{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T04:52:38Z","timestamp":1776919958712,"version":"3.51.2"},"reference-count":29,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2013,11,18]],"date-time":"2013-11-18T00:00:00Z","timestamp":1384732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Precise Point Positioning (PPP) has become a very hot topic in GNSS research and applications. However, it usually takes about several tens of minutes in order to obtain positions with better than 10 cm accuracy. This prevents PPP from being widely used in real-time kinematic positioning services, therefore, a large effort has been made to tackle the convergence problem. One of the recent approaches is the ionospheric delay constrained precise point positioning (IC-PPP) that uses the spatial and temporal characteristics of ionospheric delays and also delays from an a priori model. In this paper, the impact of the quality of ionospheric models on the convergence of IC-PPP is evaluated using the IGS global ionospheric map (GIM) updated every two hours and a regional satellite-specific correction model. Furthermore, the effect of the receiver differential code bias (DCB) is investigated by comparing the convergence time for IC-PPP with and without estimation of the DCB parameter. From the result of processing a large amount of data, on the one hand, the quality of the a priori ionosphere delays plays a very important role in IC-PPP convergence. Generally, regional dense GNSS networks can provide more precise ionosphere delays than GIM and can consequently reduce the convergence time. On the other hand, ignoring the receiver DCB may considerably extend its convergence, and the larger the DCB, the longer the convergence time. Estimating receiver DCB in IC-PPP is a proper way to overcome this problem. Therefore, current IC-PPP should be enhanced by estimating receiver DCB and employing regional satellite-specific ionospheric correction models in order to speed up its convergence for more practical applications.<\/jats:p>","DOI":"10.3390\/s131115708","type":"journal-article","created":{"date-parts":[[2013,11,19]],"date-time":"2013-11-19T03:19:41Z","timestamp":1384831181000},"page":"15708-15725","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":63,"title":["On the Convergence of Ionospheric Constrained Precise Point Positioning (IC-PPP) Based on Undifferential Uncombined Raw GNSS Observations"],"prefix":"10.3390","volume":"13","author":[{"given":"Hongping","family":"Zhang","sequence":"first","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhouzheng","family":"Gao","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"},{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maorong","family":"Ge","sequence":"additional","affiliation":[{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, Potsdam 14473, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoji","family":"Niu","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Huang","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4706-5373","authenticated-orcid":false,"given":"Rui","family":"Tu","sequence":"additional","affiliation":[{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, Potsdam 14473, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Potsdam 14473, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,11,18]]},"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."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/PL00012883","article-title":"Precise point positioning using IGS orbit and clock products","volume":"5","author":"Kouba","year":"2001","journal-title":"GPS Solut."},{"key":"ref_3","first-page":"1281","article-title":"Strong interseismic coupling, fault afterslip, and viscoelastic flow before and after the Oct. 9, 1995 Colima-Jalisco earthquake: Continuous GPS measurements from Colima, Mexico","volume":"29","author":"DeMets","year":"2002","journal-title":"Geophys. Res. Lett."},{"key":"ref_4","first-page":"360","article-title":"Demonstration of NRT GPS water vapor monitoring for numerical weather prediction in Germany","volume":"82","author":"Gendt","year":"2003","journal-title":"J. Meteo Soc. Jap."},{"key":"ref_5","unstructured":"Bock, H., Hugentobler, U., and Beutler, G. (2003). First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies, Springer."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1002\/j.2161-4296.2002.tb00260.x","article-title":"A new method for carrier-phase-based precise point positioning","volume":"49","author":"Gao","year":"2002","journal-title":"Navigation"},{"key":"ref_7","unstructured":"Bar-Sever, Y., Bell, B., Dorsey, A., and Srinivasan, J. (2003). Space Applications of the NASA Global Differential GPS System, Institute of Navigation."