{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:14:01Z","timestamp":1760235241023,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T00:00:00Z","timestamp":1628553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["4204094"],"award-info":[{"award-number":["4204094"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"General research project of Beijing education commission","award":["KM201910016007"],"award-info":[{"award-number":["KM201910016007"]}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFC0706003"],"award-info":[{"award-number":["2018YFC0706003"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science Foundation (NSFC) of China","award":["41930650"],"award-info":[{"award-number":["41930650"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>We investigate the estimation of the fractional cycle biases (FCBs) for GPS triple-frequency uncombined precise point positioning (PPP) with ambiguity resolution (AR) based on the IGS ultra-rapid predicted (IGU) orbits. The impact of the IGU orbit errors on the performance of GPS triple-frequency PPP AR is also assessed. The extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL) FCBs are generated with the single difference (SD) between satellites model using the global reference stations based on the IGU orbits. For comparison purposes, the EWL, WL and NL FCBs based on the IGS final precise (IGF) orbits are estimated. Each of the EWL, WL and NL FCBs based on IGF and IGU orbits are converted to the uncombined FCBs to implement the static and kinematic triple-frequency PPP AR. Due to the short wavelengths of NL ambiguities, the IGU orbit errors significantly impact the precision and stability of NL FCBs. An average STD of 0.033 cycles is achieved for the NL FCBs based on IGF orbits, while the value of the NL FCBs based on IGU orbits is 0.133 cycles. In contrast, the EWL and WL FCBs generated based on IGU orbits have comparable precision and stability to those generated based on IGF orbits. The use of IGU orbits results in an increased time-to-first-fix (TTFF) and lower fixing rates compared to the use of IGF orbits. Average TTFFs of 23.3 min (static) and 31.1 min (kinematic) and fixing rates of 98.1% (static) and 97.4% (kinematic) are achieved for the triple-frequency PPP AR based on IGF orbits. The average TTFFs increase to 27.0 min (static) and 37.9 min (kinematic) with fixing rates of 97.0% (static) and 96.3% (kinematic) based on the IGU orbits. The convergence times and positioning accuracy of PPP and PPP AR based on IGU orbits are slightly worse than those based on IGF orbits. Additionally, limited by the number of satellites transmitting three frequency signals, the introduction of the third frequency, L5, has a marginal impact on the performance of PPP and PPP AR. The GPS triple-frequency PPP AR performance is expected to improve with the deployment of new-generation satellites capable of transmitting the L5 signal.<\/jats:p>","DOI":"10.3390\/rs13163164","type":"journal-article","created":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T22:40:31Z","timestamp":1628635231000},"page":"3164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Estimating the Fractional Cycle Biases for GPS Triple-Frequency Precise Point Positioning with Ambiguity Resolution Based on IGS Ultra-Rapid Predicted Orbits"],"prefix":"10.3390","volume":"13","author":[{"given":"Lizhong","family":"Qu","sequence":"first","affiliation":[{"name":"School of Geomatics and Urban Spatial Information, Beijing University of Civil Engineering and Architecture, 1 Zhanlanguan Road, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geomatics and Urban Spatial Information, Beijing University of Civil Engineering and Architecture, 1 Zhanlanguan Road, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1270-5353","authenticated-orcid":false,"given":"Changfeng","family":"Jing","sequence":"additional","affiliation":[{"name":"School of Geomatics and Urban Spatial Information, Beijing University of Civil Engineering and Architecture, 1 Zhanlanguan Road, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingyi","family":"Du","sequence":"additional","affiliation":[{"name":"School of Geomatics and Urban Spatial Information, Beijing University of Civil Engineering and Architecture, 1 Zhanlanguan Road, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Geomatics and Urban Spatial Information, Beijing University of Civil Engineering and Architecture, 1 Zhanlanguan Road, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qile","family":"Zhao","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juanjuan","family":"Li","sequence":"additional","affiliation":[{"name":"54th Research Institution, China Electronics Technology Group Corporation, 589 Zhongshanxi Road, Shijiazhuang 050000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/s10291-013-0342-8","article-title":"Modeling and quality control for reliable precise point positioning integer ambiguity resolution with GNSS modernization","volume":"18","author":"Li","year":"2014","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1007\/s00190-018-1219-y","article-title":"Toward global instantaneous decimeter-level positioning using tightly coupled multi-constellation and multi-frequency GNSS","volume":"93","author":"Geng","year":"2018","journal-title":"J. Geod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00190-019-01330-1","article-title":"Speeding up PPP ambiguity resolution using triple-frequency GPS\/BeiDou\/Galileo\/QZSS data","volume":"94","author":"Geng","year":"2020","journal-title":"J. Geod."