{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T04:47:21Z","timestamp":1775710041408,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:00:00Z","timestamp":1660608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFC3000504"],"award-info":[{"award-number":["2021YFC3000504"]}]},{"name":"National Key Research and Development Program of China","award":["2021YFB3900802"],"award-info":[{"award-number":["2021YFB3900802"]}]},{"name":"National Key Research and Development Program of China","award":["41930535"],"award-info":[{"award-number":["41930535"]}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFC3000504"],"award-info":[{"award-number":["2021YFC3000504"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFB3900802"],"award-info":[{"award-number":["2021YFB3900802"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["41930535"],"award-info":[{"award-number":["41930535"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021YFC3000504"],"award-info":[{"award-number":["2021YFC3000504"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021YFB3900802"],"award-info":[{"award-number":["2021YFB3900802"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41930535"],"award-info":[{"award-number":["41930535"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Multi-frequency observations are now available from GNSSs, thereby bringing new opportunities for precise point positioning (PPP). However, they also introduce new challenges, such as inter-frequency clock bias (IFCB) between the new frequencies and the original dual-frequency observations due to triple-frequency observations, which severely impact the PPP. In this paper, we studied the estimation and correction methods of uncombined inter-frequency clock bias of GPS, BDS-3, and Galileo, analyzed the time-varying characteristics and short-term stability of IFCB, and analyzed the influence of IFCB on the positioning of the GPS, BDS-3, and Galileo, based on a triple-frequency un-differential non-combined PPP model. The obtained results show that the amplitude of Block IIF satellites of the GPS can reach up to 10\u201320 cm, and the IFCB in BDS-3, Galileo, and GPS Block III satellites can be neglected. After correction by IFCB, the 3D positioning accuracy of the GPS triple-frequency PPP was 1.73 cm and 4.75 cm in the static and kinematic modes, respectively, while the convergence time was 21.64 min and 39.61 min. Compared with the triple-frequency GPS PPP without any correction with IFCB, the static and kinematic 3D positioning accuracy in this work was improved by 27.39% and 17.34%, and the corresponding convergence time was improved by 10.55% and 15.22%, respectively. Furthermore, the delayed IFCB was also used for positioning processing, and it was found that a positioning performance comparable to that of the same day can be obtained. The standard deviation of IFCB for a single satellite was found to be no more than 1 cm, when the IFCB value of a neighboring day was subtracted from the IFCB value of same day, which proves the short-term stability of IFCB.<\/jats:p>","DOI":"10.3390\/rs14163991","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T03:15:27Z","timestamp":1660706127000},"page":"3991","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["GPS, BDS-3, and Galileo Inter-Frequency Clock Bias Deviation Time-Varying Characteristics and Positioning Performance Analysis"],"prefix":"10.3390","volume":"14","author":[{"given":"Yibiao","family":"Chen","sequence":"first","affiliation":[{"name":"School of Geomatics, Liaoning Technical University (LNTU), Fuxin 123000, China"},{"name":"Chinese Academy of Surveying and Mapping (CASM), Beijing 100830, China"}]},{"given":"Jinzhong","family":"Mi","sequence":"additional","affiliation":[{"name":"Chinese Academy of Surveying and Mapping (CASM), Beijing 100830, China"}]},{"given":"Shouzhou","family":"Gu","sequence":"additional","affiliation":[{"name":"Chinese Academy of Surveying and Mapping (CASM), Beijing 100830, China"}]},{"given":"Bo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University (LNTU), Fuxin 123000, China"},{"name":"Chinese Academy of Surveying and Mapping (CASM), Beijing 100830, China"}]},{"given":"Hongchao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University (LNTU), Fuxin 123000, China"},{"name":"Yellow River Conservancy Technical Institute (YRCTI), Kaifeng 475004, China"}]},{"given":"Lijun","family":"Yang","sequence":"additional","affiliation":[{"name":"Chinese Academy of Surveying and Mapping (CASM), Beijing 100830, China"},{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology (SDUST), Qingdao 266590, China"}]},{"given":"Yuqi","family":"Pang","sequence":"additional","affiliation":[{"name":"Chinese Academy of Surveying and Mapping (CASM), Beijing 100830, China"},{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology (SDUST), Qingdao 266590, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5005","DOI":"10.1029\/96JB03860","article-title":"Precise point positioning for the efficient and robust analysis of GPS data from large networks","volume":"102","author":"Zumberge","year":"1997","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1007\/s00190-017-1106-y","article-title":"GPS satellite clock determination in case of inter-frequency clock biases for triple-frequency precise point posi-tioning","volume":"92","author":"Guo","year":"2017","journal-title":"J. Geod."