orcid":false,"given":"Krzysztof","family":"Karwowski","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1373-0961","authenticated-orcid":false,"given":"Jacek","family":"Skibicki","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8380-0374","authenticated-orcid":false,"given":"Jacek","family":"Szmagli\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Rail Transportation and Bridges, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6177-0493","authenticated-orcid":false,"given":"Pawel","family":"Dabrowski","sequence":"additional","affiliation":[{"name":"Department of Geodesy and Oceanography, Gdynia Maritime University, Morska 81-87, 81-225 Gdynia, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6026-306X","authenticated-orcid":false,"given":"Mariusz","family":"Specht","sequence":"additional","affiliation":[{"name":"Department of Transport and Logistics, Gdynia Maritime University, Morska 81-87, 81-225 Gdynia, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8784-7738","authenticated-orcid":false,"given":"Marek","family":"Zienkiewicz","sequence":"additional","affiliation":[{"name":"Department of Geodesy, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4620-8416","authenticated-orcid":false,"given":"Slawomir","family":"Judek","sequence":"additional","affiliation":[{"name":"Department of Electrified Transportation, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcin","family":"Sk\u00f3ra","sequence":"additional","affiliation":[{"name":"Department of Navigation and Marine Hydrography, Polish Naval Academy, In\u017cyniera Jana \u015amidowicza 69, 81-103 Gdynia, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3352-624X","authenticated-orcid":false,"given":"S\u0142awomir","family":"Grulkowski","sequence":"additional","affiliation":[{"name":"Department of Rail Transportation and Bridges, Gda\u0144sk University of Technology, Gabriela Narutowicza 11-12, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,7]]},"reference":[{"key":"ref_1","unstructured":"NR (Network Rail) (2020, August 05). NR\/L3\/TRK\/0030 Iss. 1, Reinstatement of Absolute Track Geometry (WCRL Routes), Network Rail 2008. Available online: https:\/\/standards.globalspec.com\/std\/10216330\/nr-l3-trk-0030."},{"key":"ref_2","unstructured":"CEN (European Committee for Standardization) (2020, August 05). BS EN 13803:2017 Railway Applications\u2013Track\u2013Track Alignment Design Parameters\u2013Track Gauges 1435 mm and Wider. CEN. Available online: https:\/\/shop.bsigroup.com\/ProductDetail\/?pid=000000000030279796."},{"key":"ref_3","unstructured":"Szwilski, T.B., Begley, R., Dailey, P., and Sheng, Z. (2003, January 5\u20138). Determining rail track movement trajectories and alignment using HADGPS. Proceedings of the AREMA 2003 Annual Conference, Chicago, IL, USA."},{"key":"ref_4","unstructured":"Szwilski, A.B., Dailey, P., Sheng, Z., and Begley, R.D. (2005, January 29\u201330). Employing HADGPS to survey track and monitor movement at curves. Proceedings of the 8th International Conference \u201cRailway Engineering 2005\u201d, London, UK."},{"key":"ref_5","unstructured":"Glaus, R. (2020, August 05). The Swiss Trolley- A Modular System for Track Surveying. Geod\u00e4tisch-Geophys. Arb. in der Schweiz, Available online: https:\/\/www.sgc.ethz.ch\/publications.html."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/TIM.2011.2159417","article-title":"Multisensor railway track geometry surveying system","volume":"61","author":"Akpinar","year":"2012","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2495\/SDP-V11-N1-65-78","article-title":"Rail detection using lidar sensors","volume":"11","author":"Stein","year":"2016","journal-title":"Int. J. Sustain. Dev. Plan."},{"key":"ref_8","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_9","unstructured":"(2020, May 14). RILA Track. Available online: https:\/\/www.fugro.com\/our-services\/asset-integrity\/raildata\/rila-track-rila-360."},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"295","DOI":"10.2478\/ace-2014-0020","article-title":"Determining the geometrical parameters of exploited rail track using approximating spline functions","volume":"60","author":"Lenda","year":"2014","journal-title":"Arch. Civ. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1111\/mice.12392","article-title":"A method for automatically recreating the horizontal alignment geometry of existing railways","volume":"34","author":"Li","year":"2018","journal-title":"Comput.