{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T12:23:04Z","timestamp":1761394984711,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,16]],"date-time":"2017-03-16T00:00:00Z","timestamp":1489622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41104021","11173026"],"award-info":[{"award-number":["41104021","11173026"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We present quad-constellation (namely, GPS, GLONASS, BeiDou and Galileo) time group delay (TGD) and differential code bias (DCB) correction models to fully exploit the code observations of all the four global navigation satellite systems (GNSSs) for navigation and positioning. The relationship between TGDs and DCBs for multi-GNSS is clearly figured out, and the equivalence of TGD and DCB correction models combining theory with practice is demonstrated. Meanwhile, the TGD\/DCB correction models have been extended to various standard point positioning (SPP) and precise point positioning (PPP) scenarios in a multi-GNSS and multi-frequency context. To evaluate the effectiveness and practicability of broadcast TGDs in the navigation message and DCBs provided by the Multi-GNSS Experiment (MGEX), both single-frequency GNSS ionosphere-corrected SPP and dual-frequency GNSS ionosphere-free SPP\/PPP tests are carried out with quad-constellation signals. Furthermore, the author investigates the influence of differential code biases on GNSS positioning estimates. The experiments show that multi-constellation combination SPP performs better after DCB\/TGD correction, for example, for GPS-only b1-based SPP, the positioning accuracies can be improved by 25.0%, 30.6% and 26.7%, respectively, in the N, E, and U components, after the differential code biases correction, while GPS\/GLONASS\/BDS b1-based SPP can be improved by 16.1%, 26.1% and 9.9%. For GPS\/BDS\/Galileo the 3rd frequency based SPP, the positioning accuracies are improved by 2.0%, 2.0% and 0.4%, respectively, in the N, E, and U components, after Galileo satellites DCB correction. The accuracy of Galileo-only b1-based SPP are improved about 48.6%, 34.7% and 40.6% with DCB correction, respectively, in the N, E, and U components. The estimates of multi-constellation PPP are subject to different degrees of influence. For multi-constellation combination SPP, the accuracy of single-frequency is slightly better than that of dual-frequency combinations. Dual-frequency combinations are more sensitive to the differential code biases, especially for the 2nd and 3rd frequency combination, such as for GPS\/BDS SPP, accuracy improvements of 60.9%, 26.5% and 58.8% in the three coordinate components is achieved after DCB parameters correction. For multi-constellation PPP, the convergence time can be reduced significantly with differential code biases correction. And the accuracy of positioning is slightly better with TGD\/DCB correction.<\/jats:p>","DOI":"10.3390\/s17030602","type":"journal-article","created":{"date-parts":[[2017,3,16]],"date-time":"2017-03-16T11:24:28Z","timestamp":1489663468000},"page":"602","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["The Impact of Satellite Time Group Delay and Inter-Frequency Differential Code Bias Corrections on Multi-GNSS Combined Positioning"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8988-6212","authenticated-orcid":false,"given":"Yulong","family":"Ge","sequence":"first","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precise Navigation, Positioning and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Feng","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Information Science Technology, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China"},{"name":"German Research Centre for Geosciences GFZ, Telegrafenberg, Potsdam 14473, Germany"}]},{"given":"Baoqi","family":"Sun","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"Key Laboratory of Precise Navigation, Positioning and Timing Technology, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Shengli","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Ocean Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"given":"Bo","family":"Shi","sequence":"additional","affiliation":[{"name":"College of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1016\/j.asr.2013.02.019","article-title":"An analysis on combined GPS\/COMPASS data quality and its effect on single point positioning accuracy under different observing conditions","volume":"54","author":"Cai","year":"2014","journal-title":"Adv. Space Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8328","DOI":"10.1038\/srep08328","article-title":"Precise positioning with current multi-constellation Global Navigation Satellite Systems: GPS, GLONASS, Galileo and BeiDou","volume":"5","author":"Li","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_3","first-page":"65","article-title":"Precise orbit determination and point positioning using GPS, Glonass, Galileo and BeiDou","volume":"4","author":"Tegedor","year":"2014","journal-title":"J. Geod. Sci."},{"key":"ref_4","unstructured":"Teunissen, P.J., and Kleusberg, A. (1996). GPS for Geodesy, Springer."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s10291-011-0206-z","article-title":"A computationally efficient approach for estimating high-rate satellite clock corrections in realtime","volume":"16","author":"Ge","year":"2011","journal-title":"GPS Solut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1088\/0026-1394\/42\/4\/005","article-title":"Geodetic techniques for time and frequency comparisons using GPS phase and code measurements","volume":"42","author":"Ray","year":"2005","journal-title":"Metrologia"},{"key":"ref_7","unstructured":"Montenbruck, O., and Hauschild, A. (2013, January 29\u201327). Code Biases in Multi-GNSS Point Positioning. Proceedings of the 2013 ION International Technical Meeting, San Diego, CA, USA."