{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T00:30:52Z","timestamp":1760747452935,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:00:00Z","timestamp":1760659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Natural Science Foundation of Liaoning Province, China","award":["2025-BS-0398"],"award-info":[{"award-number":["2025-BS-0398"]}]},{"name":"the Open Fund of Hubei Luojia Laboratory","award":["250100018"],"award-info":[{"award-number":["250100018"]}]},{"DOI":"10.13039\/501100018617","name":"the LiaoNing Revitalization Talents Program","doi-asserted-by":"publisher","award":["XLYC2203162"],"award-info":[{"award-number":["XLYC2203162"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To address the problem of the degraded positioning accuracy of the long-baseline undifferenced network RTK (URTK) under extreme space weather conditions, herein, we propose a user-side atmospheric delay estimation strategy based on the undifferenced network RTK concept to enhance positioning performance in geomagnetic storm environments. First, an ambiguity-resolution model that jointly estimates atmospheric error parameters is used to fix the carrier-phase integer ambiguities for long-baseline reference stations. The accurately fixed inter-station ambiguities are then linearly transformed to recover station-specific undifferenced integer ambiguities; undifferenced observation errors at each reference station are computed to generate corresponding undifferenced correction terms. Lastly, recognizing that ionospheric delays vary sharply during geomagnetic storms and can severely compromise the availability of regional undifferenced correction models, we estimate the residual atmospheric parameters on the user side after applying regional corrections. Experimental results show that the server side is not significantly impacted during geomagnetic storms and can continue operating normally. On the user side, augmenting the solution with atmospheric parameter estimation effectively improves positioning availability. Under strong geomagnetic storms, the proposed mode improves user-station positioning accuracy by 63.7%, 60.7%, and 64.4% in the east (E), north (N), and up (U) components, respectively, relative to the conventional user-side solution; under moderate storm conditions, the corresponding improvements are 16.7%, 10.0%, and 11.1%.<\/jats:p>","DOI":"10.3390\/s25206433","type":"journal-article","created":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T16:13:03Z","timestamp":1760717583000},"page":"6433","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["User-Side Long-Baseline Undifferenced Network RTK Positioning Under Geomagnetic Storm Conditions Using a Power Spectral Density-Constrained Ionospheric Delay Model"],"prefix":"10.3390","volume":"25","author":[{"given":"Yixi","family":"Wang","sequence":"first","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"},{"name":"College of Surveying and Mapping Engineering, Heilongjiang Institute of Technology, Harbin 150050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8605-6536","authenticated-orcid":false,"given":"Huizhong","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuanfeng","family":"Song","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10291-004-0120-8","article-title":"An approach for instantaneous ambiguity resolution for medium- to long-range multiple reference station networks","volume":"9","author":"Hu","year":"2005","journal-title":"GPS Solut."},{"key":"ref_2","first-page":"1146","article-title":"An Algorithm of Long Distance Undifference Network RTK with BDS-3\/BDS-2 Multi-frequency Data","volume":"48","author":"Zhu","year":"2023","journal-title":"Geomat. 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