{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T06:23:54Z","timestamp":1770963834033,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T00:00:00Z","timestamp":1770422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018542","name":"Natural Science Foundation of Sichuan Province","doi-asserted-by":"publisher","award":["2024NSFSC0841"],"award-info":[{"award-number":["2024NSFSC0841"]}],"id":[{"id":"10.13039\/501100018542","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["BDCC"],"abstract":"<jats:p>The enhanced long-range navigation (eLoran) system serves as an important backup method for the global navigation satellite system (GNSS) system. In long-distance transmission scenarios, the signal propagation delay of the eLoran system is affected by fluctuations in meteorological factors along the path. Regarding these issues, such as the potential timing system errors caused by meteorological factors and the limitation on the accuracy of the timing system, in this paper, an innovative prediction model is proposed to predict the propagation delay data by fusing the propagation delay data of multiple differential reference stations on the path and the path-weighted meteorological data. By collecting and processing actual data, four types of prediction tasks were designed. Comparative analyses of the prediction performance of eight common models were conducted on a unified dataset. The results show that the Pucheng\u2013Zhengzhou path-weighted ten-factor back-propagation neural network (PZWT-BPNN) model performs the best, achieving a balance between prediction accuracy and training efficiency. This model effectively suppresses the timing errors caused by meteorological fluctuations and improves the prediction accuracy of the propagation delay of the system, providing corresponding technical support for key fields such as low-altitude economy and transportation.<\/jats:p>","DOI":"10.3390\/bdcc10020054","type":"journal-article","created":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T12:42:42Z","timestamp":1770640962000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Research on Modeling Method of eLoran Signal Propagation Delay Prediction Model: Integrating Path-Weighted Meteorological Data and Propagation Delay Data in Long-Distance Scenarios"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7640-6137","authenticated-orcid":false,"given":"Tao","family":"Jin","sequence":"first","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiyao","family":"Liu","sequence":"additional","affiliation":[{"name":"Academic of Data Science, Xi\u2019an Eurasia University, Xi\u2019an 710065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baorong","family":"Yan","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiang","family":"Jiang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Guo","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"},{"name":"Key Laboratory of Time Reference and Applications, Chinese Academy of Sciences, Xi\u2019an 710600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Hua","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shougang","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Sciences, Xi\u2019an 710600, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100039, China"},{"name":"Key Laboratory of Time Reference and Applications, Chinese Academy of Sciences, Xi\u2019an 710600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9852-9233","authenticated-orcid":false,"given":"Lu","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Software Engineering, Chengdu University of Information Technology, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1007\/s11430-022-1069-7","article-title":"Development Trends of the National Secure PNT System Based on BDS","volume":"66","author":"Yang","year":"2023","journal-title":"Sci. China-Earth Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1134\/S2075108724700202","article-title":"Navigation without GPS","volume":"15","author":"Rivkin","year":"2024","journal-title":"Gyroscopy Navig."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1017\/S0373463308005213","article-title":"GPS Jamming and the Impact on Maritime Navigation","volume":"62","author":"Grant","year":"2009","journal-title":"J. Navig."},{"key":"ref_4","first-page":"11","article-title":"GNSS Vulnerability Analysis and Assessment","volume":"46","author":"Zhao","year":"2014","journal-title":"J. Aeronaut. Astronaut. Aviat."},{"key":"ref_5","first-page":"42","article-title":"Global Navigation Satellite System (GNSS) Spoofing: A Review of Growing Risks and Mitigation Steps","volume":"6","author":"Dinesh","year":"2013","journal-title":"Def. ST Tech. Bull."