The cooperative IGS RT-GIMs: a global and accurate estimation estimation of the global ionospheric electron content distribution in real-time

. The Real-Time Working Group (RTWG) of the International GNSS Service (IGS) is dedicated to providing high-quality data, high-accuracy products for Global Navigation Satellite System (GNSS) positioning, navigation, timing, and Earth observations. As one part of real-time products, the IGS combined Real-Time Global Ionosphere Map (RT-GIM) has been generated by the real-time weighting of the RT-GIMs from IGS real-time ionosphere centers including the Chinese Academy of Sciences (CAS), Centre National d’Etudes Spatiales (CNES), Universitat Politècnica de Catalunya (UPC), and Wuhan University (WHU). weighting technique is sensitive to the accuracy of RT-GIMs. Compared with the performance of post-processed rapid Global Ionosphere Maps (GIMs) and IGS combined ﬁnal GIM (igsg) during the testing period, the accuracy of UPC RT-GIM (after 10 the transition improvement of interpolation technique) and IGS combined RT-GIM (IRTG) is equivalent to the rapid GIMs and reaches around 2.7 and 3.0 TECU (TEC Unit, 10 16 el/m 2 ) over oceans and continental regions, respectively. The accuracy of CAS RT-GIM and CNES RT-GIM is slightly worse than the rapid GIMs, while WHU RT-GIM requires a further upgrade to obtain similar performance. In addition, the strong response to the recent geomagnetic storms has been found in the Global Electron Content (GEC) of IGS RT-GIMs (especially UPC RT-GIM and IGS combined RT-GIM). The IGS RT-GIMs turn out 15 to be reliable sources of real-time global VTEC information and have great potential for real-time applications including range error correction for transionospheric radio signals(such as GNSS positioning, search and rescue, air trafﬁc, radar altimetry, and radioastronomy), the monitoring of space weather (such as geomagnetic and ionospheric storms, ionospheric disturbance) and detection of natural hazards on a global scale(such as hurricanes/typhoons, ionospheric anomalies associated with earthquakes). All the IGS combined RT-GIMs generated and analyzed during the testing period are available at http://doi.org/10.5281/zenodo. (Liu et al., 2021b).


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The accuracy of RT-GIMs is typically worse than post-processed GIMs due to the short span of ionospheric observations, sparse distribution of stations, higher noises in carrier-to-code leveling, or difficulty in carrier ambiguity estimation in real-time processing mode. While RT-GIMs perform slightly worse than post-processed GIMs, it is found that RT-GIMs are helpful to reduce the convergence time of dual-frequency Precise Point Positioning (PPP) and strengthen the solution (Li et al., 2013). With the corrections of RT-GIMs, the accuracy of single-frequency PPP reaches decimeter and meter level in horizontal and vertical 60 directions (Ren et al., 2019), while the ::::::::::: instantaneous :::::::::::: (single-epoch) Real-Time Kinematic (RTK) Positioning over medium and long-baseline is able to achieve few centimeters level ::::: obtain ::::: higher ::::::: success ::: rate :: of ::: the ::::::::: ambiguity ::::: fixing ::: and :::::::: reliability : for rover stations : in :::: few ::::::::: centimeters ::::: level (Tomaszewski et al., 2020). In addition, the feasibility of ionospheric storm monitoring based on RT-GIMs is tested . A first fusion of IGS-GIMs and ionosondes data from the Global Ionosphere Radio Observatory (GIRO) paves the way for the improvement of real-time International Reference Ionosphere (Froń et al., tation methods of IGS RT-GIMs from different ionosphere centers and the generation of IRTG. In addition, the performance of different RT-GIMs and real-time weighting technique is shown and discussed. The conclusions and future improvements are given in the final section.
Currently, two methods are commonly used for the calculation of real-time STEC. The first method is the so-called Carrier-to-
. φ is the relative rotation between receiver and satellite antennas. B GF = B 1 − B 2 :::: B GF ::::: equals ::: to ::::::: B 1 − B 2 , 100 while B 1 and B 2 are the carrier phase ambiguities including the corresponding phase bias at first and second frequency, respectively. P GF,i and L GF,i are the P GF and L GF at epoch i wthin continuous arc. k is the smoothing arc length. andP GF,k ::::: length :: of ::::::::: smoothing ::: arc :::: from ::::::::: beginning ::::: epoch :: to ::::: epoch :: t, :::: and ::::: P GF,t represents the smoothed P GF : of :::::: epoch : t : which is significantly affected by the pseudorange multipath in real-time mode than in post-processing. TEC model (for example, described in terms of tomographic voxel-based basis functions) in Eq. 2 (Hernández-Pajares et al., 1997. Although the STEC from the second method is accurate and free of code multipath and thermal noise in postprocessing, the convergence time can affect the accuracy of the STEC, most likely in the isolated receivers. In addition, the computation methods of RT-GIMs from different IGS real-time ionosphere centers were compared in detail at the next subsection and summarized in Table 1. Since the dissemination of RT-GIMs adopts spherical harmonic expansions, some :::: Some : ionosphere centers (CAS, CNES, WHU) directly estimate :: and :::::::::: disseminate : spherical harmonic coefficients in sunfixed reference frame as Eq. 4 (RTCM-SC, 2014;Li et al., 2020), while UPC generates the RT-GIM in IONEX format and transforms RT-GIM into spherical harmonic coefficients for the dissemination.

