{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T05:55:48Z","timestamp":1768974948139,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2021,7,28]],"date-time":"2021-07-28T00:00:00Z","timestamp":1627430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Wen-bin Shen","award":["42030105"],"award-info":[{"award-number":["42030105"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The present Global Navigation Satellite System (GNSS) can provide at least double-frequency observations, and especially the Galileo Navigation Satellite System (Galileo) can provide five-frequency observations for all constellation satellites. In this contribution, precision point positioning (PPP) models with Galileo E1, E5a, E5b, E5 and E6 frequency observations are established, including a dual-frequency (DF) ionospheric-free (IF) combination model, triple-frequency (TF) IF combination model, quad-frequency (QF) IF combination model, four five-frequency (FF) IF com-bination models and an FF uncombined (UC) model. The observation data of five stations for seven days are selected from the multi-GNSS experiment (MGEX) network, forming four time-frequency links ranging from 454.6 km to 5991.2 km. The positioning and time-frequency transfer performances of Galileo multi-frequency PPP are compared and evaluated using GBM (which denotes precise satellite orbit and clock bias products provided by Geo Forschung Zentrum (GFZ)), WUM (which denotes precise satellite orbit and clock bias products provided by Wuhan University (WHU)) and GRG (which denotes precise satellite orbit and clock bias products provided by the Centre National d\u2019Etudes Spatiales (CNES)) precise products. The results show that the performances of the DF, TF, QF and FF PPP models are basically the same, the frequency stabilities of most links can reach sub10\u221216 level at 120,000 s, and the average three-dimensional (3D) root mean square (RMS) of position and average frequency stability (120,000 s) can reach 1.82 cm and 1.18 \u00d7 10\u221215, respectively. The differences of 3D RMS among all models are within 0.17 cm, and the differences in frequency stabilities (in 120,000 s) among all models are within 0.08 \u00d7 10\u221215. Using the GRG precise product, the solution performance is slightly better than that of the GBM or WUM precise product, the average 3D RMS values obtained using the WUM and GRG precise products are 1.85 cm and 1.77 cm, respectively, and the average frequency stabilities at 120,000 s can reach 1.13 \u00d7 10\u221215 and 1.06 \u00d7 10\u221215, respectively.<\/jats:p>","DOI":"10.3390\/rs13152972","type":"journal-article","created":{"date-parts":[[2021,7,28]],"date-time":"2021-07-28T21:21:04Z","timestamp":1627507264000},"page":"2972","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Modeling and Performance Evaluation of Precise Positioning and Time-Frequency Transfer with Galileo Five-Frequency Observations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1645-6937","authenticated-orcid":false,"given":"Wei","family":"Xu","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Time and Frequency Geodesy Center, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9267-5982","authenticated-orcid":false,"given":"Wen-Bin","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Time and Frequency Geodesy Center, Wuhan University, Wuhan 430079, China"},{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3437-4820","authenticated-orcid":false,"given":"Cheng-Hui","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Time and Frequency Geodesy Center, Wuhan University, Wuhan 430079, China"}]},{"given":"Li-Hong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Time and Frequency Geodesy Center, Wuhan University, Wuhan 430079, China"}]},{"given":"Lei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Time and Frequency Geodesy Center, Wuhan University, Wuhan 430079, China"}]},{"given":"Zi-Yu","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Resource, Environmental Science and Engineering, Hubei University of Science and Technology, Xianning 437100, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1186\/s43020-020-00023-x","article-title":"Status, perspectives and trends of satellite navigation","volume":"1","author":"Hein","year":"2020","journal-title":"Satell. Navig."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s43020-019-0006-0","article-title":"Basic performance and future developments of BeiDou global navigation satellite system","volume":"1","author":"Yang","year":"2020","journal-title":"Satell. Navig."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1007\/s10291-016-0544-y","article-title":"GLONASS CDMA L3 ambiguity resolution and positioning","volume":"21","author":"Zaminpardaz","year":"2016","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1007\/s10291-018-0800-4","article-title":"Precise regional L5 positioning with IRNSS and QZSS: Stand-alone and combined","volume":"23","author":"Wang","year":"2018","journal-title":"GPS Solut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s10291-013-0311-2","article-title":"Precise position determination using a Galileo E5 single-frequency receiver","volume":"18","author":"Diessongo","year":"2013","journal-title":"GPS Solut."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"064008","DOI":"10.1088\/1361-6501\/ab69d5","article-title":"Assessment of multi-frequency global navigation satellite system precise point positioning models using GPS, BeiDou, GLONASS, Galileo and QZSS","volume":"31","author":"Su","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"56528","DOI":"10.1109\/ACCESS.2020.2982506","article-title":"A new cycle slip detection and repair method for Galileo four-frequency observations","volume":"8","author":"Chen","year":"2020","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s10291-018-0817-8","article-title":"A triple-frequency cycle slip detection and correction method based on modified HMW combinations applied on GPS and BDS","volume":"23","author":"Zhao","year":"2019","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/s00190-013-0619-2","article-title":"Triple-frequency GPS precise point positioning with rapid ambiguity resolution","volume":"87","author":"Geng","year":"2013","journal-title":"J. Geod."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/s00190-019-01341-y","article-title":"Beyond three frequencies: An extendable model for single-epoch decimeter-level point positioning by exploiting Galileo and BeiDou-3 signals","volume":"94","author":"Geng","year":"2020","journal-title":"J. Geod."