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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 ℓ distance between VTEC measurements at the IPPs and the VTECs from the database, adding a ℓ 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., 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.

In the original publication of the articles, “Methodology and consistency of slant and vertical assessments for ionospheric electron content models” and “Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle”, a common typo affecting the text only (not the computations) has been recently noticed. It compromised the definition of the scaling factor from Global Navigation Satellite Systems ionospheric delay to electron content is clarified in this erratum.

Benefiting from global multi-frequency and multi-constellation GNSS measurements provided by the experimental International GNSS real-time service (IGS RTS), a predicting-plus-modeling approach employed by Chinese Academy of Sciences (CAS) for the routine generation of real-time global ionospheric maps (RT-GIM) is first reported. Along with RT-GIMs generated by Universitat Politècnica de Catalunya (UPC), the quality of CAS and UPC RT-GIMs in IONEX format is assessed during a low soar activity period from September 2017 to December 2019. The differential slant total electron contents (dSTEC) derived from 50 GPS stations of the IGS and Jason-3 vertical TECs (VTEC) over the ocean are used as references. In comparison with different reference TECs, CAS and UPC RT-GIMs are approximately 1.7–4.9% and 8.6–12.5% worse than the respective post-processed GIMs CASG and UQRG, respectively. Using RTCM ionospheric data streams from CAS, Centre National d’Etudes Spatiales (CNES) and UPC, the first experimental IGS combined RT-GIM is generated and validated in actual real-time conditions. Compared to Jason-3 VTEC measurements available during the period of common availability, from October 2018 to April 2019, RT-GIM discrepancies present similar relative RMS errors, which are 33, 36, 36 and 38% for CNES, combined one, UPC and CAS, respectively. Aside from a better understanding of the influence of working in the original IONEX versus RTCM ionospheric formats, the update to a new experimental adaptation of RT strategy is highlighted by UPC, and the computation of multi-layer RT-GIM is emphasized by CAS in view of the inadequacy of single-layer ionospheric assumption in the presence of large latitudinal gradients., The authors acknowledge the IGS and other agencies for providing real-time GNSS data and products. This work was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDA17010202), the National Natural Science Foundation of China (41674043, 41704038), the National Key Research Program of China (2017YFGH002206), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00190-017-1088-9. In the context of the International GNSS Service (IGS), several IGS Ionosphere Associated Analysis Centers have developed different techniques to provide global ionospheric maps (GIMs) of vertical total electron content (VTEC) since 1998. In this paper we present a comparison of the performances of all the GIMs created in the frame of IGS. Indeed we compare the classical ones (for the ionospheric analysis centers CODE, ESA/ESOC, JPL and UPC) with the new ones (NRCAN, CAS, WHU). To assess the quality of them in fair and completely independent ways, two assessment methods are used: a direct comparison to altimeter data (VTEC-altimeter) and to the difference of slant total electron content (STEC) observed in independent ground reference stations (dSTEC-GPS). The main conclusion of this study, performed during one solar cycle, is the consistency of the results between so many different GIM techniques and implementations.

This is a post-peer-review, pre-copyedit version of an article published in Gps solutions. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10291-018-0767-1 The number of existing global positioning system (GPS) single-frequency receivers continues growing. More than 90% of GPS receivers are implemented as low-cost single-frequency chipsets embedded in smartphones. This provides new opportunities, in particular for ionospheric sounding. In this context, we present the new sidereal days ionospheric graphic (SIg) combination of single-frequency GNSS measurements. SIg is able to monitor, for each given GNSS transmitter–receiver pair, the vertical total electron content (VTEC) relative to the previous observation with the same or almost the same line-of-sight (LOS) vector. In such arrangements the SIg multipath error mostly cancels, thus increasing the accuracy of the ¿VTEC significantly. This happens for the GPS constellation after one sidereal day (about 23 h 56 m) and for Galileo after 10 sidereal days approximately. Moreover, we show that the required calibration of the corresponding carrier phase ambiguity can be accurately performed by means of VTEC global ionospheric maps (GIMs). The results appear almost as accurate as those based on the dual-frequency technique, i.e., about 1 TECU or better, and with much more precision and resolution than the GIM values in the ionospheric region sounded by each given single-frequency receiver. The performance is demonstrated using actual data from 9 permanent GPS receivers during a total solar eclipse on August 21, 2017 over North America, where the corresponding ionospheric footprint is clearly detected in agreement with the total solar eclipse predictions. The advantages of extending SIg to lower carrier frequencies and the feasibility of applying it to other global navigation satellite system (GNSS) systems are also studied. This is shown in terms of a fully consistent VTEC depletion signature of the same eclipse phenomena, obtained with Galileo-only data in North America at mid and low latitude. Finally the SIg feasibility, including the cycle slip detection, is shown as well with actual mass-market single frequency GPS receivers at mid and high latitude.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00190-017-1032-z A summary of the main concepts on global ionospheric map(s) [hereinafter GIM(s)] of vertical total electron content (VTEC), with special emphasis on their assessment, is presented in this paper. It is based on the experience accumulated during almost two decades of collaborative work in the context of the international global navigation satellite systems (GNSS) service (IGS) ionosphere working group. A representative comparison of the two main assessments of ionospheric electron content models (VTEC-altimeter and difference of Slant TEC, based on independent global positioning system data GPS, dSTEC-GPS) is performed. It is based on 26 GPS receivers worldwide distributed and mostly placed on islands, from the last quarter of 2010 to the end of 2016. The consistency between dSTEC-GPS and VTEC-altimeter assessments for one of the most accurate IGS GIMs (the tomographic-kriging GIM ‘UQRG’ computed by UPC) is shown. Typical error RMS values of 2 TECU for VTEC-altimeter and 0.5 TECU for dSTEC-GPS assessments are found. And, as expected by following a simple random model, there is a significant correlation between both RMS and specially relative errors, mainly evident when large enough number of observations per pass is considered. The authors expect that this manuscript will be useful for new analysis contributor centres and in general for the scientific and technical community interested in simple and truly external ways of validating electron content models of the ionosphere.