{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T01:43:29Z","timestamp":1778809409168,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T00:00:00Z","timestamp":1670889600000},"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":["42274030"],"award-info":[{"award-number":["42274030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["20ZR1462000"],"award-info":[{"award-number":["20ZR1462000"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22120210522"],"award-info":[{"award-number":["22120210522"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007219","name":"Shanghai Natural Science Foundation","doi-asserted-by":"publisher","award":["42274030"],"award-info":[{"award-number":["42274030"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007219","name":"Shanghai Natural Science Foundation","doi-asserted-by":"publisher","award":["20ZR1462000"],"award-info":[{"award-number":["20ZR1462000"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007219","name":"Shanghai Natural Science Foundation","doi-asserted-by":"publisher","award":["22120210522"],"award-info":[{"award-number":["22120210522"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities","award":["42274030"],"award-info":[{"award-number":["42274030"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["20ZR1462000"],"award-info":[{"award-number":["20ZR1462000"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["22120210522"],"award-info":[{"award-number":["22120210522"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Integrity monitoring (IM) is essential if GNSS positioning technologies are to be fully trusted by future intelligent transport systems. A tighter and conservative stochastic model can shrink protection levels in the position domain and therefore enhance the user-level integrity. In this study, the stochastic models for vehicle-based GNSS positioning are refined in three respects: (1) Gaussian bounds of precise orbit and clock error products from the International GNSS Service are used; (2) a variable standard deviation to characterize the residual tropospheric delay after model correction is adopted; and (3) an elevation-dependent model describing the receiver-related errors is adaptively refined using least-squares variance component estimation. The refined stochastic models are used for positioning and IM under the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) framework, which is considered the basis for multi-constellation GNSS navigation to support air navigation in the future. These refinements are assessed via global simulations and real data experiments. Different schemes are designed and tested to evaluate the corresponding enhancements on ARAIM availability for both aviation and ground vehicle-based positioning applications.<\/jats:p>","DOI":"10.3390\/s22249797","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T03:21:52Z","timestamp":1670988112000},"page":"9797","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["ARAIM Stochastic Model Refinements for GNSS Positioning Applications in Support of Critical Vehicle Applications"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7663-7743","authenticated-orcid":false,"given":"Ling","family":"Yang","sequence":"first","affiliation":[{"name":"College of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nan","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7276-1488","authenticated-orcid":false,"given":"Chris","family":"Rizos","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering, University of New South Wales, Sydney 2033, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiping","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hong Kong 999077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2762","DOI":"10.1109\/TITS.2017.2766768","article-title":"GNSS Position Integrity in Urban Environments: A Review of Literature","volume":"19","author":"Zhu","year":"2018","journal-title":"IEEE Trans. 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