{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T10:33:24Z","timestamp":1768559604392,"version":"3.49.0"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2014,11,25]],"date-time":"2014-11-25T00:00:00Z","timestamp":1416873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In order to catch up the short-term clock variation of GNSS satellites, clock corrections must be estimated and updated at a high-rate for Precise Point Positioning (PPP). This estimation is already very time-consuming for the GPS constellation only as a great number of ambiguities need to be simultaneously estimated. However, on the one hand better estimates are expected by including more stations, and on the other hand satellites from different GNSS systems must be processed integratively for a reliable multi-GNSS positioning service. To alleviate the heavy computational burden, epoch-differenced observations are always employed where ambiguities are eliminated. As the epoch-differenced method can only derive temporal clock changes which have to be aligned to the absolute clocks but always in a rather complicated way, in this paper, an efficient method for  high-rate clock estimation is proposed using the concept of \u201ccarrier-range\u201d realized by means of PPP with integer ambiguity resolution. Processing procedures for both post- and real-time processing are developed, respectively. The experimental validation shows that the computation time could be reduced to about one sixth of that of the existing methods for post-processing and less than 1 s for processing a single epoch of a network with about  200 stations in real-time mode after all ambiguities are fixed. This confirms that the proposed processing strategy will enable the high-rate clock estimation for future multi-GNSS networks in post-processing and possibly also in real-time mode.<\/jats:p>","DOI":"10.3390\/s141222300","type":"journal-article","created":{"date-parts":[[2014,11,25]],"date-time":"2014-11-25T11:01:31Z","timestamp":1416913291000},"page":"22300-22312","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Efficient High-Rate Satellite Clock Estimation for PPP Ambiguity Resolution Using Carrier-Ranges"],"prefix":"10.3390","volume":"14","author":[{"given":"Hua","family":"Chen","sequence":"first","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"}]},{"given":"Weiping","family":"Jiang","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"}]},{"given":"Maorong","family":"Ge","sequence":"additional","affiliation":[{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, Potsdam 14473, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7379-5276","authenticated-orcid":false,"given":"Jens","family":"Wickert","sequence":"additional","affiliation":[{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, Potsdam 14473, Germany"}]},{"given":"Harald","family":"Schuh","sequence":"additional","affiliation":[{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, Potsdam 14473, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2014,11,25]]},"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":"1083","DOI":"10.1007\/s00190-009-0326-1","article-title":"High-rate GPS clock corrections from CODE: Support of 1 Hz applications","volume":"83","author":"Bock","year":"2009","journal-title":"J. Geod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1007\/s10291-005-0131-0","article-title":"Rapid orbit determination of LEO satellites using IGS clock and ephemeris products","volume":"9","author":"Montenbruck","year":"2005","journal-title":"GPS Solut."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s10291-010-0191-7","article-title":"Satellite clock estimation at 1 Hz for real time kinematic PPP applications","volume":"15","author":"Zhang","year":"2010","journal-title":"GPS Solut."},{"key":"ref_5","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":"2011","journal-title":"GPS Solut."},{"key":"ref_6","unstructured":"Blewitt, G., Bertiger, W., and Weiss, J.P. (July, January 28). Ambizap3 and GPS Carrier-range: A New Data Type with IGS Applications. Newcastle, UK."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Blewitt, G. (2008). Fixed point theorems of GPS carrier phase ambiguity resolution and their application to massive network processing: Ambizap. J. Geophys. Res., 113.","DOI":"10.1029\/2008JB005736"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1007\/s00190-014-0727-7","article-title":"An enhanced strategy for GNSS data processing of massive networks","volume":"88","author":"Chen","year":"2014","journal-title":"J. Geod."},{"key":"ref_9","unstructured":"Schaer, S., and Steigenberger, P. (2006, January 8\u201311). Determination and use of GPS differential code bias values. Darmstadt, Germany."},{"key":"ref_10","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_11","unstructured":"Melbourne, W.G. (1985, January 15\u201319). The case for ranging in GPS-based geodetic systems. Rockville, MD, USA."},{"key":"ref_12","unstructured":"W\u00fcbbena, G. (1985, January 15\u201319). Software developments for geodetic positioning with GPS using TI-4100 code and carrier measurements. Rockville, MD, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2","DOI":"10.5081\/jgps.11.1.2","article-title":"A Novel Real-time Precise Positioning Service System: Global Precise Point Positioning with Regional Augmentation","volume":"11","author":"Ge","year":"2012","journal-title":"J. GPS"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1017\/S0373463312000112","article-title":"Improving the Estimation of Uncalibrated Fractional Phase Offsets for PPP Ambiguity Resolution","volume":"65","author":"Li","year":"2012","journal-title":"J. Navig."},{"key":"ref_15","unstructured":"Collins, P. (2008, January 28\u201330). Isolating and estimating undifferenced GPS integer ambiguities. San Diego, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1002\/j.2161-4296.2009.tb01750.x","article-title":"Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination","volume":"56","author":"Laurichesse","year":"2009","journal-title":"Navig J. Inst. Navig."},{"key":"ref_17","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_18","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1007\/BF02899825","article-title":"PANDA Software and Its Preliminary Result of Positioning and Orbit Determination","volume":"8","author":"Liu","year":"2003","journal-title":"Wuhan Univ. J. Nat. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Shi, C., Zhao, Q., Geng, J., Lou, Y., Ge, M., and Liu, J. (2008, January 29). Recent development of PANDA software in GNSS data processing. Wuhan, China.","DOI":"10.1117\/12.816261"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s00190-006-0044-x","article-title":"A new data processing strategy for huge GNSS global networks","volume":"80","author":"Ge","year":"2006","journal-title":"J. Geod."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10291-013-0310-3","article-title":"Real-time precise point positioning regional augmentation for large GPS reference networks","volume":"18","author":"Li","year":"2014","journal-title":"GPS Solut."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1007\/s00190-010-0399-x","article-title":"Integer ambiguity resolution in precise point positioning: Method comparison","volume":"84","author":"Geng","year":"2010","journal-title":"J. Geod."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/12\/22300\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:09:53Z","timestamp":1760216993000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/12\/22300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,25]]},"references-count":22,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2014,12]]}},"alternative-id":["s141222300"],"URL":"https:\/\/doi.org\/10.3390\/s141222300","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,25]]}}}