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","unstructured":"Dardanelli, G., and Maltese, A. (2022). On the accuracy of cadastral marks: Statistical analyses to assess the congruence among GNSS-based positioning and official maps. Remote Sens., 14.","DOI":"10.3390\/rs14164086"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Son, P.W., Park, S.G., Han, Y., Seo, K., and Fang, T.H. (2023). Demonstration of the Feasibility of the Korean eLoran System as a Resilient PNT in a Testbed. Remote Sens., 15.","DOI":"10.3390\/rs15143586"},{"key":"ref_9","unstructured":"Wu, H.T. (2002). Study on the Independent Time Service and Date Communication over Loran-C. [Ph.D. Thesis, University of Chinese Academy of Sciences (National Time Service Center)]. Available online: https:\/\/d.wanfangdata.com.cn\/thesis\/W010252."},{"key":"ref_10","unstructured":"Van Willigen, D., Offermans, G.W.A., and Helwig, A.W.S. (1998, January 20\u201323). EUROFIX: Definition and current status. Proceedings of the IEEE 1998 Position Location and Navigation Symposium, Palm Springs, CA, USA. Available online: https:\/\/www.semanticscholar.org\/paper\/EUROFIX%3A-definition-and-current-status-Willigen-Offermans\/b6406c270b48e09b8fe424586c9434778551b175."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Liu, S.Y., Guo, W., Hua, Y., and Kou, W.D. (2023). ELoran Propagation Delay Prediction Model Based on a BP Neural Network for a Complex Meteorological Environment. Sensors, 23.","DOI":"10.20944\/preprints202304.1051.v1"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Johnson, G.W., Swaszek, P.F., Hartnett, R.J., Shalaev, R., and Wiggins, M. (2007, January 16\u201317). An Evaluation of eLoran as a Backup to GPS. Proceedings of the 2007 IEEE Conference on Technologies for Homeland Security, Woburn, MA, USA. Available online: https:\/\/ieeexplore.ieee.org\/document\/4227790.","DOI":"10.1109\/THS.2007.370027"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Pu, Y.R., Li, Z.W., and Zhou, L.L. (2014, January 26\u201329). Propagation of LF Ground-wave Through Inhomogeneous Atmosphere. Proceedings of the 2014 3rd Asia-Pacific Conference on Antennas & Propagation, Harbin, China. Available online: https:\/\/ieeexplore.ieee.org\/document\/6992583.","DOI":"10.1109\/APCAP.2014.6992583"},{"key":"ref_14","unstructured":"Zhou, Z.H. (2016). Machine Learning, Tsinghua University Press. [1st ed.]."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Suthaharan, S. (2016). Machine Learning Models and Algorithms for Big Data Classification, Springer. Available online: https:\/\/link.springer.com\/book\/10.1007\/978-1-4899-7641-3.","DOI":"10.1007\/978-1-4899-7641-3"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Thomasberger, A., Nielsen, M.M., Flindt, M.R., Pawar, S., and Svane, N. (2023). Comparative Assessment of Five Machine Learning Algorithms for Supervised Object-Based Classification of Submerged Seagrass Beds Using High-Resolution UAS Imagery. Remote Sens., 15.","DOI":"10.3390\/rs15143600"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Jin, T., Liu, S., Yan, B., Guo, W., Huang, C., Hua, Y., Zhang, S., Li, X., and Xu, L. (2025). A Meteorological Data-Driven eLoran Signal Propagation Delay Prediction Model: BP Neural Network Modeling for Long-Distance Scenarios. Remote Sens., 17.","DOI":"10.3390\/rs17132269"},{"key":"ref_18","first-page":"71","article-title":"ASF modification of Loran-C based on BP neural network","volume":"2","author":"Xu","year":"2006","journal-title":"Ship Electron. Eng."},{"key":"ref_19","unstructured":"Yang, H., Wang, L., Pu, Y., and Xi, X. (2017, January 16\u201319). Analysis of diurnal variation on long-wave ground wave propagation delay. Proceedings of the 2017 Sixth Asia-Pacific Conference on Antennas and Propagation (APCAP), Xi\u2019an, China. Available online: https:\/\/ieeexplore.ieee.org\/document\/8420742."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1109\/LAWP.2019.2900271","article-title":"Analysis and Modeling of Temporal Variation Properties for LF Ground-Wave Propagation Delay","volume":"4","author":"Pu","year":"2019","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_21","first-page":"114","article-title":"A modification method of Loran C ASF Based on Neural networks","volume":"11","author":"Wang","year":"2020","journal-title":"Mod. Navig."},{"key":"ref_22","first-page":"17","article-title":"Correlation analysis and modeling of long wave propagation delay variation and temperature","volume":"4","author":"Wang","year":"2020","journal-title":"Bull. Sci. