{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T15:30:20Z","timestamp":1779377420467,"version":"3.53.1"},"reference-count":41,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T00:00:00Z","timestamp":1724889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Beijing Municipal Education Commission Research Project Funding","award":["KM202311232015"],"award-info":[{"award-number":["KM202311232015"]}]},{"name":"Beijing Municipal Education Commission Research Project Funding","award":["4244091"],"award-info":[{"award-number":["4244091"]}]},{"name":"Beijing Natural Science Foundation Project","award":["KM202311232015"],"award-info":[{"award-number":["KM202311232015"]}]},{"name":"Beijing Natural Science Foundation Project","award":["4244091"],"award-info":[{"award-number":["4244091"]}]},{"name":"Open Project of Beijing Key Laboratory of High Dynamic Navigation Technology","award":["KM202311232015"],"award-info":[{"award-number":["KM202311232015"]}]},{"name":"Open Project of Beijing Key Laboratory of High Dynamic Navigation Technology","award":["4244091"],"award-info":[{"award-number":["4244091"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In urban road environments, global navigation satellite system (GNSS) signals may be interrupted due to occlusion by buildings and obstacles, resulting in reduced accuracy and discontinuity of combined GNSS\/inertial navigation system (INS) positioning. Improving the accuracy and robustness of combined GNSS\/INS positioning systems for land vehicles in the presence of GNSS interruptions is a challenging task. The main objective of this paper is to develop a method for predicting GNSS information during GNSS outages based on a long short-term memory (LSTM) neural network to assist in factor graph-based combined GNSS\/INS localization, which can provide a reliable combined localization solution during GNSS signal outages. In an environment with good GNSS signals, a factor graph fusion algorithm is used for data fusion of the combined positioning system, and an LSTM neural network prediction model is trained, and model parameters are determined using the INS velocity, inertial measurement unit (IMU) output, and GNSS position incremental data. In an environment with interrupted GNSS signals, the LSTM model is used to predict the GNSS positional increments and generate the pseudo-GNSS information and the solved results of INS for combined localization. In order to verify the performance and effectiveness of the proposed method, we conducted real-world road test experiments on land vehicles installed with GNSS receivers and inertial sensors. The experimental results show that, compared with the traditional combined GNSS\/INS factor graph localization method, the proposed method can provide more accurate and robust localization results even in environments with frequent GNSS signal loss.<\/jats:p>","DOI":"10.3390\/s24175605","type":"journal-article","created":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T08:01:47Z","timestamp":1724918507000},"page":"5605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Hybrid Algorithm of LSTM and Factor Graph for Improving Combined GNSS\/INS Positioning Accuracy during GNSS Interruptions"],"prefix":"10.3390","volume":"24","author":[{"given":"Fuchao","family":"Liu","sequence":"first","affiliation":[{"name":"School of Automation, Beijing Information Science & Technology University, Beijing 100192, China"},{"name":"Beijing Key Laboratory of High Dynamic Navigation Technology, Beijing Information Science & Technology University, Beijing 100192, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hailin","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Information Science & Technology University, Beijing 100192, China"},{"name":"Beijing Key Laboratory of High Dynamic Navigation Technology, Beijing Information Science & Technology University, Beijing 100192, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3390-632X","authenticated-orcid":false,"given":"Wenjue","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Information Science & Technology University, Beijing 100192, China"},{"name":"Beijing Key Laboratory of High Dynamic Navigation Technology, Beijing Information Science & Technology University, Beijing 100192, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2854","DOI":"10.1109\/TITS.2016.2529000","article-title":"High-precision vehicle navigation in urban environments using an MEM\u2019s IMU and single-frequency GPS receiver","volume":"17","author":"Zhao","year":"2016","journal-title":"IEEE Trans. Intel. Trans. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jin, S., Wang, Q., and Dardanelli, G. (2022). A review on multi-GNSS for earth observation and emerging applications. Remote Sens., 14.","DOI":"10.3390\/rs14163930"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6864","DOI":"10.48084\/etasr.3908","article-title":"Complexity and limitations of GNSS signal reception in highly obstructed enviroments","volume":"11","author":"Hussain","year":"2021","journal-title":"Eng. Technol. Appl. Sci. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"153960","DOI":"10.1109\/ACCESS.2020.2973759","article-title":"GNSS vulnerabilities and existing solutions: A review of the literature","volume":"9","author":"Zidan","year":"2020","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Boguspayev, N., Akhmedov, D., Raskaliyev, A., Kim, A., and Sukhenko, A. (2023). A comprehensive review of GNSS\/INS integration techniques for land and air vehicle applications. Appl. Sci., 13.","DOI":"10.3390\/app13084819"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Dong, Y., Wang, D., Zhang, L., Li, Q., and Wu, J. (2020). Tightly coupled GNSS\/INS integration with robust sequential kalman filter for accurate vehicular navigation. Sensors, 20.","DOI":"10.3390\/s20020561"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Falco, G., Pini, M., and Marucco, G. (2017). Loose and tight GNSS\/INS integrations: Comparison of performance assessed in real urban scenarios. Sensors, 17.","DOI":"10.3390\/s17020255"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"9467","DOI":"10.1109\/JSEN.2023.3251389","article-title":"Robust state estimation via maximum correntropy EKF on matrix lie groups with application to low-cost INS\/GPS integrated navigation system","volume":"23","author":"Guo","year":"2023","journal-title":"IEEE Sensors J."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ibrahim, A., Abosekeen, A., Azouz, A., and Noureldin, A. (2023). Enhanced Autonomous Vehicle Positioning Using a Loosely Coupled INS\/GNSS-Based Invariant-EKF Integration. Sensors, 23.","DOI":"10.3390\/s23136097"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.inffus.2020.08.005","article-title":"Unscented kalman filter with process noise covariance estimation for vehicular INS\/GPS integration system","volume":"64","author":"Hu","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Al Bitar, N., and Gavrilov, A.I. (2020, January 25\u201327). Neural networks aided unscented Kalman filter for integrated INS\/GNSS systems. Proceedings of the 2020 27th Saint Petersburg International Conference on Integrated Navigation Systems (ICINS), St. Petersburg, Russia.","DOI":"10.23919\/ICINS43215.2020.9133878"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wen, W., Kan, Y.C., and Hsu, L.T. (2019, January 16\u201320). Performance comparison of GNSS\/INS integrations based on EKF and factor graph optimization. Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, FL, USA.","DOI":"10.33012\/2019.17129"},{"key":"ref_13","unstructured":"Sugimoto, S., Kubo, Y., and Tanikawara, M. (2009, January 22\u201325). A review and applications of the nonlinear filters to GNSS\/INS integrated algorithms. Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009), Savannah, GA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Osman, M., Hussein, A., and Al-Kaff, A. (2019, January 4\u20136). Intelligent vehicles localization approaches between estimation and information: A review. Proceedings of the 2019 IEEE International Conference on Vehicular Electronics and Safety (ICVES), Cairo, Egypt.","DOI":"10.1109\/ICVES.2019.8906426"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Tang, C., Zhang, L., Zhang, Y., and Song, H. (2018). Factor graph-assisted distributed cooperative positioning algorithm in the GNSS system. Sensors, 18.","DOI":"10.3390\/s18113748"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Beuchert, J., Camurri, M., and Fallon, M. (June, January 29). Factor graph fusion of raw GNSS sensing with IMU and lidar for precise robot localization without a base station. Proceedings of the 2023 IEEE International Conference on Robotics and Automation (ICRA), London, UK.","DOI":"10.1109\/ICRA48891.2023.10161522"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zeng, Q., Chen, W., Liu, J., and Wang, H. (2017). An improved multi-sensor fusion navigation algorithm based on the factor graph. Sensors, 17.","DOI":"10.3390\/s17030641"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1109\/TIE.2022.3150077","article-title":"A novel plug-and-play factor graph method for asynchronous absolute\/relative measurements fusion in multisensor positioning","volume":"70","author":"Bai","year":"2022","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1002\/navi.421","article-title":"Factor graph optimization for GNSS\/INS integration: A comparison with the extended kalman filter","volume":"68","author":"Wen","year":"2021","journal-title":"NAVIGATION J. Inst. Navig."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106370","DOI":"10.1016\/j.ast.2020.106370","article-title":"Tightly coupled integrated navigation system via factor graph for UAV indoor localization","volume":"108","author":"Song","year":"2021","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12044","DOI":"10.1109\/ACCESS.2021.3051715","article-title":"A multi-sensor information fusion method based on factor graph for integrated navigation system","volume":"9","author":"Xu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6175","DOI":"10.1109\/TITS.2020.2988531","article-title":"3D mapping database aided GNSS based collaborative positioning using factor graph optimization","volume":"22","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Intell. Trans. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2004","DOI":"10.1109\/TRO.2021.3133730","article-title":"GVINS: Tightly coupled GNSS\u2013visual\u2013inertial fusion for smooth and consistent state estimation","volume":"38","author":"Cao","year":"2022","journal-title":"IEEE Trans. Robot."