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1017\/S0373463318000486","article-title":"Improving Galileo\u2019s carrier phase time transfer based on prior constraint information","volume":"72","author":"Zhang","year":"2018","journal-title":"J. Navig."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s10291-020-01062-2","article-title":"Sub-10\u221216 accuracy GNSS frequency transfer with IPPP","volume":"25","author":"Petit","year":"2021","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Leute, J., Petit, G., Exertier, P., Samain, E., Rovera, D., and Uhrich, P. (2018, January 10\u201312). High accuracy continuous time transfer with GPS IPPP and T2L2. Proceedings of the 2018 European Frequency and Time Forum (EFTF), Turin, Italy.","DOI":"10.1109\/EFTF.2018.8409043"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1186\/s43020-020-00012-0","article-title":"Precise time scales and navigation systems: Mutual benefits of timekeeping and positioning","volume":"1","author":"Tavella","year":"2020","journal-title":"Satell. Navig."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1080\/14498596.2019.1658652","article-title":"Assessing the performance of multi-frequency GPS, Galileo and BeiDou PPP ambiguity resolution","volume":"65","author":"Duong","year":"2019","journal-title":"J. Spat. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1016\/j.asr.2018.10.011","article-title":"RTK model and positioning performance analysis using Galileo four-frequency observations","volume":"63","author":"Tu","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1007\/s10291-019-0906-3","article-title":"An analysis of inter-system biases in BDS\/GPS precise point positioning","volume":"23","author":"Liu","year":"2019","journal-title":"GPS Solut."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"107356","DOI":"10.1016\/j.measurement.2019.107356","article-title":"Assessment of the BDS-3 on-board clocks and their impact on the PPP time transfer performance","volume":"153","author":"Qin","year":"2020","journal-title":"Measurement"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/s10291-019-0930-3","article-title":"Galileo PPP rapid ambiguity resolution with five-frequency observations","volume":"24","author":"Li","year":"2019","journal-title":"GPS Solut."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/s10291-020-0955-7","article-title":"Performance of Galileo precise time and frequency transfer models using quad-frequency carrier phase observations","volume":"24","author":"Zhang","year":"2020","journal-title":"GPS Solut."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1016\/j.asr.2020.04.054","article-title":"Assessing GPS\/Galileo real-time precise point positioning with ambiguity resolution based on phase biases from CNES","volume":"66","author":"Liu","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3147","DOI":"10.1016\/j.asr.2021.02.009","article-title":"Galileo real-time orbit determination with multi-frequency raw observations","volume":"67","author":"Kuang","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_25","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_26","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1186\/s43020-020-00014-y","article-title":"PPP models and performances from single- to quad-frequency BDS observations","volume":"1","author":"Jin","year":"2020","journal-title":"Satell. Navig."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ge, Y., Cao, X., Shen, F., Yang, X., and Wang, S. (2021). BDS-3\/Galileo time and frequency transfer with quad-frequency precise point positioning. Remote Sens., 13.","DOI":"10.3390\/rs13142704"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Leick, A., Rapoport, L., and Tatarnikov, D. (2015). GPS Satellite Surveying, John Wiley & Sons. [4th ed.].","DOI":"10.1002\/9781119018612"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/s10291-021-01100-7","article-title":"Characteristics of phase bias from CNES and its application in multi-frequency and multi-GNSS precise point positioning with ambiguity resolution","volume":"25","author":"Liu","year":"2021","journal-title":"GPS Solut."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1007\/s00190-019-01229-x","article-title":"Triple-frequency PPP ambiguity resolution with multi-constellation GNSS: BDS and Galileo","volume":"93","author":"Li","year":"2019","journal-title":"J. Geod."},{"key":"ref_31","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_32","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s00190-017-1071-5","article-title":"Joint estimation of vertical total electron content (VTEC) and satellite differential code biases (SDCBs) using low-cost receivers","volume":"92","author":"Zhang","year":"2018","journal-title":"J. Geod."},{"key":"ref_33","unstructured":"Petit, G., and Luzum, B. (2010). IERS Conventions (2010), Bureau International des Poids et Mesures Sevres. IERS Technical Note No. 36."},{"key":"ref_34","unstructured":"Kouba, J. (2009). A Guide to Using International GNSS Service (IGS) Products."},{"key":"ref_35","unstructured":"Wu, J.-T., Wu, S.C., Hajj, G.A., Bertiger, W.I., and Lichten, S.M. (1991, January 19\u201322). Effects of antenna orientation on GPS carrier phase. Proceedings of the Astrodynamics 1991, San Diego, CA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1007\/s10236-006-0086-x","article-title":"Modelling the global ocean tides: Modern insights from FES2004","volume":"56","author":"Lyard","year":"2006","journal-title":"Ocean Dyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF02522083","article-title":"Contributions to the theory of atmospheric refraction","volume":"107","author":"Saastamoinen","year":"1973","journal-title":"Bull. G\u00e9od\u00e9sique (1946\u20131975)"},{"key":"ref_38","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":"Heinkelmann","year":"2007","journal-title":"J. Geod."},{"key":"ref_39","first-page":"3","article-title":"Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data","volume":"33","author":"Niell","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"107836","DOI":"10.1016\/j.measurement.2020.107836","article-title":"Performance of ionospheric-free PPP time transfer models with BDS-3 quad-frequency observations","volume":"160","author":"Ge","year":"2020","journal-title":"Measurement"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/15\/2972\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:36:12Z","timestamp":1760164572000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/15\/2972"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,28]]},"references-count":40,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["rs13152972"],"URL":"https:\/\/doi.org\/10.3390\/rs13152972","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,28]]}}}