The computation of RT-GIMs by different IGS real-time ionosphere centers
The strategies for generating RT-GIMs differ between IGS RT ::::::: real-time : ionospheric analysis centers (ACs). In this subsection, a brief introduction on the generation of RT-GIMs from individual ACs as well as the strategy comparison between different ACs are given.
130 The post-processed GIM of CAS has been computed and uploaded to IGS since 2015. :::: 2015 ::::::::::::: (Li et al., 2015). : A predictingplus-modeling approach is used by CAS for the computation of RT-GIM . CAS RT-GIM is generated with multi-GNSS, GPS and GLONASS L1+L2, BeiDou B1+B2 and Galileo E1+E5a RT ::::::: real-time : data streams, provided by the IGS and regional GNSS tracking network stations. The real-time differential code biases (DCB) are estimated as part of the 135 local ionospheric VTEC modeling using a generalized trigonometric series (GTS) function as Eq. 5. And then three-day aligned biases are incorporated to increase the robustness of real-time DCBs .
where r is receiver and s is satellite. ϕ d and λ d are the difference between IPP and station in latitude and longitude, respectively.
z is the satellite zenith angle, M (z) is the mapping function. n, m, k :::: i, j, l represent the degrees in the polynomials model and 140 Fourier series expansion. E n,m , C k , S k :::::::: E i,j , C l , S l : are unknown parameters.

Centre National d'Etudes Spatiales
In the framework of the Real Time Service to 12 in May of 2017 (Laurichesse and Blot, 2015).

Wuhan University
The daily rapid and final GIM products have been generated with WHU new software named GNSS Ionosphere Monitoring and Analysis Software (GIMAS) since 21 June 2018 (Zhang and Zhao, 2018). At the end of the year 2020, WHU has also published a first RT-GIM product.

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WHU uses the Spherical Harmonic Expansion (SHE) ::::::: spherical :::::::: harmonic ::::::::: expansion : model and the formula is identical to Eq. 4. Currently, only the GPS real-time data streams from about 120 globally distributed IGS stations are used. The double frequency code and carrier phase observations with a cut-off angle of 10 degrees are used to gather precise geometry-free ionospheric data with the CCL method as Eq. 1 : 3 and ionospheric mapping function with the layer height of 450 km. In order to avoid the influence of satellite and receiver DCB on ionospheric parameters estimation, WHU directly uses the previous 210 estimated DCB from WHU rapid GIM product. According to previous experience, the real-time data is not enough to model the ionosphere precisely on a global scale with SHE ::::::: spherical :::::::: harmonic ::::::::: expansion technique. Considering the lack and the uneven distribution of the GPS-derived ionospheric data, 2-day predicted GIM as external ionospheric information is also incorporated. It is important to balance the weight between the real-time data and the background information. Both the RT-GIM quality and the root mean square (RMS) map are influenced by the weight (Zhang and Zhao, 2019).

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In the year 2021, WHU is going to focus on how to further improve the accuracy of RT-GIM and update the computation method. The precise WHU RT-GIMs with multi-GNSS data and the application of WHU RT-GIM in the GNSS positioning as well as space physics domain, are expected as next steps.
In addition, the RT-dSTEC assessment is based on Root Mean Square (RMS) of the dSTEC error calculated by Eq. 8. In order to adapt to the real-time processing mode, the reference STEC ambiguous measurement L GF (t E ref ) ::::::: L GF,t ref is set to be the first elevation angle higher than 10 • within continuous phase-arc to enable the dSTEC ::::::::: RT-dSTEC : calculation in the 235 elevation-ascending arc.
3.3 The sensibility of RT-weighting ::::::: real-time ::::::::: weighting : technique RT-dSTEC assessment of RT-GIMs was automatically running in real-time mode, and used for RT-weighting ::::::: real-time ::::::::: weighting in the combination of IGS RT-GIMs. In order to compare with the dSTEC-GPS assessment, the RT-dSTEC assessment with 345 RT-stations ::::::: real-time :::::: stations : in Fig. 1 was also performed on January 03 and January 05 in 2021. As can be seen in Table 5, the rank of RT-GIMs in RT-dSTEC assessment is similar to dSTEC-GPS assessment, but the RMS error values are larger. And the larger RMS error is coinciding with the much lower elevation angle of the observation reference in RT-dSTEC assessment.

Data availability
The IGS real-time combined GIMs during the testing period are available from Zenodo at http://doi.org/10.5281/zenodo. 5042622 (Liu et al., 2021b) in IONEX format . In addition, more archived IGS combined RT-GIMs can be found at http://chapman.upc.es/irtg/archive/ and the latest IGS combined RT-GIMs are available in real-time mode at In this paper, we have summarized the computation methods of RT-GIMs from four individual IGS ionosphere centers and introduced the new version of IGS combined RT-GIM. According to the results of Jason3-VTEC and dSTEC-GPS assessment, it could be concluded as follows:
-The quality of most IGS RT-GIMs is close to post-processed GIMs.

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-The difference among RT-GIMs with 20-minute and full temporal resolution can be neglected over oceans in Jason3-VTEC assessment (see Fig. 3 and Table 4), while the difference is visible in some RT-GIMs over continental regions in dSTEC-GPS assessment (see Table 4). The lower accuracy of GIMs with full temporal resolution (2 or 5 minutes) might be related to the uneven distribution of ionospheric observations, the weight between predicted GIMs and realtime observations. