GPS Solutions

, 22:107 | Cite as

A modified three-dimensional ionospheric tomography algorithm with side rays

  • Yibin YaoEmail author
  • Changzhi Zhai
  • Jian Kong
  • Qingzhi Zhao
  • Cunjie Zhao
Original Article


The three-dimensional ionospheric tomography (3DCIT) algorithm based on Global Navigation Satellite System (GNSS) observations have been developed into an effective tool for ionospheric monitoring in recent years. However, because the rays that come into or come out from the side of the inversion region cannot be used, the distribution of the rays in the edge and bottom part of the inversion region is scarce and the electron density cannot be effectively improved in the inversion process. We present a three-dimensional tomography algorithm with side rays (3DCIT-SR) applying the side rays to the inversion. The partial slant total electron content (STEC) of side rays in the inversion region is obtained based on the NeQuick2 model and GNSS-STEC. The simulation experiment results show that the algorithm can effectively improve the distribution of GNSS rays in the inversion region. Meanwhile, the iteration accuracy has also been significantly improved. After the same number of iterations, the iterative results of 3DCIT-SR are closer to the truth than 3DCIT, in particular, the inversion of the edge regions is improved noticeably. The GNSS data of the International GNSS Service (IGS) stations in Europe are used to perform real data experiments, and the inversion results show that the electron density profiles of 3DCIT-SR are closer to the ionosonde measurements. The accuracy improvement of 3DCIT-SR is up to 56.3% while the improvement is more obvious during the magnetic storm compared to the case of a calm ionospheric state .


Three-dimensional ionospheric tomography GNSS Side rays Inversion 



The authors would like to thank the International Global Navigation Satellite System Service (IGS) for the data used in this work. The authors also thank the Global Ionosphere Radio Observatory for the ionosonde data. The ionosonde (PQ052) data were downloaded from


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Copyright information

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

Authors and Affiliations

  1. 1.School of Geodesy and GeomaticsWuhan UniversityWuhanChina
  2. 2.Chinese Antarctic Center of Surveying and MappingWuhan UniversityWuhanChina
  3. 3.College of GeomaticsXi’an University of Science and TechnologyXi’anChina

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