{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:32:50Z","timestamp":1774276370497,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,10]],"date-time":"2019-01-10T00:00:00Z","timestamp":1547078400000},"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":["41674016, 41274016, 41604024"],"award-info":[{"award-number":["41674016, 41274016, 41604024"]}],"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>With the modernization of Global Navigation Satellite System (GNSS), triple- or multi-frequency signals have become available from more and more GNSS satellites. The additional signals are expected to enhance the performance of precise point positioning (PPP) with ambiguity resolution (AR). To deal with the additional signals, we propose a unified modeling strategy for multi-frequency PPP AR based on raw uncombined observations. Based on the unified model, the fractional cycle biases (FCBs) generated from multi-frequency observations can be flexibly used, such as for dual- or triple- frequency PPP AR. Its efficiency is verified with Galileo and BeiDou triple-frequency observations collected from globally distributed MGEX stations. The estimated FCB are assessed with respect to residual distributions and standard deviations. The obtained results indicate good consistency between the input float ambiguities and the generated FCBs. To assess the performance of the triple-frequency PPP AR, 11 days of MGEX data are processed in three-hour sessions. The positional biases in the ambiguity-fixed solutions are significantly reduced compared with the float solutions. The improvements are 49.2%, 38.3%, and 29.6%, respectively, in east\/north\/up components for positioning with BDS, while the corresponding improvements are 60.0%, 29.0%, and 21.1% for positioning with Galileo. These results confirm the efficiency of the proposed approach, and that the triple-frequency PPP AR can bring an obvious benefit to the ambiguity-float PPP solution.<\/jats:p>","DOI":"10.3390\/rs11020116","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T04:10:16Z","timestamp":1547179816000},"page":"116","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["A Unified Model for Multi-Frequency PPP Ambiguity Resolution and Test Results with Galileo and BeiDou Triple-Frequency Observations"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1440-0446","authenticated-orcid":false,"given":"Guorui","family":"Xiao","sequence":"first","affiliation":[{"name":"Geodetic Institute, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany"},{"name":"Zhengzhou Institute of Surveying and Mapping, Zhengzhou 450052, China"}]},{"given":"Pan","family":"Li","sequence":"additional","affiliation":[{"name":"The German Research Centre for Geosciences (GFZ), D-14473 Potsdam, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6449-6696","authenticated-orcid":false,"given":"Yang","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Geomatics Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada"}]},{"given":"Bernhard","family":"Heck","sequence":"additional","affiliation":[{"name":"Geodetic Institute, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,10]]},"reference":[{"key":"ref_1","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_2","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. 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