{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:08Z","timestamp":1760146628377,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:00:00Z","timestamp":1732665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Laboratory","award":["614201004012209"],"award-info":[{"award-number":["614201004012209"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The legacy Global Navigation Satellite System (GNSS) satellite clock offsets obtained by the dual-frequency undifferenced (UD) ionospheric-free (IF) model absorb the code and phase time-variant hardware delays, which leads to the inconsistency of the precise satellite clock estimated by different frequencies. The dissimilarity of the satellite clock offsets generated by different frequencies is called the inter-frequency clock bias (IFCB). Estimates of the IFCB typically employ epoch-differenced (ED) geometry-free ionosphere-free (GFIF) observations from global networks. However, this method has certain theoretical flaws by ignoring the receiver time-variant biases. We proposed a new undifferenced model coupled with satellite clock offsets, and further converted the IFCB into the code and phase time-variant mixed observable-specific signal bias (OSB) to overcome the defects of the traditional model and simplify the bias correction process of multi-frequency precise point positioning (PPP). The new model not only improves the mixed OSB performance, but also avoids the negative impact of the receiver time-variant biases on the satellite mixed OSB estimation. The STD and RMS of the original OSB can be improved by 7.5\u201360.9% and 9.4\u201366.1%, and that of ED OSB (it can reflect noise levels) can be improved by 50.0\u201387.5% and 60.0\u201388.9%, respectively. Similarly, the corresponding PPP performance for using new mixed OSB is better than that of using the traditional IFCB products. Thus, the proposed pseudorange and phase time-variant mixed OSB concept and the new undifferenced model coupled with satellite clock offsets are reliable, applicable, and effective in multi-frequency PPP.<\/jats:p>","DOI":"10.3390\/rs16234433","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T08:17:42Z","timestamp":1732695462000},"page":"4433","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["BDS-3\/GNSS Undifferenced Pseudorange and Phase Time-Variant Mixed OSB Considering the Receiver Time-Variant Biases and Its Benefit on Multi-Frequency PPP"],"prefix":"10.3390","volume":"16","author":[{"given":"Guoqiang","family":"Jiao","sequence":"first","affiliation":[{"name":"Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3039-5106","authenticated-orcid":false,"given":"Ke","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Space Information, Space Engineering University, Beijing 101416, China"},{"name":"Key Laboratory of Smart Earth, Beijing 100094, China"},{"name":"National Key Laboratory of Space Target Awareness, Beijing 101416, China"}]},{"given":"Min","family":"Fan","sequence":"additional","affiliation":[{"name":"Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China"}]},{"given":"Yuze","family":"Yang","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}]},{"given":"Huaquan","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Space Information, Space Engineering University, Beijing 101416, China"},{"name":"Key Laboratory of Smart Earth, Beijing 100094, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"2135","DOI":"10.1016\/j.scib.2021.06.013","article-title":"Featured services and performance of BDS-3","volume":"66","author":"Yang","year":"2021","journal-title":"Sci. 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