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1109\/LAWP.2021.3057942","article-title":"Accuracy Improvement Model for Predicting Propagation Delay of Loran-C Signal Over a Long Distance","volume":"20","author":"Pu","year":"2021","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Di, J., Wu, M., Fu, J., Li, W., Jin, X., and Liu, J. (2025). Comparative Analysis of Time-Series Forecasting Models for eLoran Systems: Exploring the Effectiveness of Dynamic Weighting. Sensors, 25.","DOI":"10.3390\/s25144462"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"112067","DOI":"10.1109\/ACCESS.2025.3581615","article-title":"Enhancing eLoran Timing Accuracy via Machine Learning with Meteorological and Terrain Data","volume":"13","author":"Kang","year":"2025","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1017\/S0373463399008231","article-title":"Eurofix system and its developments","volume":"52","author":"Offermans","year":"1999","journal-title":"J. Navig."},{"key":"ref_27","first-page":"1407","article-title":"Research of Loran-C data demodulation and decoding technology","volume":"33","author":"Li","year":"2012","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_28","unstructured":"Gao, Y., Hua, Y., Li, S.F., and Yang, C.Z. (2015, January 19\u201322). Acquisition method of Loran-C signal based on matched filter. Proceedings of the 2015 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Ningbo, China. Available online: https:\/\/www.semanticscholar.org\/paper\/Acquisition-method-of-Loran-C-signal-based-on-Gao-Hua\/3db4cce8e11d02e5ceb45db404ba35d5da44e92e."},{"key":"ref_29","unstructured":"McCullough, J.R., Irwin, B.J., and Bowles, R.M. (1985, January 15\u201317). Loran-C latitude-longitude conversion at sea: Programming considerations. Proceedings of the 1985 National Technical Meeting of The Institute of Navigation, San Diego, CA, USA. Available online: https:\/\/pubs.usgs.gov\/publication\/70012288."},{"key":"ref_30","unstructured":"Yang, H.J. (2019). Monitoring and Study on Temporal Variation Properties of Long-Wave Ground Wave Propagation Delay. [Master\u2019s Thesis, Xi\u2019an University of Technology]. Available online: https:\/\/kns.cnki.net\/kcms2\/article\/abstract?v=lSOmZDqoX8MGVvyCG7MNAZgGYc3PT-Yum-5JYVYEyPHpJ1rA-Pgu1moFdGkhGWI8wYNpriHepJW8lLNsTILH-YM1F1yLYRQ2h0lQeCpCjAFMYOO5OOri-MuUqQS655NYrn-FDHxETQvbBsOMiWzJw9SGIJfVkNL-9GMGMj9i84XSnTJeDRqBBdBHJ5PdQpRD&uniplatform=NZKPT&language=CHS."},{"key":"ref_31","unstructured":"Zheng, X.Y. (2021). Low-Frequency Ground Wave Propagation Delay in Land-Based Long-Wave Navigation and Timing System. [Master\u2019s Thesis, Xi\u2019an University of Technology]. Available online: https:\/\/kns.cnki.net\/kcms2\/article\/abstract?v=lSOmZDqoX8NyqmRnW1uAMq4QPBdGetxCloUuAtwAXsmUb7JpoQ3NGklTxoN8IKZRAC4QUpfU2KzI6EQKOtLAFpT6ZYUBE7eX4InGFPC01e92oH179i4fiXi0BSX4_G7Fy9UwE8MFn0LvapScguVtnllV5Zp-Tj0_JRm0Jy_c8ZVGGTLyDR_IyoNr5B-Qyt9A&uniplatform=NZKPT&language=CHS."},{"key":"ref_32","unstructured":"(2017). General Specification for Long Wave Timing Receiver (Standard No. GJB9210-2017). Available online: https:\/\/www.antpedia.com\/standard\/1327724479.html."},{"key":"ref_33","first-page":"7","article-title":"Method for calculating the distance between receiving and sending of long wave timing","volume":"08","author":"Tu","year":"1980","journal-title":"Time Freq. Bull."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","article-title":"Ridge Regression: Biased Estimation for Nonorthogonal Problems","volume":"12","author":"Hoerl","year":"1970","journal-title":"Technometrics"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_36","unstructured":"Drucker, H., Burges, C., Kaufman, L., Smola, A., and Vapnik, V. (1996, January 2\u20135). Support Vector Regression Machines. Proceedings of the Advances in Neural Information Processing Systems 9 (NIPS 1996), Denver, CO, USA. Available online: https:\/\/www.semanticscholar.org\/paper\/Support-Vector-Regression-Machines-Drucker-Burges\/e52fb14e4beccc5e88a33c1fe5c7d6e780831ae1?p2df."},{"key":"ref_37","first-page":"514","article-title":"Gaussian Processes for Regression","volume":"8","author":"Williams","year":"1996","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1109\/72.97934","article-title":"A General Regression Neural Network","volume":"2","author":"Specht","year":"1991","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long Short-Term Memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_41","unstructured":"Shi, X., Chen, Z., Wang, H., Yeung, D., Wong, W., and Woo, W. (2015). Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting. arXiv."}],"container-title":["Big Data and Cognitive Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-2289\/10\/2\/54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T05:38:42Z","timestamp":1770961122000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-2289\/10\/2\/54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,7]]},"references-count":41,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["bdcc10020054"],"URL":"https:\/\/doi.org\/10.3390\/bdcc10020054","relation":{},"ISSN":["2504-2289"],"issn-type":[{"value":"2504-2289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,7]]}}}