{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T06:22:41Z","timestamp":1771482161919,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,1,31]],"date-time":"2022-01-31T00:00:00Z","timestamp":1643587200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R &amp; D Program of China","award":["No.2020YFB0505602-02"],"award-info":[{"award-number":["No.2020YFB0505602-02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Ionospheric delay is a critical error source in Global Navigation Satellite Systems (GNSSs) and a principal aspect of Satellite Based Augmentation System (SBAS) corrections. Grid Ionospheric Vertical Delays (GIVDs) are derived from the delays on Ionosphere Pierce Points (IPPs), which are observed by SBAS reference stations. SBAS master stations calculate ionospheric delay corrections by several methods, such as planar fit or Kriging. However, when there are not enough IPPs around an Ionosphere Grid Point (IGP) or the IPPs are unevenly distributed, the fitting accuracy of planar fit or Kriging is unsatisfactory. Moreover, the integrity bounds of Grid Ionospheric Vertical Errors (GIVEs) are overly conservative. Since Artificial Neural Networks (ANNs) are widely used in ionospheric research due to their self-adaptation, parallelism, non-linearity, robustness, and learnability, the ANN method for GIVD and GIVE derivation is proposed in this article. Networks are separately trained for IGPs, and five years of historical data are applied on network training. Principal Component Analysis (PCA) is applied for dimensionality reduction of geomagnetic and solar indices, which is employed as a network input feature. Furthermore, the GIVE algorithm of the ANN method is derived based on the distribution of the residual random variable. Finally, experiments are conducted on 12 IGPs over the East China region. Under normal ionospheric conditions, compared with the planar fit and Kriging methods, the residual reduction of the ANN method is approximately 15%. The ANN method fits the ionospheric delay residual error better. The percentage of GIVE availability under 2.7 m increases at least 25 points in comparison to Kriging. Under disturbed conditions, due to a lack of training samples, the ANN method is incompetent compared with planar fit or Kriging.<\/jats:p>","DOI":"10.3390\/rs14030676","type":"journal-article","created":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T22:16:18Z","timestamp":1643753778000},"page":"676","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Artificial Neural Network-Based Ionospheric Delay Correction Method for Satellite-Based Augmentation Systems"],"prefix":"10.3390","volume":"14","author":[{"given":"Shan","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical Electronic and Information Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China"}]},{"given":"Ding","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Electronic and Information Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China"}]},{"given":"Junren","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Machine Intelligence, Peking University, Beijing 100871, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,31]]},"reference":[{"key":"ref_1","unstructured":"ICAO (2018). Annex 10\u2014Aeronautical Telecommunications\u2014Volume I\u2014Radio Navigational Aids, International Civil Aviation Organization. [8th ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Segura, D.I., Garcia, A.R., Alonso, M.T., Sanz, J., Juan, J.M., Casado, G.G., and Martinez, M.L. (2020). EGNOS 1046 Maritime Service Assessment. Sensors, 20.","DOI":"10.3390\/s20010276"},{"key":"ref_3","unstructured":"RTCA (2013). Minimum Operational Performance Standards for Global Positioning System\/Wide Area Augmentation System Airborne Equipment, DO-229D, Radio Technical Commission for Aeronautics (RTCA)."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1016\/j.asr.2020.04.032","article-title":"Generation of DFMC SBAS corrections for BDS-3 satellites and improved positioning performances","volume":"66","author":"Zhao","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1007\/s10291-016-0569-2","article-title":"GNSS satellite-based augmentation systems for Australia","volume":"21","author":"Choy","year":"2017","journal-title":"Gps Solut."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ciecko, A., Bakula, M., Grunwald, G., and Cwiklak, J. (2020). Examination of Multi-Receiver GPS\/EGNOS Positioning with Kalman Filtering and Validation Based on CORS Stations. Sensors, 20.","DOI":"10.3390\/s20092732"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Nie, Z.X., Zhou, P.Y., Liu, F., Wang, Z.J., and Gao, Y. (2019). Evaluation of Orbit, Clock and Ionospheric Corrections from Five Currently Available SBAS L1 Services: Methodology and Analysis. Remote Sens., 11.","DOI":"10.3390\/rs11040411"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chen, J.P., Wang, A.H., Zhang, Y.Z., Zhou, J.H., and Yu, C. (2020). BDS Satellite-Based Augmentation Service Correction Parameters and Performance Assessment. Remote Sens., 12.","DOI":"10.3390\/rs12050766"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kim, M., and Kim, J. (2021). SBAS-Aided GPS Positioning with an Extended Ionosphere Map at the Boundaries of WAAS Service Area. Remote Sens, 13.","DOI":"10.3390\/rs13010151"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Schluter, S., and Hoque, M.M. (2020). An SBAS Integrity Model to Overbound Residuals of Higher-Order Ionospheric Effects in the Ionosphere-Free Linear Combination. Remote Sens., 12.","DOI":"10.3390\/rs12152467"},{"key":"ref_11","unstructured":"(2022, January 26). China Satellite Navigation Office, Available online: http:\/\/www.beidou.gov.cn\/xt\/gfxz\/202008\/P020200803362065480963.pdf."