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.
Highlights
The global ionospheric maps (GIMs) are defined as a twodimensional array, where the elements represent the vertical total electron content (VTEC) mapped to a single-layer ionospheric shell at an effective height, corresponding to a partition in rectangles defined according to latitude and longitude divisions
Compared with the VTEC data processed by GPS legacy, GPS RINEX version 3, and multi-global navigation satellite systems (GNSS) RINEX version 3 approaches, atomic decomposition interpolator of GIMs (ADIGIM) can improve any of the three Kriging results of some southern high latitude regions for the arbitrarily day, in spite of which applies the historical database of legacy Kriging GIMs for the interpolation
Since the middle of 2019, ADIGIM interpolation has been implemented in the beta test phase for real-time global ionospheric map (RT-GIM) computation, which we denote as the UPC ADIGIM RT-GIM, hereafter UADG, and is an evolution of the current UPC RT-GIM products URTG and USRG
Summary
The global ionospheric maps (GIMs) are defined as a twodimensional array, where the elements represent the vertical total electron content (VTEC) mapped to a single-layer ionospheric shell at an effective height, corresponding to a partition in rectangles defined according to latitude and longitude divisions. To obtain estimates of VTEC values in areas that are not well covered by the GNSS receiver network, several techniques have been developed for interpolating VTEC values such as spherical harmonics (Schaer 1999; Feltens 2007), integrated using the generalized trigonometric series functions (Li et al 2015) and with the inequality-constrained least squares (Zhang et al 2013), using a three-shell model with bi-linear spline interpolation (Mannucci et al 1998), tomography with splines (Hernández-Pajares et al 1999), and tomography with Kriging (Orús et al 2005) These techniques, applied to the post-processed GNSS observation data, have provided excellent estimates for the global state of the ionosphere, with less than 30% relative errors and 3.6–5.3 TECUs (1 TECU = 1016 el/m2 ≈ 16 cm delay in L1 GPS signal) of standard deviation, according to a long-term validation by different approaches (Roma-Dollase et al 2018). The paper is structured as follows: First, we discuss the UPC RT Tomographic Ionospheric Model (UPC RTTOMION) for GNSS data processing, we present the methodology of interpolation using the ADIGIM algorithm, and the performance and robustness assessment
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