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Virtual reference station technology for voxels without signal ray in ionospheric tomography based on machine learning

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Abstract

A new three-dimensional computerized ionospheric tomography model (VRS-ML-CIT) was developed in this study combining virtual reference station (VRS) and machine learning (ML) technology. Compared to the traditional VRS technology, the fitting and interpolation method generates virtual observations at each epoch. The ML technology was employed in this study to model both temporal and spatial variations of virtual observation in VRSs. Simultaneously, these ML-based VRSs are built associatively with unilluminated voxels (voxels without real observations) rather than relying solely on real reference stations, which can effectively reduce the proportion of unilluminated voxels, ensure the inversion efficiency, and improve the accuracy of virtual observations. We validate VRS-ML-CIT using observations of 153 GPS and two ionosonde stations in Europe. The results show that the test accuracy of the virtual observation is about 0.8 TECU, which offers an improvement of 40% over the previous non-machine learning VRS method. With the addition of virtual observations, the proportion of unilluminated voxels in VRS-ML-CIT declined from 30 to 12% on average. In comparison with the CIT result derived with only real observations (OBS-CIT), the error of the estimated slant total electron content in the proposed method reaches the same level for the illuminated voxels, even exceeding that of OBS-CIT in some periods. Moreover, the latitude–altitude maps and profiles of the IED from unilluminated voxels demonstrate the excellent performance of the proposed method.

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Data availability

The GPS observation data are available at ftp://ftp.epncb.oma.be/pub/obs. The ionosonde data are available at ftp://ftp.ngdc.noaa.gov/ionosonde/data. The Geomagnetic index data are available at https://wdc.kugi.kyoto-u.ac.jp/wdc/Sec3.html. The IRI2016 model data are available at https://ccmc.gsfc.nasa.gov/modelweb/models/iri2016_vitmo.php.

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Acknowledgements

The authors thank the anonymous reviewers for their valuable comments on the manuscript. We are grateful to the EUREF Permanent GNSS Network which provides the GPS observation data and also thank Lowell GIRO Data Center (LGDC) for providing the ionosonde data. This research was supported by the National Nature Science Foundation of China (No. 42004025, 42004012, 42104025, 42204037), The China Postdoctoral Science Foundation (No. 2021M702509); the Hunan Provincial Natural Science Foundation of China (No. 2022JJ30254); Natural Resources Science and Technology Project of Hunan Province (No. 2022-07, 2022-29).

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Authors and Affiliations

  1. School of Earth Sciences and Spatial Information Engineering, Hunan University of Science and Technology, Xiangtan, 411201, China

    Dunyong Zheng, Pengfei Yuan, Changyong He, Dongfang Lin, Mengguang Liao & Zhaohui Xiong

  2. National-Local Joint Engineering Laboratory of Geo-Spatial Information Technology, Hunan University of Science and Technology, Xiangtan, 411201, China

    Dunyong Zheng, Pengfei Yuan, Changyong He, Dongfang Lin, Mengguang Liao & Zhaohui Xiong

  3. School of Geodesy and Geomatics, Wuhan University, Wuhan, 430079, China

    Yibin Yao

  4. Institute of Space Sciences, Shandong University, Weihai, 264209, China

    Wenfeng Nie

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  1. Dunyong Zheng
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Contributions

DZ wrote the main manuscript text. PY, CH and ZX calculated the STEC based on GNSS data and Nequick2 model. YY and CH participated in discussing the details of the proposed tomography method. WN provided the software of GNSS data processing. ML and DL participated in discussing the error handling method of the proposed method. All authors reviewed the manuscript.

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Correspondence to Changyong He.

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Zheng, D., Yuan, P., He, C. et al. Virtual reference station technology for voxels without signal ray in ionospheric tomography based on machine learning. GPS Solut 27, 166 (2023). https://doi.org/10.1007/s10291-023-01512-7

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