{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:38:35Z","timestamp":1760236715934,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,15]],"date-time":"2021-12-15T00:00:00Z","timestamp":1639526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) enables the estimation the ionospheric vertical total electron content (VTEC) as well as the by-product of the satellite Pseudorange observable-specific signal bias (OSB). The single-frequency PPP models, with the ionosphere-float and ionosphere-free approaches in ionospheric studies, have recently been discussed by the authors. However, the multi-frequency observations can improve the performances of the ionospheric research compared with the single-frequency approaches. This paper presents three dual-frequency PPP approaches using the BeiDou Navigation Satellite System (BDS) B1I\/B3I observations to investigate ionospheric activities. Datasets collected from the globally distributed stations are used to evaluate the performance of the ionospheric modeling with the ionospheric single- and multi-layer mapping functions (MFs), respectively. The characteristics of the estimated ionospheric VTEC and BDS satellite pseudorange OSB are both analyzed. The results indicated that the three dual-frequency PPP models could all be applied to the ionospheric studies, among which the dual-frequency ionosphere-float PPP model exhibits the best performance. The three dual-frequency PPP models all possess the capacity for ionospheric applications in the GNSS community.<\/jats:p>","DOI":"10.3390\/rs13245093","type":"journal-article","created":{"date-parts":[[2021,12,15]],"date-time":"2021-12-15T21:47:36Z","timestamp":1639604856000},"page":"5093","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Three Dual-Frequency Precise Point Positioning Models for the Ionospheric Modeling and Satellite Pseudorange Observable-Specific Signal Bias Estimation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3039-5106","authenticated-orcid":false,"given":"Ke","family":"Su","sequence":"first","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Multi-GNSS Positioning and Analysis System R&D Center, Qingdao 266000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5108-4828","authenticated-orcid":false,"given":"Shuanggen","family":"Jin","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"797","DOI":"10.5194\/angeo-30-797-2012","article-title":"A new global model for the ionospheric F2 peak height for radio wave propagation","volume":"30","author":"Hoque","year":"2012","journal-title":"Ann. 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