{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:35:15Z","timestamp":1760240115519,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T00:00:00Z","timestamp":1550534400000},"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":["41674029"],"award-info":[{"award-number":["41674029"]}],"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>The time-varying characteristic of the bias in the GPS code observation is investigated using triple-frequency observations. The method for estimating the combined code bias is presented and the twelve-month (1 January\u201331 December 2016) triple-frequency GPS data set from 114 International GNSS Service (IGS) stations is processed to analyze the characteristic of the combined code bias. The results show that the main periods of the combined code bias are 12, 8, 6, 4, 4.8 and 2.67 h. The time-varying characteristic of the combined code bias, which is the combination of differential code bias (DCB) (P1\u2013P5) and DCB (P1\u2013P2), shows that the real satellite DCBs are also time-varying. The difference between the two sets of the computed constant parts of the combined code bias, with the IGS DCB products of DCB (P1\u2013P2) and DCB (P1\u2013P2) and the mean of the estimated 24-h combined code bias series, further show that the combined code bias cannot be replaced by the DCB (P1\u2013P2) and DCB (P1\u2013P5) products. The time-varying part of inter-frequency clock bias (IFCB) can be estimated by the phase and code observations and the phase based IFCB is the combinations of the triple-frequency satellite uncalibrated phase delays (UPDs) and the code-based IFCB is the function of the DCBs. The performances of the computed the IFCB with different methods in single point positioning indicate that the accuracy for the constant part of the combined code bias is reduced, when the IGS DCB products are used to compute. These performances also show that the time-varying part of IFCB estimated with phase observation is better than that of code observation. The predicted results show that 98% of the predicted constant part of the combined code bias can be corrected and the attenuation of the predicted accuracy is much less evident. However, the accuracy of the predicted time-varying part decreases significantly with the predicted time.<\/jats:p>","DOI":"10.3390\/rs11040428","type":"journal-article","created":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T03:05:52Z","timestamp":1550631952000},"page":"428","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Investigation and Validation of the Time-Varying Characteristic for the GPS Differential Code Bias"],"prefix":"10.3390","volume":"11","author":[{"given":"Haojun","family":"Li","sequence":"first","affiliation":[{"name":"College of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China"}]},{"given":"Jingxin","family":"Xiao","sequence":"additional","affiliation":[{"name":"College of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China"}]},{"given":"Weidong","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Marine Sciences, Shanghai Ocean University, Shanghai 201306, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1007\/s10291-016-0572-7","article-title":"Review of code and phase biases in multi-GNSS positioning","volume":"21","author":"Hakansson","year":"2017","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1029\/94RS00449","article-title":"Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from Global Positioning System observations","volume":"29","author":"Sardon","year":"1994","journal-title":"Radio Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/S0273-1177(00)00164-2","article-title":"Total electron content in Australia corrected for receiver\/satellite bias and compared with IRI and PIM predictions","volume":"27","author":"Goodwin","year":"2001","journal-title":"Adv. Space Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1186\/BF03352422","article-title":"A new technique for mapping of total electron content using GPS network in Japan","volume":"54","author":"Otsuka","year":"2002","journal-title":"Earth Planets Space"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1109\/TAES.1987.310829","article-title":"Ionospheric time-delay algorithm for single frequency GPS users","volume":"23","author":"Klobuchar","year":"1987","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_6","unstructured":"Schaer, S. (1999). Mapping and Predicting the Earth\u2019s Ionosphere Using the Global Positioning System. [Ph.D. Thesis, Astronomical Institute, University of Bern]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.asr.2013.03.005","article-title":"The realization and convergence analysis of combined PPP based on raw observation","volume":"52","author":"Tu","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1007\/s001900000117","article-title":"Modeling and estimation of C1\u2013P1 bias in GPS receivers","volume":"74","author":"Gao","year":"2001","journal-title":"J. Geod."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1007\/s10291-016-0584-3","article-title":"Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution","volume":"21","author":"Tian","year":"2017","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s00190-007-0187-4","article-title":"Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations","volume":"82","author":"Ge","year":"2008","journal-title":"J. Geod."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s00190-011-0502-y","article-title":"Carrier-phase inter-frequency biases of GLONASS receivers","volume":"86","author":"Wanninger","year":"2011","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s00190-016-0983-9","article-title":"On the short-term temporal variations of GNSS receiver differential phase biases","volume":"91","author":"Zhang","year":"2017","journal-title":"J. Geod."},{"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":"2186","DOI":"10.1007\/s11433-012-4897-0","article-title":"Estimation of the inter-frequency clock bias for the satellites of PRN25 and PRN01","volume":"55","author":"Li","year":"2012","journal-title":"Sci. China-Phys. Mech. Astron."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","unstructured":"Leick, A., Rapoport, L., and Tatarnikov, D. (2015). GPS Satellite Surveying, Wiley. [4th ed.].","DOI":"10.1002\/9781119018612"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s10291-015-0438-4","article-title":"A new differential code bias (C1\u2013P1) estimation method and its performance evaluation","volume":"20","author":"Li","year":"2016","journal-title":"GPS Solut."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1007\/s10291-016-0578-1","article-title":"Impact of GPS differential code bias in dual- and triple-frequency positioning and satellite clock estimation","volume":"21","author":"Li","year":"2017","journal-title":"GPS Solut."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1088\/0026-1394\/45\/6\/S22","article-title":"A review of time and frequency transfer methods","volume":"45","author":"Levine","year":"2008","journal-title":"Metrologia"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1002\/navi.64","article-title":"Differential Code Bias Estimation using Multi-GNSSO bservations and Global Ionosphere Maps","volume":"61","author":"Montenbruck","year":"2014","journal-title":"Navigation"},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s00190-015-0867-4","article-title":"Determination of differential code biases with multi-GNSS observations","volume":"90","author":"Wang","year":"2016","journal-title":"J. Geod."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s10291-015-0437-5","article-title":"Is the long-term variation of the estimated GPS differential code biases associated with ionospheric variability?","volume":"20","author":"Zhong","year":"2016","journal-title":"GPS Solut."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.asr.2018.04.033","article-title":"The influence of grounding on GPS receiver differential code biases","volume":"62","author":"Choi","year":"2018","journal-title":"Adv. Space Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1134\/S001679321506016X","article-title":"Influence of GPS\/GLONASS differential code biases on the determination accuracy of the absolute total electron content in the ionosphere","volume":"55","author":"Yasyukevich","year":"2015","journal-title":"Geomagn. Aeron."},{"key":"ref_28","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."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/4\/428\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:33:16Z","timestamp":1760185996000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/4\/428"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,19]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["rs11040428"],"URL":"https:\/\/doi.org\/10.3390\/rs11040428","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2019,2,19]]}}}