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Journal of Geodesy

, Volume 93, Issue 6, pp 877–888 | Cite as

Helmert-VCE-aided fast-WTLS approach for global ionospheric VTEC modelling using data from GNSS, satellite altimetry and radio occultation

  • Andong HuEmail author
  • Zishen Li
  • Brett Carter
  • Suqin Wu
  • Xiaoming Wang
  • Robert Norman
  • Kefei ZhangEmail author
Original Article
  • 288 Downloads

Abstract

Vertical total electron content (VTEC) global ionospheric maps (GIM) are commonly used to correct the ionospheric delay of global navigation satellite system (GNSS) signals for single-frequency positioning and other ionospheric studies. The measurements observed by inhomogeneously distributed ground reference stations are the only data used to generate the GIMs. Thus the accuracy of the GIMs over ocean and polar regions is relatively poor due to the lack of measurements over these regions. In this study, space-borne VTECs obtained from ocean-altimetry and GNSS radio occultation measurements are incorporated into the modelling process. Since the three types of VTEC data have different qualities, the weight for each type of data is determined using the Helmert-variance component estimation (Helmert-VCE) method. In addition, unlike the traditional weighted least squares (WLS) estimation method in which the design matrix of observation equations is fixed, in this study, the design matrix, especially those elements in design matrix that are derived from the coordinates of either tangent point or ionospheric pierce point, are considered to be inaccurate. Thus they are adjusted together with the unknown coefficient parameters of the fitting model using the fast-weighted total least squares (fast-WTLS) technique. The proposed approach, named Helmert-WTLS, was tested using the data in the period of day of year (DOY) 217–224, 2016 and validated using GIMs produced by the research team for ionosphere and precise positioning based on BDS/GNSS (GIPP) at the Academy of Opto-Electronics, Chinese Academy of Sciences (CAS). Comparison results showed that the GIMs (with a 2 h temporal resolution) generated using the new approach can improve the determination of ionospheric TEC by 0.28 TEC units (TECU) over those from the Helmert-VCE-aided WLS approach (w.r.t CAS references, respectively) and by 1.61 TECU better than those from WLS, in terms of the mean of all root-mean-squares errors of all 2 h time slots in the 8-day testing period. In addition, in comparison with out-of-sample Jason-3 observations, results from the proposed method also outperformed Helmert-VCE-aided WLS, CAS and CODE models by 1.5, 2.4 and 2.4 TECU, respectively.

Keywords

Global navigation satellite system (GNSS) Radio occultation Satellite altimetry VTEC GIM WTLS Helmert-VCE 

Notes

Acknowledgements

This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA17010304) and Australian Research Council project (LP160100561). This work was also funded by the Jiangsu dual creative talents and teams programme projects awarded in 2017. We also would like to acknowledge the support of the Natural Science Foundation of China (41730109, 41674043, 41704038, 41874040), Beijing Nova programme (xx2017042), Beijing Youth Talent Support program (2017000021223ZK13), Pioneer Hundred Talents Program, National Key Research and Development Plan (2016YFB0501405) of the Chinese Academy of Sciences and Beijing Natural Science Foundation (8184092). Andong Hu acknowledges the China Scholarship Council for the provision of a scholarship for his study at the SPACE Research Centre, RMIT University. Zishen Li acknowledges the Australian Dept. of Education and Training for the provision of an Endeavour scholarship for his research at the SPACE Research Centre. We thank IGS for providing GNSS data and precise DCB values for all transmitters and receivers, UCAR/CDAAC for providing ionPrf data, and CNES and NOAA for providing Jason-3 IGDR data.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.SPACE Research Centre, School of SciencesRMIT UniversityMelbourneAustralia
  2. 2.School of Environmental Science and Spatial InformaticsChina University of Mining and TechnologyXuzhouChina
  3. 3.Academy of Opto-ElectronicsChinese Academy of SciencesBeijingChina

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