},{"key":"ref_8","unstructured":"Ye, S.R. (2002). Theory and its Realization of GPS Precise Point Positioning Using Un-Differenced Phase Observation, Wuhan University."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1007\/s00190-010-0404-4","article-title":"Rapid re-convergences to ambiguity-fixed solutions in precise point positioning","volume":"84","author":"Geng","year":"2010","journal-title":"J. Geod."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1061\/(ASCE)SU.1943-5428.0000017","article-title":"Global navigation satellite system ambiguity resolution with constraints from normal equations","volume":"136","author":"Li","year":"2009","journal-title":"J. Surv. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kleusberg, A., and Teunissen, P.J.G. (1996). GPS for Geodesy. Lecture Notes in Earth Science, Springer-Verlag.","DOI":"10.1007\/BFb0117676"},{"key":"ref_12","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_13","unstructured":"Laurichesse, D., Mercier, F., Berthias, J.P., and Bijac, J. (2008, January 28\u201330). Real Time Zero-Difference Ambiguities Fixing and Absolute RTK. San Diego, CA, USA."},{"key":"ref_14","unstructured":"Collins, P., Lahaye, F., Heroux, P., and Bisnath, S. (2008, January 16\u201319). Precise Point Positioning with Ambiguity Resolution Using the Decoupled Clock Model. Savannah, GA, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","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_16","unstructured":"Beran, T., Kim, D., and Langley, R.B. (2003, January 9\u201312). High-Precision Single-Frequency GPS Point Positioning. Portland, OR, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1698","DOI":"10.1016\/j.asr.2012.03.016","article-title":"An improved approach to model ionospheric delays for single-frequency precise point positioning","volume":"49","author":"Shi","year":"2012","journal-title":"Adv. Space Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"RS2016","DOI":"10.1029\/2011RS004880","article-title":"Wide area RTK: A satellite navigation system based on precise real-time ionospheric modeling","volume":"47","author":"Juan","year":"2012","journal-title":"Radio Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4213","DOI":"10.1109\/TGRS.2012.2189888","article-title":"Enhanced precise point positioning for GNSS users","volume":"50","author":"Juan","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","unstructured":"Schaer, S., Gurtner, W., and Feltens, J. (1998, January 9\u201311). IONEX: The Ionosphere Map Exchange Format Version 1. Darmstadt, Germany."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1029\/97RS02707","article-title":"A global mapping technique for GPS-derived ionospheric total electron content measurements","volume":"33","author":"Mannucci","year":"1998","journal-title":"Radio Sci."},{"key":"ref_22","first-page":"59","article-title":"Mapping and predicting the earth's ionosphere using the global positioning system","volume":"59","author":"Schaer","year":"1999","journal-title":"Geod. Geophys. Arb. Schweiz"},{"key":"ref_23","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_24","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_25","unstructured":"Zou, X., Tang, W., Shi, C., and Liu, J. (2012). China Satellite Navigation Conference (CSNC) 2012 Proceedings, Springer."},{"key":"ref_26","unstructured":"Dach, R., Hungentobler, U., Fridez, P., and Michael, M. (2007). Bernese GPS Software Version 5.0, University of Bern."},{"key":"ref_27","unstructured":"Wilson, B.D., and Mannucci, A.J. (1993, January 22\u201324). Instrumental Biases in Ionospheric Measurement Derived from GPS Data, Salt Lake City, UT, USA."},{"key":"ref_28","unstructured":"Le, A.Q., Tiberius, C.C.J.M., van der Marel, H., and Jakowski, N. (1998). Observing our Changing Earth, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s10712-010-9105-z","article-title":"A review of higher order ionospheric refraction effects on dual frequency GPS","volume":"32","author":"Petrie","year":"2011","journal-title":"Surv. Geophys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/11\/15708\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:50:40Z","timestamp":1760219440000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/11\/15708"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,18]]},"references-count":29,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2013,11]]}},"alternative-id":["s131115708"],"URL":"https:\/\/doi.org\/10.3390\/s131115708","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,18]]}}}