{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:14:18Z","timestamp":1760242458981,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,15]],"date-time":"2017-07-15T00:00:00Z","timestamp":1500076800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The joint use of multi-frequency signals brings new prospects for precise positioning and has become a trend in Global Navigation Satellite System (GNSS) development. However, a new type of inter-frequency clock bias (IFCB), namely the difference between satellite clocks computed with different ionospheric-free carrier phase combinations, was noticed. Consequently, the B1\/B3 precise point positioning (PPP) cannot directly use the current B1\/B2 clock products. Datasets from 35 globally distributed stations are employed to investigate the IFCB. For new generation BeiDou Navigation Satellite System (BDS) satellites, namely BDS-3 satellites, the IFCB between B1\/B2a and B1\/B3 satellite clocks, between B1\/B2b and B1\/B3 satellite clocks, between B1C\/B2a and B1C\/B3 satellite clocks, and between B1C\/B2b and B1C\/B3 satellite clocks is analyzed, and no significant IFCB variations can be observed. The IFCB between B1\/B2 and B1\/B3 satellite clocks for BDS-2 satellites varies with time, and the IFCB variations are generally confined to peak amplitudes of about 5 cm. The IFCB of BDS-2 satellites exhibits periodic signal, and the accuracy of prediction for IFCB, namely the root mean square (RMS) statistic of the difference between predicted and estimated IFCB values, is 1.2 cm. A triple-frequency PPP model with consideration of IFCB is developed. Compared with B1\/B2-based PPP, the positioning accuracy of triple-frequency PPP with BDS-2 satellites can be improved by 12%, 25% and 10% in east, north and vertical directions, respectively.<\/jats:p>","DOI":"10.3390\/rs9070734","type":"journal-article","created":{"date-parts":[[2017,7,18]],"date-time":"2017-07-18T03:45:16Z","timestamp":1500349516000},"page":"734","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Considering Inter-Frequency Clock Bias for BDS Triple-Frequency Precise Point Positioning"],"prefix":"10.3390","volume":"9","author":[{"given":"Lin","family":"Pan","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"},{"name":"Collaborative Innovation Center for Geospatial Technology, 129 Luoyu Road, Wuhan 430079, China"},{"name":"Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"given":"Xingxing","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"},{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, 14473 Potsdam, Germany"}]},{"given":"Xiaohong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"},{"name":"Collaborative Innovation Center for Geospatial Technology, 129 Luoyu Road, Wuhan 430079, China"},{"name":"Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"given":"Cuixian","family":"Lu","sequence":"additional","affiliation":[{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, 14473 Potsdam, Germany"}]},{"given":"Qile","family":"Zhao","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"given":"Jingnan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"},{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,15]]},"reference":[{"key":"ref_1","unstructured":"CSNO (2016). BeiDou Navigation Satellite System Signal in Space Interface Control Document (Open Service Signal), China Satellite Navigation Office. version 2.1."},{"key":"ref_2","unstructured":"Tsai, Y.H., Yang, W.C., Chang, F.R., and Ma, C.L. (2004, January 2\u20134). Using multi-frequency for GPS positioning and receiver autonomous integrity monitoring. Proceedings of the 2004 IEEE International Conference on Control Applications, Taipei, Taiwan."},{"key":"ref_3","unstructured":"Teunissen, P.J.G., Joosten, P., and Tiberius, C. (2002, January 24\u201327). A comparison of TCAR, CIR and LAMBDA GNSS ambiguity resolution. Proceedings of the ION-GPS-2002, Institute of Navigation, Portland, OR, USA."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1017\/S0373463314000824","article-title":"Precise point positioning using triple-frequency GPS measurements","volume":"68","author":"Elsobeiey","year":"2015","journal-title":"J. Navig."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1007\/s00190-016-0920-y","article-title":"Modeling and assessment of triple-frequency BDS precise point positioning","volume":"90","author":"Guo","year":"2016","journal-title":"J. Geod."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1016\/j.jastp.2008.03.007","article-title":"Total electron content monitoring using triple frequency GNSS data: A three-step approach","volume":"70","author":"Spits","year":"2008","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6385","DOI":"10.1109\/TGRS.2015.2438395","article-title":"Multi-GNSS meteorology: Real-time retrieving of atmospheric water vapor from BeiDou, Galileo, GLONASS, and GPS observations","volume":"53","author":"Li","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s00190-015-0802-8","article-title":"Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo","volume":"89","author":"Li","year":"2015","journal-title":"J. Geod."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"33499","DOI":"10.1038\/srep33499","article-title":"Global ionospheric modelling using multi-GNSS: BeiDou, Galileo, GLONASS and GPS","volume":"6","author":"Ren","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1080\/00396265.2016.1151628","article-title":"Performance evaluation of single-frequency point positioning with GPS, GLONASS, BeiDou and Galileo","volume":"49","author":"Pan","year":"2017","journal-title":"Surv. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.geog.2016.07.007","article-title":"Reference satellite selection method for GNSS high-precision relative positioning","volume":"8","author":"Gao","year":"2017","journal-title":"Geod. Geodyn."