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yoon, H., Seok, H., Lim, C., and Park, B. (2020). An Online SBAS Service to Improve Drone Navigation Performance in High-Elevation Masked Areas. Sensors, 20.","DOI":"10.3390\/s20113047"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.rinp.2018.06.057","article-title":"Validation of CAS\u2019s final global ionospheric maps during different geomagnetic activities from 2015 to 2017","volume":"10","author":"Liu","year":"2018","journal-title":"Results Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1109\/TAES.2020.3029623","article-title":"Reexamining Low-Latitude Ionospheric Error Bounds: An SBAS Approach for Brazil","volume":"57","author":"Pullen","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"105178","DOI":"10.1016\/j.jastp.2019.105178","article-title":"SBAS performance improvement with a new undersampled ionosphere threat model based on relative coverage metric","volume":"198","author":"Zhang","year":"2020","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Sparks, L., Blanch, J., and Pandya, N. (2011). Estimating ionospheric delay using kriging: 2. Impact on satellite-based augmentation system availability. Radio Sci., 46.","DOI":"10.1029\/2011RS004781"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1109\/5.533954","article-title":"Wide area augmentation of the global positioning system","volume":"84","author":"Enge","year":"1996","journal-title":"Proc. IEEE"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105092","DOI":"10.1016\/j.jastp.2019.105092","article-title":"Ionosphere modeling in the context of Algerian Satellite-based Augmentation System","volume":"193","author":"Takka","year":"2019","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2002RS002845","article-title":"Sudden ionospheric delay decorrelation and its impact on the Wide Area Augmentation System (WAAS)","volume":"39","author":"Sparks","year":"2004","journal-title":"Radio Sci."},{"key":"ref_20","first-page":"1","article-title":"Estimating ionospheric delay using kriging: 1. Methodology","volume":"46","author":"Sparks","year":"2011","journal-title":"Radio Sci."},{"key":"ref_21","first-page":"2307","article-title":"Adaptative Ionospheric Electron Content Estimation Method","volume":"46","author":"Trilles","year":"2012","journal-title":"I Navig. Sat. Div. Int."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1007\/BF02907577","article-title":"Differential Areas for Differential Stations (DADS): A New Method of Establishing Grid Ionospheric Model","volume":"47","author":"Yuan","year":"2002","journal-title":"Chin. Sci. Bull."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1080\/10020070412331344711","article-title":"A Generalized Trigonometric Series Function Model for Determining Ionospheric Delay","volume":"14","author":"Yuan","year":"2004","journal-title":"Prog. Nat. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"103","DOI":"10.4401\/ag-7297","article-title":"TEC Regional Modeling and Prediction Using ANN Method and Single Frequency Receivers over IRAN","volume":"61","author":"Sabzehee","year":"2018","journal-title":"Ann. Geophys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1007\/s10509-019-3545-9","article-title":"Modeling and predicting seasonal ionospheric variations in Turkey using artificial neural network (ANN)","volume":"364","author":"Inyurt","year":"2019","journal-title":"Astrophys. Space Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"105052","DOI":"10.1016\/j.jastp.2019.05.016","article-title":"Feed forward neural network based ionospheric model for the East African region","volume":"191","author":"Tebabal","year":"2019","journal-title":"J. Atmos Sol.-Terr. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"e2020SW002525","DOI":"10.1029\/2020SW002525","article-title":"Storm-Time Modeling of the African Regional Ionospheric Total Electron Content Using Artificial Neural Networks","volume":"18","author":"Okoh","year":"2020","journal-title":"Space Weather"},{"key":"ref_28","first-page":"371","article-title":"Implementation of Hybrid Ionospheric TEC Forecasting Algorithm Using PCA-NN Method","volume":"12","author":"Mallika","year":"2019","journal-title":"IEEE J.-Stars"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhang, Z.X., Pan, S.G., Gao, C.F., Zhao, T., and Gao, W. (2019). Support Vector Machine for Regional Ionospheric Delay Modeling. Sensors, 19.","DOI":"10.3390\/s19132947"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"77","DOI":"10.5194\/angeo-37-77-2019","article-title":"Extending the coverage area of regional ionosphere maps using a support vector machine algorithm","volume":"37","author":"Kim","year":"2019","journal-title":"Ann. Geophys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10509-020-03907-1","article-title":"Ionospheric TEC prediction using Long Short-Term Memory deep learning network","volume":"366","author":"Wen","year":"2021","journal-title":"Astrophys. Space Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1016\/j.asr.2018.11.011","article-title":"Using TensorFlow-based Neural Network to estimate GNSS single frequency ionospheric delay (IONONet)","volume":"63","author":"Perez","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1049\/cje.2021.02.006","article-title":"An Improved Ionospheric Delay Correction Method for SBAS","volume":"30","author":"Wang","year":"2021","journal-title":"Chin. J. Electron."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2873","DOI":"10.1016\/j.asr.2020.05.010","article-title":"Ionospheric correlation analysis and spatial threat model for SBAS in China region","volume":"66","author":"Jin","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_35","unstructured":"Kingma, D.P., and Ba, J.J. (2015, January 7\u20139). Adam: A method for stochastic optimization. Proceedings of the 3rd International Conference for Learning Representations (ICLR), San Diego, CA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/S0893-6080(99)00080-5","article-title":"Construction of confidence intervals for neural networks based on least squares estimation","volume":"13","author":"Rivals","year":"2000","journal-title":"Neural Netw."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3177","DOI":"10.1016\/j.asr.2019.01.044","article-title":"Assessment study of ionosphere correction model using single- and multi-shell algorithms approach over sub-Saharan African region","volume":"63","author":"Abe","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s001900100182","article-title":"An improvement to ionospheric delay correction for single-frequency GPS users\u2014The APR-I scheme","volume":"75","author":"Yuan","year":"2001","journal-title":"J. Geod."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1007\/s001900100197","article-title":"Auto-covariance estimation of variable samples (ACEVS) and its application for monitoring random ionospheric disturbances using GPS","volume":"75","author":"Yuan","year":"2001","journal-title":"J. Geod."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/3\/676\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:11:59Z","timestamp":1760134319000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/3\/676"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,31]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["rs14030676"],"URL":"https:\/\/doi.org\/10.3390\/rs14030676","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,31]]}}}