{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T01:52:02Z","timestamp":1783389122926,"version":"3.54.6"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2015,6,10]],"date-time":"2015-06-10T00:00:00Z","timestamp":1433894400000},"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>Reliable and rapid ambiguity resolution (AR) is the key to fast precise point positioning (PPP). We propose a modified partial ambiguity resolution (PAR) method, in which an elevation and standard deviation criterion are first used to remove the low-precision ambiguity estimates for AR. Subsequently the success rate and ratio-test are simultaneously used in an iterative process to increase the possibility of finding a subset of decorrelated ambiguities which can be fixed with high confidence. One can apply the proposed PAR method to try to achieve an ambiguity-fixed solution when full ambiguity resolution (FAR) fails. We validate this method using data from 450 stations during DOY 021 to 027, 2012. Results demonstrate the proposed PAR method can significantly shorten the time to first fix (TTFF) and increase the fixing rate. Compared with FAR, the average TTFF for PAR is reduced by 14.9% for static PPP and 15.1% for kinematic PPP. Besides, using the PAR method, the average fixing rate can be increased from 83.5% to 98.2% for static PPP, from 80.1% to 95.2% for kinematic PPP respectively. Kinematic PPP accuracy with PAR can also be significantly improved, compared to that with FAR, due to a higher fixing rate.<\/jats:p>","DOI":"10.3390\/s150613627","type":"journal-article","created":{"date-parts":[[2015,6,10]],"date-time":"2015-06-10T14:05:21Z","timestamp":1433945121000},"page":"13627-13643","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":76,"title":["Precise Point Positioning with Partial Ambiguity Fixing"],"prefix":"10.3390","volume":"15","author":[{"given":"Pan","family":"Li","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaohong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,10]]},"reference":[{"key":"ref_1","unstructured":"Teunissen, P.J.G., Joosten, P., and Tiberius, C. (1999, January 25\u201327). Geometry-free ambiguity success rates in case of partial fixing. Proceedings of the ION NTM, San Diego, CA, USA."},{"key":"ref_2","unstructured":"Cao, W., O\u2019Keefe, K., and Cannon, M. (2007, January 25\u201328). Partial ambiguity fixing within multiple frequencies and systems. Proceedings of the ION GNSS, Fort Worth, TX, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00190-009-0343-0","article-title":"Partial integer decorrelation: Optimum trade-off between variance reduction and bias amplification","volume":"84","author":"Henkel","year":"2010","journal-title":"J. Geod."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/s10291-010-0198-0","article-title":"Increasing GNSS RTK availability with a new single-epoch batch partial ambiguity resolution algorithm","volume":"15","author":"Parkins","year":"2011","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00190-012-0573-4","article-title":"Reliability of partial ambiguity fixing with multiple GNSS constellations","volume":"87","author":"Wang","year":"2013","journal-title":"J. Geod."},{"key":"ref_6","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_7","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_8","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":"Navigation"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s00190-010-0371-9","article-title":"Single receiver phase ambiguity resolution with GPS data","volume":"84","author":"Bertiger","year":"2010","journal-title":"J. Geod."},{"key":"ref_10","first-page":"223","article-title":"PPP-RTK: Results of CORS network-based PPP with integer ambiguity resolution","volume":"42","author":"Teunissen","year":"2010","journal-title":"J. Aeronaut. Astronaut. Aviat. Ser. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1002\/j.2161-4296.2010.tb01772.x","article-title":"Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing","volume":"57","author":"Collins","year":"2010","journal-title":"Navigation"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1007\/s00190-012-0559-2","article-title":"Zero-difference GPS ambiguity resolution at CNES-CLS IGS Analysis Center","volume":"86","author":"Loyer","year":"2012","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.asr.2012.08.008","article-title":"Ambiguity resolution in precise point positioning with hourly data for global single receiver","volume":"51","author":"Zhang","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1664","DOI":"10.1016\/j.asr.2010.03.030","article-title":"Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning","volume":"47","author":"Geng","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_15","unstructured":"Verhagen, S., Teunissen, P.J.G., van der Marel, H., and Li, B. (2011, January 15\u201317). GNSS ambiguity resolution: Which subset to fix?. Proceedings of the 2011 IGNSS Symposium, International Global Navigation Satellite Systems Society, Sydney, Australia."