{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T13:07:10Z","timestamp":1770988030389,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T00:00:00Z","timestamp":1770940800000},"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":["52472344"],"award-info":[{"award-number":["52472344"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Major Cultivation Project of University Research Innovation Platform","award":["2024CXPT-17"],"award-info":[{"award-number":["2024CXPT-17"]}]},{"name":"Gansu Provincial Talent Innovation and Entrepreneurship Program","award":["2022-RC-56"],"award-info":[{"award-number":["2022-RC-56"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The integrated strapdown inertial navigation system (SINS)\/global navigation satellite system (GNSS) has been widely adopted in railway positioning applications. However, conventional filtering-based approaches are fundamentally constrained by their dependence on instantaneous state estimates while failing to exploit valuable historical measurement information. To overcome this limitation, we develop a factor graph optimization (FGO) framework to enhance data utilization efficiency. During GNSS signal outages, existing implementations typically preserve only SINS factors while excluding GNSS observations, leading to unbounded error growth. To bridge this gap, our novel solution integrates a gated recurrent unit (GRU) with an Improved Bidirectional Long Short-Term Memory (IBiLSTM) network to generate accurate pseudo-GNSS observations through effective learning from both preceding and subsequent GNSS data sequences. Comprehensive evaluation under GNSS-denied conditions demonstrates that our approach achieves significant improvements over conventional neural network-aided methods, with horizontal root mean square error (RMSE) reductions of 49.22% (simulation) and 36.24% (onboard vehicle). Subsequent FGO processing yields additional performance gains, further reducing RMSE by 46.67% (simulation) and 35.31% (onboard vehicle). This innovative methodology effectively maintains positioning accuracy and ensures navigation continuity during GNSS outages, thereby offering a robust solution for train positioning systems in challenging environments.<\/jats:p>","DOI":"10.3390\/s26041226","type":"journal-article","created":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T12:06:59Z","timestamp":1770984419000},"page":"1226","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Train Factor Graph Fusion Localization Method Assisted by GRU-IBiLSTM for Low-Cost SINS\/GNSS"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6466-526X","authenticated-orcid":false,"given":"Cheng","family":"Chen","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangwu","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinye","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1109\/TVT.2023.3307736","article-title":"Metro Train Autonomous Positioning Using Zero-Velocity Update Based on Train Motion Characteristics","volume":"73","author":"Zhang","year":"2023","journal-title":"IEEE Trans. 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