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Liu, G., Zhang, X., and Li, P. (2019). Improving the Performance of Galileo Uncombined Precise Point Positioning Ambiguity Resolution Using Triple-Frequency Observations. Remote Sens., 11.","DOI":"10.3390\/rs11030341"},{"key":"ref_4","first-page":"1084","article-title":"New progress of PPP\/PPP-RTK and positioning performance comparison of BDS\/GNSS PPP","volume":"49","author":"Zhang","year":"2020","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108890","DOI":"10.1016\/j.measurement.2020.108890","article-title":"Analytical performance and validations of the Galileo five-frequency precise point positioning models","volume":"172","author":"Su","year":"2021","journal-title":"Measurement"},{"key":"ref_6","first-page":"427","article-title":"BDS-3 performan ceassessment: PNT, SBAS, PPP, SMC and SAR","volume":"50","author":"Cai","year":"2021","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_7","first-page":"61","article-title":"Modeling and assessment of GPS\/BDS\/Galileo treple-frequency precise point positioning","volume":"50","author":"Zhou","year":"2021","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhou, W., Cai, H., Chen, G., Jiao, W., He, Q., and Yang, Y. (2022). Multi-GNSS Combined Orbit and Clock Solutions at iGMAS. Sensors, 22.","DOI":"10.3390\/s22020457"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s10291-019-0828-0","article-title":"Regional BDS satellite clock estimation with triple-frequency ambiguity resolution based on un-differenced observation","volume":"23","author":"Yang","year":"2019","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1016\/j.asr.2017.01.011","article-title":"The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS)\u2014Achievements, prospects and challenges","volume":"59","author":"Montenbruck","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1016\/j.asr.2012.10.031","article-title":"Three frequency GNSS navigation prospect demonstrated with semi-simulated data","volume":"51","author":"Li","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_12","first-page":"8","article-title":"Three\u2019s the Challenge: A Close Look at GPS SVN62 Triple-frequency Signal Combinations Finds Carrier-phase Variations on the New L5","volume":"21","author":"Montenbruck","year":"2010","journal-title":"GPS World"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s10291-011-0232-x","article-title":"Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite","volume":"16","author":"Montenbruck","year":"2012","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1007\/s10291-016-0571-8","article-title":"Characteristics of inter-frequency clock bias for Block IIF satellites and its effect on triple-frequency GPS precise point positioning","volume":"21","author":"Pan","year":"2017","journal-title":"GPS Solut."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/s10291-020-00992-1","article-title":"GPS + Galileo + BeiDou precise point positioning with triple-frequency ambiguity resolution","volume":"24","author":"Li","year":"2020","journal-title":"GPS Solut."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1007\/s00190-019-01310-5","article-title":"GPS satellite inter-frequency clock bias estimation using triple-frequency raw observations","volume":"93","author":"Fan","year":"2019","journal-title":"J. Geod."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhao, Q., Wang, G., Liu, Z., Hu, Z., Dai, Z., and Liu, J. (2016). Analysis of BeiDou Satellite Measurements with Code Multipath and Geometry-Free Iono-sphere-Free Combinations. Sensors, 16.","DOI":"10.3390\/s16010123"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s10291-012-0272-x","article-title":"Initial assessment of the COMPASS\/BeiDou-2 regional navigation satellite system","volume":"17","author":"Montenbruck","year":"2013","journal-title":"GPS Solut."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1002\/navi.27","article-title":"Orbit and Clock Determination of QZS-1 Based on the CONGO Network","volume":"60","author":"Steigenberger","year":"2013","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2048","DOI":"10.1016\/j.asr.2017.02.002","article-title":"Handling the satellite inter-frequency biases in triple-frequency observations","volume":"59","author":"Zhao","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s10291-022-01255-x","article-title":"GNSS carrier phase time-variant observable-specific signal bias (OSB) handling: An absolute bias perspective in multi-frequency PPP","volume":"26","author":"Su","year":"2022","journal-title":"GPS Solut."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s00190-020-01365-9","article-title":"Research on empirical correction models of GPS Block IIF and BDS satellite inter-frequency clock bias","volume":"94","author":"Gong","year":"2020","journal-title":"J. Geod."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1007\/s10291-015-0486-9","article-title":"Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS","volume":"20","author":"Li","year":"2016","journal-title":"GPS Solut."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1007\/s10291-021-01161-8","article-title":"Estimation and analysis of GPS inter-fequency clock biases from long-term triple-frequency ob-servations","volume":"25","author":"Zhang","year":"2021","journal-title":"GPS Solut."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1007\/s00190-018-1125-3","article-title":"Three-frequency BDS precise point positioning ambiguity resolution based on raw observables","volume":"92","author":"Li","year":"2018","journal-title":"J. Geod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10291-012-0283-7","article-title":"Fast estimation and analysis of the inter-frequency clock bias for Block IIF satellites","volume":"17","author":"Li","year":"2013","journal-title":"GPS Solut."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/16\/3991\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:10:48Z","timestamp":1760141448000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/16\/3991"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,16]]},"references-count":26,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["rs14163991"],"URL":"https:\/\/doi.org\/10.3390\/rs14163991","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,16]]}}}