},{"key":"ref_16","unstructured":"Shi, J., and Gao, Y. (2012, January 17\u201321). A fast integer ambiguity resolution method for PPP. Proceedings of the ION GNSS, Nashville, TN, USA."},{"key":"ref_17","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_18","doi-asserted-by":"crossref","first-page":"10187","DOI":"10.1029\/JB094iB08p10187","article-title":"Carrier phase ambiguity resolution for the Global Positioning System applied to geodetic baselines up to 2000 km","volume":"94","author":"Blewitt","year":"1989","journal-title":"J. Geophys. Res."},{"key":"ref_19","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_20","unstructured":"Melbourne, W.G. (1985, January 15\u201319). The case for ranging in GPS-based geodetic systems. Proceedings of the First International Symposium on Precise Positioning with the Global Positioning System, Rockville, MD, USA."},{"key":"ref_21","unstructured":"Wei, M., and Schwarz, K.P. (1995, January 12\u201315). Fast ambiguity resolution using an integer nonlinear programming method. Proceedings of the ION GNSS, Palm Springs, CA, USA."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s00190-010-0400-8","article-title":"Ambiguity validation with combined ratio test and ellipsoidal integer aperture estimator","volume":"84","author":"Ji","year":"2010","journal-title":"J. Geod."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1002\/j.2161-4296.2005.tb01736.x","article-title":"On the reliability of integer ambiguity resolution","volume":"52","author":"Verhagen","year":"2005","journal-title":"Navigation"},{"key":"ref_25","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_26","unstructured":"Teunissen, P.J.G., and Verhagen, S. (June, January 29). GNSS Ambiguity Resolution: When and How to Fix or not to Fix?. Proceedings of the VI Hotine-Marussi Symposium of Theoretical and Computational Geodesy: Challenge and Role of Modern Geodesy, Wuhan, China."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF03655276","article-title":"Rapid static positioning based on the fast ambiguity resolution approach FARA: Theory and first results","volume":"15","author":"Frei","year":"1990","journal-title":"Manuscr. Geod."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1179\/003962609X390058","article-title":"The GNSS ambiguity ratio-test revisited: A better way of using it","volume":"41","author":"Teunissen","year":"2009","journal-title":"Surv. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/s00190-013-0632-5","article-title":"Assessment of correct fixing rate for precise point positioning ambiguity resolution on global scale","volume":"87","author":"Zhang","year":"2013","journal-title":"J. Geod."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s00190-008-0281-2","article-title":"GNSS processing at CODE: Status report","volume":"83","author":"Dach","year":"2009","journal-title":"J. Geod."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s10291-005-0134-x","article-title":"Absolute phase center corrections of satellite and receiver antennas","volume":"9","author":"Schmid","year":"2009","journal-title":"GPS Solut."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF03655303","article-title":"Effects of antenna orientation on GPS carrier phase","volume":"18","author":"Wu","year":"1993","journal-title":"Manuscr. Geod."},{"key":"ref_33","first-page":"247","article-title":"Atmospheric correction for troposphere and stratosphere in radio ranging of satellites","volume":"Volume 15","author":"Henriksen","year":"1972","journal-title":"the Use of Artificial Satellites for Geodesy, Geophysics Monograph Series"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Boehm, J., Niell, A., Tregoning, P., and Schuh, H. (2006). Global Mapping Functions (GMF): A new empirical mapping function based on numerical weather model data. Geophys. Res. Lett., 33.","DOI":"10.1029\/2005GL025546"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s00190-011-0503-x","article-title":"Ray-traced slant factors for mitigating the tropospheric delay at the observation level","volume":"86","author":"Urquhart","year":"2012","journal-title":"J. Geod."},{"key":"ref_36","unstructured":"Takasu, T., and Yasuda, A. (2010, January 21\u201324). Kalman-filter-based integer ambiguity resolution strategy for long-baseline RTK with ionosphere and troposphere estimation. Proceedings of the ION GNSS, Portland, OR, USA."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wessel, P., and Smith, W.H.F. (1998). New, improved version of generic mapping tools released. EOS Trans. 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