{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T22:01:22Z","timestamp":1778277682582,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T00:00:00Z","timestamp":1672099200000},"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":["42174035"],"award-info":[{"award-number":["42174035"]}],"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":["ZR2021QD148"],"award-info":[{"award-number":["ZR2021QD148"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Talent Introduction Plan for Youth Innovation Team in Universities of Shandong Province","award":["42174035"],"award-info":[{"award-number":["42174035"]}]},{"name":"Talent Introduction Plan for Youth Innovation Team in Universities of Shandong Province","award":["ZR2021QD148"],"award-info":[{"award-number":["ZR2021QD148"]}]},{"name":"Shandong Provincial Natural Science Foundation, China","award":["42174035"],"award-info":[{"award-number":["42174035"]}]},{"name":"Shandong Provincial Natural Science Foundation, China","award":["ZR2021QD148"],"award-info":[{"award-number":["ZR2021QD148"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The global navigation satellite system (GNSS) and inertial navigation system (INS) integrated navigation system have been widely used in Intelligent Transportation Systems (ITSs). However, the positioning error of integrated navigation systems is rapidly divergent when GNSS outages occur. Motion constraint and back propagation (BP) neural networks can provide additional knowledge to solve this issue. However, the predictions of a neural network have outliers and motion constraint is difficult to adapt according to the motion states of vehicles and boats. Therefore, this paper fused a BP neural network with motion constraints, and proposed a motion-constrained GNSS\/INS integrated navigation method based on a BP neural network (MC-BP method). The pseudo-measurement of the GNSS was predicted using a fitting model trained by the BP neural network. At the same time, the prediction outliers were detected and corrected using motion constraint. To assess the performance of the proposed method, simulated and real data experiments were conducted with a vehicle on land and a boat offshore. A classical GNSS\/INS integration algorithm, a motion-constrained GNSS\/INS algorithm, and the proposed method were compared through data processing. Compared with the classical GNSS\/INS integration algorithm and the motion-constrained GNSS\/INS algorithm, the positioning accuracies of the proposed method were improved by 90% and 64%, respectively, in the vehicle land experiment. Similar performances were found in the offshore boat experiment. Using the proposed MC-BP method, improved meter-level-positioning results can be achieved with the GNSS\/INS integration algorithm when GNSS outages occur.<\/jats:p>","DOI":"10.3390\/rs15010154","type":"journal-article","created":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T05:30:27Z","timestamp":1672205427000},"page":"154","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Motion-Constrained GNSS\/INS Integrated Navigation Method Based on BP Neural Network"],"prefix":"10.3390","volume":"15","author":[{"given":"Ying","family":"Xu","sequence":"first","affiliation":[{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"},{"name":"Qingdao Key Laboratory of Beidou Navigation and Intelligent Spatial Information Technology Application, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changhui","family":"Jiang","sequence":"additional","affiliation":[{"name":"GEOLOC Laboratory, Universit\u00e9 Gustave Eiffel, 77454 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0804-3972","authenticated-orcid":false,"given":"Zeyu","family":"Li","sequence":"additional","affiliation":[{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8851-0261","authenticated-orcid":false,"given":"Cheng","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Land Surveying and Geoinformatics, China University of Geosciences, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dun","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of GNSS High Precision Positioning and Ionosphere Correction, No. 22nd Research Institute, CETC, Qingdao 266108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiping","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shandong Provincial Institute of Land Surveying and Mapping, Jinan 250013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5201","DOI":"10.1109\/TITS.2020.2970276","article-title":"Joint computing and caching in 5G-Envisioned internet of vehicles: A deep reinforcement learning-based traffic control system","volume":"22","author":"Ning","year":"2020","journal-title":"IEEE Trans. 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