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.cja.2021.09.001","article-title":"Factor graph based navigation and positioning for control system design: A review","volume":"35","author":"Wu","year":"2022","journal-title":"Chin. J. Aeronaut."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1134\/S2075108720010022","article-title":"Artificial intelligence based methods for accuracy improvement of integrated navigation systems during GNSS signal outages: An analytical overview","volume":"11","author":"Gavrilov","year":"2020","journal-title":"Gyroscopy Navig."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Siemuri, A., Kuusniemi, H., Elmusrati, M.S., V\u00e4lisuo, P., and Shamsuzzoha, A. (2021, January 1\u20133). Machine learning utilization in GNSS\u2014Use cases, challenges and future applications. Proceedings of the 2021 International Conference on Localization and GNSS (ICL-GNSS), Tampere, Finland.","DOI":"10.1109\/ICL-GNSS51451.2021.9452295"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"111358","DOI":"10.1016\/j.knosys.2023.111358","article-title":"Spatial memory-augmented visual navigation based on hierarchical deep reinforcement learning in unknown environments","volume":"285","author":"Jin","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Jwo, D.J., Biswal, A., and Mir, I.A. (2023). Artificial neural networks for navigation systems: A review of recent research. Appl. Sci., 13.","DOI":"10.3390\/app13074475"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2043","DOI":"10.1007\/s11277-021-08758-9","article-title":"Integrated navigation on vehicle based on low-cost SINS\/GNSS using deep learning","volume":"126","author":"Liu","year":"2022","journal-title":"Wirel. Pers. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.measurement.2017.01.053","article-title":"A hybrid fusion algorithm for GPS\/INS integration during GPS outages","volume":"103","author":"Yao","year":"2017","journal-title":"Measurement"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.dt.2019.08.011","article-title":"An INS\/GNSS integrated navigation in GNSS denied environment using recurrent neural network","volume":"16","author":"Dai","year":"2020","journal-title":"Def. Technol."},{"key":"ref_32","first-page":"1","article-title":"Smartphone PDR\/GNSS integration via factor graph optimization for pedestrian navigation","volume":"71","author":"Jiang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"112926","DOI":"10.1016\/j.measurement.2023.112926","article-title":"A multi-sensor fusion positioning approach for indoor mobile robot using factor graph","volume":"216","author":"Zhang","year":"2023","journal-title":"Measurement"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"11346","DOI":"10.1109\/TVT.2023.3270424","article-title":"An Enhanced Adaptable Factor Graph for Simultaneous Localization and Calibration in GNSS\/IMU\/Odometer Integration","volume":"72","author":"Bai","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/TRO.2021.3100156","article-title":"Associating uncertainty to extended poses for on lie group imu preintegration with rotating earth","volume":"38","author":"Brossard","year":"2021","journal-title":"IEEE Trans. Rob."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1016\/j.asr.2016.09.019","article-title":"An analysis of GPT2\/GPT2w+ Saastamoinen models for estimating zenith tropospheric delay over Asian area","volume":"59","author":"Liu","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"14534","DOI":"10.1109\/JSEN.2023.3278723","article-title":"FGO-GIL: Factor graph optimization-based GNSS RTK\/INS\/LiDAR Tightly Coupled Integration for precise and continuous navigation","volume":"23","author":"Li","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"107565","DOI":"10.1016\/j.ymssp.2020.107565","article-title":"An improved integrated navigation method with enhanced robustness based on factor graph","volume":"155","author":"Wei","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"108391","DOI":"10.1016\/j.measurement.2020.108391","article-title":"A new method for compensating the errors of integrated navigation systems using artificial neural networks","volume":"168","author":"Gavrilov","year":"2021","journal-title":"Measurement"},{"key":"ref_40","unstructured":"Chen, Y., Jiang, W., Wang, J., Cai, B., Liu, D., Ba, X., and Yang, Y. (2023). A LSTM-assisted GNSS\/INS integration system using IMU recomputed error information for train localization. IEEE Trans. Aerosp. Electro. Syst., 1\u201313."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Fang, W., Jiang, J., Lu, S., Gong, Y., Tao, Y., Tang, Y., Yan, P., Luo, H., and Liu, J. (2020). A LSTM algorithm estimating pseudo measurements for aiding INS during GNSS signal outages. Remote Sens., 12.","DOI":"10.3390\/rs12020256"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5605\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:45:01Z","timestamp":1760111101000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5605"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,29]]},"references-count":41,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["s24175605"],"URL":"https:\/\/doi.org\/10.3390\/s24175605","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,29]]}}}