{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T21:48:39Z","timestamp":1775080119237,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T00:00:00Z","timestamp":1720396800000},"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":["52101358"],"award-info":[{"award-number":["52101358"]}],"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":["41906154"],"award-info":[{"award-number":["41906154"]}],"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":["2024A1515030159"],"award-info":[{"award-number":["2024A1515030159"]}],"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":["BE2022783"],"award-info":[{"award-number":["BE2022783"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangdong Provincial Natural Science Foundation","award":["52101358"],"award-info":[{"award-number":["52101358"]}]},{"name":"Guangdong Provincial Natural Science Foundation","award":["41906154"],"award-info":[{"award-number":["41906154"]}]},{"name":"Guangdong Provincial Natural Science Foundation","award":["2024A1515030159"],"award-info":[{"award-number":["2024A1515030159"]}]},{"name":"Guangdong Provincial Natural Science Foundation","award":["BE2022783"],"award-info":[{"award-number":["BE2022783"]}]},{"name":"Jiangsu Provincial Key Research and Development Program","award":["52101358"],"award-info":[{"award-number":["52101358"]}]},{"name":"Jiangsu Provincial Key Research and Development Program","award":["41906154"],"award-info":[{"award-number":["41906154"]}]},{"name":"Jiangsu Provincial Key Research and Development Program","award":["2024A1515030159"],"award-info":[{"award-number":["2024A1515030159"]}]},{"name":"Jiangsu Provincial Key Research and Development Program","award":["BE2022783"],"award-info":[{"award-number":["BE2022783"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In GNSS\/IMU integrated navigation systems, factors like satellite occlusion and non-line-of-sight can degrade satellite positioning accuracy, thereby impacting overall navigation system results. To tackle this challenge and leverage historical pseudorange information effectively, this paper proposes a graph optimization-based GNSS\/IMU model with virtual constraints. These virtual constraints in the graph model are derived from the satellite\u2019s position from the previous time step, the rate of change of pseudoranges, and ephemeris data. This virtual constraint serves as an alternative solution for individual satellites in cases of signal anomalies, thereby ensuring the integrity and continuity of the graph optimization model. Additionally, this paper conducts an analysis of the graph optimization model based on these virtual constraints, comparing it with traditional graph models of GNSS\/IMU and SLAM. The marginalization of the graph model involving virtual constraints is analyzed next. The experiment was conducted on a set of real-world data, and the results of the proposed method were compared with tightly coupled Kalman filtering and the original graph optimization method. In instantaneous performance testing, the method maintains an RMSE error within 5% compared with real pseudorange measurement, while in a continuous performance testing scenario with no available GNSS signal, the method shows approximately a 30% improvement in horizontal RMSE accuracy over the traditional graph optimization method during a 10-second period. This demonstrates the method\u2019s potential for practical applications.<\/jats:p>","DOI":"10.3390\/s24134419","type":"journal-article","created":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T12:21:03Z","timestamp":1720441263000},"page":"4419","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Study on Graph Optimization Method for GNSS\/IMU Integrated Navigation System Based on Virtual Constraints"],"prefix":"10.3390","volume":"24","author":[{"given":"Haiyang","family":"Qiu","sequence":"first","affiliation":[{"name":"School of Naval Architecture and Ocean Engineering, Guangzhou Maritime University, Guangzhou 510725, China"}]},{"given":"Yun","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Automation, Jiangsu University of Science and Technology, Zhenjiang 212003, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1863-4813","authenticated-orcid":false,"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Naval Architecture and Ocean Engineering, Guangzhou Maritime University, Guangzhou 510725, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1887-6222","authenticated-orcid":false,"given":"Lei","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430072, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ai, Q., Zhang, B., Yuan, Y., Xu, T., Chen, Y., and Tan, B. 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