},{"key":"ref_4","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":"2012","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1007\/s10291-015-0483-z","article-title":"Generating GPS satellite fractional cycle bias for ambiguity-fixed precise point positioning","volume":"20","author":"Li","year":"2016","journal-title":"GPS Solut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","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_7","unstructured":"Laurichesse, D., Banville, S., and Innovation: Instantaneous Centimeter-level Multi-frequency Precise Point Positioning (2021, June 01). GPS World 4 July 2018. Available online: https:\/\/www.gpsworld.com\/innovation-instantaneous-centimeter-level-multi-frequency-precise-point-positioning\/."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1007\/s10291-016-0583-4","article-title":"Maintaining real-time precise point positioning during outages of orbit and clock corrections","volume":"21","author":"Deo","year":"2017","journal-title":"GPS Solut."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s10291-009-0138-z","article-title":"The impact of errors in predicted GPS orbits on zenith troposphere delay estimation","volume":"14","year":"2010","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10291-014-0380-x","article-title":"An impact analysis of arc length on orbit prediction and clock estimation for PPP ambiguity resolution","volume":"19","author":"Li","year":"2015","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/s00190-016-0885-x","article-title":"Improved PPP ambiguity resolution by COES FCB estimation","volume":"90","author":"Li","year":"2016","journal-title":"J. Geod."},{"key":"ref_12","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":"2011","journal-title":"GPS Solut."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xie, X., Fang, R., Geng, T., Wang, G., Zhao, Q., and Liu, J. (2018). Characterization of GNSS signals tracked by the iGMAS network considering recent BDS-3 satellites. Remote Sens., 10.","DOI":"10.3390\/rs10111736"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s00190-018-1176-5","article-title":"GPS inter-frequency clock bias estimation for both uncombined and ionospheric-free combined triple-frequency precise point positioning","volume":"93","author":"Pan","year":"2019","journal-title":"J. Geod."},{"key":"ref_15","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":"2015","journal-title":"J. Geod."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10291-019-0854-y","article-title":"Precise point positioning ambiguity resolution by integrating BDS-3e into BDS-2 and GPS","volume":"23","author":"Qu","year":"2019","journal-title":"GPS Solut."},{"key":"ref_17","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 positioning","volume":"92","author":"Guo","year":"2018","journal-title":"J. Geod."},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s00190-013-0611-x","article-title":"A method for improving uncalibrated phase delay estimation and ambiguity-fixing in real-time precise point positioning","volume":"87","author":"Li","year":"2013","journal-title":"J. Geod."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF00863419","article-title":"The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation","volume":"70","author":"Teunissen","year":"1995","journal-title":"J. Geod."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1007\/s001900050199","article-title":"Success probability of integer GPS ambiguity rounding and bootstrapping","volume":"72","author":"Teunissen","year":"1998","journal-title":"J. Geod."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"27525","DOI":"10.3390\/s151127525","article-title":"Improving ambiguity resolution for medium baselines using combined GPS and BDS dual\/triple-frequency observations","volume":"15","author":"Gao","year":"2015","journal-title":"Sensors"},{"key":"ref_24","unstructured":"Peter, J.G., and Montenbruck, O. (2017). The International GNSS Service. Teunissen, In Handbook of Global Navigation Satellite Systems, Springer. [1st ed.]."},{"key":"ref_25","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."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/s00190-015-0789-1","article-title":"Ionospheric effects in uncalibrated phase delay estimation and ambiguity-fixed PPP based on raw observable model","volume":"89","author":"Gu","year":"2015","journal-title":"J. Geod."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Nandarajah, N., Khodabandeh, A., Wang, K., Choudhury, M., and Teunissen, P.J.G. (2018). Multi-GNSS PPP-RTK: From Large- to Small-Scale Networks. Sensors, 18.","DOI":"10.3390\/s18041078"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10291-019-0929-9","article-title":"Multi-GNSS fractional cycle bias products generation for GNSS ambiguity-fixed PPP at Wuhan University","volume":"24","author":"Hu","year":"2020","journal-title":"GPS. Solut."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Liu, G., Guo, F., Wang, J., Du, M., and Qu, L. (2020). Triple-frequency GPS un-differenced and uncombined PPP ambiguity resolution using observable-specific satellite signal biases. Remote Sens., 12.","DOI":"10.3390\/rs12142310"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/16\/3164\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:43:40Z","timestamp":1760165020000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/16\/3164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,10]]},"references-count":29,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["rs13163164"],"URL":"https:\/\/doi.org\/10.3390\/rs13163164","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,8,10]]}}}