-Aided. Civ. Inf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5565","DOI":"10.3390\/rs70505565","article-title":"Automatic Extraction of Railroad Centerlines from Mobile Laser Scanning Data","volume":"7","author":"Elberink","year":"2015","journal-title":"Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.icte.2017.11.010","article-title":"Vision based rail track extraction and monitoring through drone imagery","volume":"5","author":"Singh","year":"2019","journal-title":"ICT Express"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Xiong, Z., Li, Q., Mao, Q., and Zou, Q.A. (2017). 3D Laser Profiling System for Rail Surface Defect Detection. Sensors, 17.","DOI":"10.3390\/s17081791"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4750","DOI":"10.1109\/JSTARS.2014.2312378","article-title":"Automated extraction of 3-d railway tracks from mobile laser scanning point clouds","volume":"7","author":"Yang","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.measurement.2012.08.023","article-title":"Railway track geometry determination using adaptive Kalman filtering model","volume":"46","author":"Akpinar","year":"2013","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"157241","DOI":"10.1109\/ACCESS.2019.2946981","article-title":"Kinematic Measurement of the Railway Track Centerline Position by GNSS\/INS\/Odometer Integration","volume":"7","author":"Zhou","year":"2019","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"303","DOI":"10.2478\/v10174-011-0021-x","article-title":"Selected problems of determining the course of railway routes by use of GPS network solution","volume":"23","author":"Koc","year":"2011","journal-title":"Arch. Transp."},{"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. Meas. Syst."},{"key":"ref_21","first-page":"32","article-title":"Research project BRIK: Development of an innovative method for determining the precise trajectory of a railway vehicle","volume":"7","author":"Wilk","year":"2019","journal-title":"Transp. Overv."},{"key":"ref_22","first-page":"18","article-title":"Installation of GNSS receivers on a mobile platform\u2014methodology and measurement aspects","volume":"60","author":"Dabrowski","year":"2019","journal-title":"Sci. J. Marit. Univ. Szczec."},{"key":"ref_23","first-page":"26","article-title":"Analysis of Positioning Methods Using Global Navigation Satellite Systems (GNSS) in Polish State Railways (PKP)","volume":"62","author":"Specht","year":"2020","journal-title":"Sci. J. Marit. Univ. Szczec."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Specht, M., Specht, C., Wilk, A., Koc, W., Smolarek, L., Czaplewski, K., Karwowski, K., D\u0105browski, P.S., Skibicki, J., and Chrostowski, P. (2020). Testing the Positioning Accuracy of GNSS Solutions during the Tramway Track Mobile Satellite Measurements in Diverse Urban Signal Reception Conditions. Energies, 13.","DOI":"10.3390\/en13143646"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Koc, W., Specht, C., Szmaglinski, J., and Chrostowski, P. (2019). A method for determination and compensation of a cant influence in a track centerline identification using GNSS methods and inertial measurement. Appl. Sci., 9.","DOI":"10.3390\/app9204347"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"D\u0105browski, P.S., Specht, C., Felski, A., Koc, W., Wilk, A., Czaplewski, K., Karwowski, K., Jask\u00f3lski, K., Specht, M., and Chrostowski, P. (2020). The Accuracy of a Marine Satellite Compass under Terrestrial Urban Conditions. J. Mar. Sci., 8.","DOI":"10.3390\/jmse8010018"},{"key":"ref_27","first-page":"24","article-title":"Mobile satellite measurements on the Pomeranian Metropolitan Railway","volume":"5","author":"Specht","year":"2016","journal-title":"Transp. Overv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1007\/s40864-017-0071-3","article-title":"The Analysis of Tram Tracks Geometric Layout Based on Mobile Satellite Measurements","volume":"3","author":"Specht","year":"2017","journal-title":"Urban Rail Transit"},{"key":"ref_29","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."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/679817","article-title":"Analytical method of modelling the geometric system of communication route","volume":"2014","author":"Koc","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","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."},{"key":"ref_32","unstructured":"Chrostowski, P., Koc, W., and Palikowska, K. (2017). Prospects in elongation of railway transition curves. P I Civil Eng-Transp., 1\u201312."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/16\/4408\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:57:44Z","timestamp":1760176664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/16\/4408"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,7]]},"references-count":32,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["s20164408"],"URL":"https:\/\/doi.org\/10.3390\/s20164408","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,8,7]]}}}