},{"key":"ref_13","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_14","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_15","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_16","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10291-011-0245-5","article-title":"Signal, orbit and attitude analysis of Japan\u2019s first QZSS satellite Michibiki","volume":"16","author":"Hauschild","year":"2012","journal-title":"GPS Solut."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1179\/1752270615Y.0000000032","article-title":"A comparative analysis of measurement noise and multipath for four constellations: GPS, BeiDou, GLONASS and Galileo","volume":"48","author":"Cai","year":"2016","journal-title":"Surv. Rev."},{"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","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 ionospheric-free combinations. Sensors, 16.","DOI":"10.3390\/s16010123"},{"key":"ref_20","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_21","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_22","doi-asserted-by":"crossref","first-page":"9921","DOI":"10.1029\/95JB00868","article-title":"Geodesy using the global positioning system: The effects of signal scattering","volume":"100","author":"Elosegui","year":"1995","journal-title":"J. Geophys. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2646","DOI":"10.1109\/TAP.2015.2414950","article-title":"Validating the variability of snow accumulation and melting from GPS reflected signals: Forward modeling","volume":"63","author":"Najibi","year":"2015","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ning, Y., Yuan, Y., Chai, Y., and Huang, Y. (2016). Analysis of the Bias on the Beidou GEO Multipath Combinations. Sensors, 16.","DOI":"10.3390\/s16081252"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1016\/j.asr.2014.03.005","article-title":"Sensing snow height and surface temperature variations in Greenland from GPS reflected signals","volume":"53","author":"Jin","year":"2014","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4006","DOI":"10.3390\/rs5084006","article-title":"Physical reflectivity and polarization characteristics for snow and ice-covered surfaces interacting with GPS signals","volume":"5","author":"Najibi","year":"2013","journal-title":"Remote Sens."},{"key":"ref_27","first-page":"B04401","article-title":"Modeling GPS phase multipath with SNR: Case study from the Salar de Uyuni, Boliva","volume":"113","author":"Bilich","year":"2008","journal-title":"J. Geophys. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1007\/s10291-014-0423-3","article-title":"BeiDou satellite-induced code pseudorange variations: Diagnosis and therapy","volume":"19","author":"Wanninger","year":"2015","journal-title":"GPS Solut."},{"key":"ref_29","unstructured":"Welch, G., and Bishop, G. (1995). An Introduction to the Kalman Filter, University of North Carolina at Chapel Hill."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1080\/00050334.1995.10558564","article-title":"A comparison of four methods of weighting double difference pseudorange measurements","volume":"40","author":"Gerdan","year":"1995","journal-title":"Aust. Surviv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1007\/s10291-014-0421-5","article-title":"Three-carrier ambiguity resolution using the modified TCAR method","volume":"19","author":"Zhao","year":"2015","journal-title":"GPS Solut."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1007\/s00190-015-0816-2","article-title":"Single-frequency precise point positioning: An analytical approach","volume":"89","author":"Sterle","year":"2015","journal-title":"J. Geod."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"L07304","DOI":"10.1029\/2005GL025546","article-title":"Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data","volume":"33","author":"Boehm","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_34","unstructured":"(2017, July 14). M_Map: A mapping package for Matlab. Available online: https:\/\/www.eoas.ubc.ca\/~rich\/map.html."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"S213","DOI":"10.1088\/0026-1394\/48\/4\/S13","article-title":"BDS navigation satellite system and its timescales","volume":"48","author":"Han","year":"2011","journal-title":"Metrologia"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1002\/cpa.3160410705","article-title":"Ortho-normal bases of compactly supported wavelets","volume":"41","author":"Daubechies","year":"1988","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/PL00012839","article-title":"Precision, cross correlation, and time correlation of GPS phase and code observations","volume":"4","author":"Bona","year":"2000","journal-title":"GPS Solut."},{"key":"ref_38","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_39","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10291-012-0273-9","article-title":"Modeling and assessment of combined GPS\/GLONASS precise point positioning","volume":"17","author":"Cai","year":"2013","journal-title":"GPS Solut."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s00190-015-0854-9","article-title":"On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory","volume":"90","author":"Odijk","year":"2016","journal-title":"J. Geod."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/7\/734\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:42:51Z","timestamp":1760208171000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/7\/734"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,15]]},"references-count":40,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["rs9070734"],"URL":"https:\/\/doi.org\/10.3390\/rs9070734","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2017,7,15]]}}}