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Real-time interpolation of global ionospheric maps by means of sparse representation

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A Correction to this article was published on 07 August 2021

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Abstract

In this paper, we propose a method for the generation of real-time global ionospheric map (RT-GIM) of vertical total electron content (VTEC) from GNSS measurements. The need for interpolation arises from the fact that the ionospheric pierce point (IPP) measurements from satellites to stations are not distributed uniformly over the ionosphere, leaving unfilled gaps at oceans or poles. The method we propose is based on using a high-quality historical database of post-processed GIMs that comprises more than two solar cycles, calculates the GIM by weighted superposition on a subset of the database with the compatible solar condition. The linear combination of GIMs in the database was obtained by minimizing a \(\ell _2\) distance between VTEC measurements at the IPPs and the VTECs from the database, adding a \(\ell _1\) penalization on the weights to assure a sparse solution. The process uses a Sun-fixed geomagnetic reference frame. This method uses the atomic decomposition/least absolute shrinkage and selection operator (LASSO), which will be denoted as atomic decomposition interpolator of GIMs (ADIGIM). As the computation is done in milliseconds, the interpolation is performed in real time. In this work, two products were developed, denoted as UADG and UARG, the UADG in real time and UARG with a latency of 24 h to benefit from the availability of a greater number of stations. The altimeter JASON3 VTEC measurements were used as reference. The quality of interpolated RT-GIMs from day 258 of 2019 to 155 of the year 2020 is compared with other RT/non-RT GIM products such as those from International GNSS Service (IGS), Centre National d’Etudes Spatiales (CNES), Chinese Academy of Sciences (CAS), Polytechnic University of Catalonia (UPC) and others. The RT ADIGIM performance proved to be better, nearly as good as the rapid or final GIMs computed retrospectively with delays of hours to days. Besides, the non-RT ADIGIM quality is as good or better than most GIM products. The oceanic regions have been included in the assessment which showed that ADIGIM interpolation gives the best estimation (referred to JASON3). The developed method, UADG, will constitute the next-generation UPC RT-GIM, and also UARG will improve the current product UQRG (the current UPC rapid GIM product computed retrospectively) due to its complementary information.

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Data availability

The experimental UADG and UARG are archived in format of IONEX format, which are open accessible from UPC HTTP site (available at http://chapman.upc.es/tomion/real-time/quick/archive.uadg/). The data for this paper are available and they can be requested from any of the authors in particular from Heng Yang (h.yang@upc.edu) and Enric Monte Moreno (enric.monte@upc.edu).

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Acknowledgements

This work has been partially supported by the Project PID2019-107579RB-I00 (MICINN). Also was partially supported by the 2017 SGR-0851 Grant of the Generalitat de Catalunya and by the EU Project 101007599 - PITHIA-NRF. The authors acknowledge the GIM products of the IGS and the ionosphere associated analysis centers. The main code of this project was done in Python using the machine learning library scikit-learn.

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Authors and Affiliations

  1. Department of Signal Theory and Communications, TALP, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain

    Heng Yang & Enric Monte-Moreno

  2. School of Electronic Information and Engineering, Yangtze Normal University, Chongqing, 408100, China

    Heng Yang

  3. Department of Applied Mathematics IV, IonSAT, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain

    Heng Yang & Manuel Hernández-Pajares

  4. IEEC-CSIC, Campus UAB, Carrer de Can Magrans s/n, 08193, Cerdanyola del Vallès, Spain

    David Roma-Dollase

Authors
  1. Heng Yang
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  2. Enric Monte-Moreno
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  3. Manuel Hernández-Pajares
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  4. David Roma-Dollase
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Contributions

The mathematical background was worked by HY, EM, and MHP. The experiments were done by HY. The writing of the paper was done by HY and EM. DRD provided the multiGNSS part of the data.

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Correspondence to Enric Monte-Moreno.

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Yang, H., Monte-Moreno, E., Hernández-Pajares, M. et al. Real-time interpolation of global ionospheric maps by means of sparse representation. J Geod 95, 71 (2021). https://doi.org/10.1007/s00190-021-01525-5

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