},{"key":"ref_8","unstructured":"The Receiver Independent Exchange Format (RINEX) Version 3.02. Available online: ftp:\/\/igs.org\/pub\/data\/format\/rinex302.pdf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5081\/jgps.12.1.1","article-title":"The BeiDou Navigation Message","volume":"12","author":"Montenbruck","year":"2013","journal-title":"J. Glob. Position Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s00190-015-0788-2","article-title":"Timing group delay and differential code bias corrections for BeiDou positioning","volume":"89","author":"Guo","year":"2015","journal-title":"J. Geod."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s00190-013-0622-7","article-title":"Initial results of precise orbit and clock determination for COMPASS navigation satellite system","volume":"87","author":"Zhao","year":"2013","journal-title":"J. Geod."},{"key":"ref_12","unstructured":"Deng, Z., Zhao, Q., Springer, T., Prange, L., and Uhlemann, M. (2014, January 23\u201327). Orbit and clock determination-BeiDou. Proceedings of the IGS workshop, Pasadena, CA, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1016\/j.asr.2012.09.039","article-title":"Evaluation of COMPASS ionospheric model in GNSS positioning","volume":"51","author":"Wu","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1109\/7.104264","article-title":"Variability of GPS satellite differential group delay biases","volume":"27","author":"Coker","year":"1991","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1899","DOI":"10.1029\/97RS01457","article-title":"Estimation of total electron content using GPS data: How stable are the differential satellite and receiver instrumental biases?","volume":"32","author":"Zarraoa","year":"1997","journal-title":"Radio Sci."},{"key":"ref_16","unstructured":"Schaer, S., and Steigenberger, P. (2006, January 8\u201312). Determination and use of GPS differential code bias values. Proceedings of the IGS Workshop, Sydney, Australia."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1007\/s00190-012-0565-4","article-title":"Two-step method for the determination of the differential code biases of COMPASS satellites","volume":"86","author":"Li","year":"2012","journal-title":"J. Geod."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s10291-003-0051-9","article-title":"The activities of the Ionosphere Working Group of the International GPS Service (IGS)","volume":"7","author":"Feltens","year":"2003","journal-title":"GPS Solut."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s00190-008-0266-1","article-title":"The IGS VTEC maps: A reliable source of ionospheric information since 1998","volume":"83","author":"Juan","year":"2009","journal-title":"J. Geod."},{"key":"ref_20","first-page":"42","article-title":"IGS-MGEX: Preparing the ground for multi-constellation GNSS science","volume":"9","author":"Montenbruck","year":"2014","journal-title":"Espace"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s00190-008-0300-3","article-title":"The International GNSS Service in a changing landscape of Global Navigation Satellite Systems","volume":"83","author":"Dow","year":"2009","journal-title":"J. Geod."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1002\/navi.64","article-title":"2014-Differential code bias estimation using multi-gnss observations and global ionosphere maps","volume":"61","author":"Montenbruck","year":"2014","journal-title":"Navigation"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s10291-014-0390-8","article-title":"Broadcast versus precise ephemerides: A multi-GNSS perspective","volume":"19","author":"Montenbruck","year":"2014","journal-title":"GPS Solut."},{"key":"ref_24","unstructured":"Schaer, S. (2012, January 18\u201319). Overview of GNSS biases. Proceedings of the Workshop on GNSS Biases, Bern, Switzerland."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.asr.2015.04.001","article-title":"Precise point positioning with quad-constellations: GPS, BeiDou, GLONASS and Galileo","volume":"56","author":"Cai","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1007\/s00190-007-0135-3","article-title":"Short Note: A global model of pressure and temperature for geodetic applications","volume":"81","author":"Boehm","year":"2007","journal-title":"J. Geod."},{"key":"ref_27","unstructured":"CSNO (2013). BeiDou Navigation Satellite System Signal in Space Interface Control Document\u2014Open Service Signal, version 2.0."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1856","DOI":"10.1016\/j.jastp.2008.01.015","article-title":"A new version of the NeQuick ionosphere electron density model","volume":"70","author":"Nava","year":"2008","journal-title":"J. Atmos. Sol. Terr. Phys."},{"key":"ref_29","unstructured":"Petit, G., and Luzum, B. (2010). IERS Conventions 2010, Bureau International des Poids et Mesures."},{"key":"ref_30","unstructured":"Wu, J.T., Wu, S.C., Hajj, G.A., Bertiger, W.I., and Lichten, S.M. (1992, January 19\u201322). Effects of antenna orienation on GPS carrier phase. Proceedings of the AAS\/AIAA Astrodynamics Conference, Durango, CO, USA."},{"key":"ref_31","unstructured":"Rizos, C., Montenbruck, O., Weber, R., Weber, G., Neilan, R., and Hugentobler, U. (2013, January 23\u201325). The IGS MGEX experiment as a milestone for a comprehensive multi-GNSS service. Proceedings of the ION PNT Meeting, Honolulu, HI, USA."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/978-981-10-0940-2_26","article-title":"Convergence Time Analysis of Multi-constellation Precise Point Positioning Based on iGMAS Products","volume":"Volume 390","author":"Ge","year":"2016","journal-title":"China Satellite Navigation Conference (CSNC) 2016 Proceedings: Volume III"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/602\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:30:37Z","timestamp":1760207437000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,16]]},"references-count":32,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["s17030602"],"URL":"https:\/\/doi.org\/10.3390\/s17030602","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,3,16]]}}}