{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T10:48:03Z","timestamp":1768560483956,"version":"3.49.0"},"reference-count":22,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2024,8,14]],"date-time":"2024-08-14T00:00:00Z","timestamp":1723593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundation of China","award":["42074028"],"award-info":[{"award-number":["42074028"]}]},{"name":"the National Natural Science Foundation of China","award":["41704021"],"award-info":[{"award-number":["41704021"]}]},{"name":"the National Natural Science Foundation of China","award":["41701513"],"award-info":[{"award-number":["41701513"]}]},{"name":"the National Natural Science Foundation of China","award":["ZR2020MD042"],"award-info":[{"award-number":["ZR2020MD042"]}]},{"name":"the National Natural Science Foundation of China","award":["ZR2020MD065"],"award-info":[{"award-number":["ZR2020MD065"]}]},{"name":"the Natural Science Foundation of Shandong Province, China","award":["42074028"],"award-info":[{"award-number":["42074028"]}]},{"name":"the Natural Science Foundation of Shandong Province, China","award":["41704021"],"award-info":[{"award-number":["41704021"]}]},{"name":"the Natural Science Foundation of Shandong Province, China","award":["41701513"],"award-info":[{"award-number":["41701513"]}]},{"name":"the Natural Science Foundation of Shandong Province, China","award":["ZR2020MD042"],"award-info":[{"award-number":["ZR2020MD042"]}]},{"name":"the Natural Science Foundation of Shandong Province, China","award":["ZR2020MD065"],"award-info":[{"award-number":["ZR2020MD065"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Long-distance Real-Time Kinematic (RTK) positioning is crucial for applications in remote areas, such as maritime environments. Achieving 2\u20133 cm accuracy with RTK requires successful ambiguity resolution, which involves two main steps: identifying the best integer ambiguity candidate and confirming its validity. While previous research has largely concentrated on the first step, including the development of Cascading Ambiguity Resolution methods, and reducing tropospheric delay, studies on the validation of ambiguity for long-distance RTK are limited. This study conducts a thorough examination of ambiguity validation for long-distance RTK, focusing on two prevalent methods: the theoretical success rate and the R-ratio test. The results reveal several key insights. Firstly, the six commonly used bounds for the theoretical success rate are not an accurate reflection of the actual success rate, making them unsuitable for long-distance RTK applications. Secondly, the R-ratio test proves to be dependable when the threshold is set above 1.7, assuming there is a minimum observation period of one minute and at least ten satellites are visible. However, the probability of successfully resolving ambiguities with the R-ratio test does not surpass 50%. Additionally, if ambiguity resolution is not achieved within 20 min, simply prolonging the observation time is generally unproductive. To improve the performance of ambiguity resolution in practical situations that require extended observation times, this research proposes a novel ambiguity validation method. This new approach is based on the duration for which an integer ambiguity resolution candidate maintains the best status. This method aims to provide a reliable means of validating ambiguities in cases where the R-ratio test fails.<\/jats:p>","DOI":"10.3390\/rs16162982","type":"journal-article","created":{"date-parts":[[2024,8,14]],"date-time":"2024-08-14T09:20:51Z","timestamp":1723627251000},"page":"2982","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Detailed Investigation on Ambiguity Validation of Long-Distance RTK"],"prefix":"10.3390","volume":"16","author":[{"given":"Shengyue","family":"Ji","sequence":"first","affiliation":[{"name":"Department of Geomatics, China University of Petroleum (East China), Qingdao 266580, China"}]},{"given":"Jing","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Geomatics, China University of Petroleum (East China), Qingdao 266580, China"}]},{"given":"Duojie","family":"Weng","sequence":"additional","affiliation":[{"name":"Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1787-5191","authenticated-orcid":false,"given":"Wu","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s10291-009-0131-6","article-title":"Three carrier ambiguity resolution: Distance-independent performance demonstrated using semi-generated triple frequency GPS signals","volume":"14","author":"Li","year":"2010","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s00190-015-0869-2","article-title":"A new approach to modernized GPS phase-only ambiguity resolution over long baselines","volume":"90","author":"Chu","year":"2016","journal-title":"J. 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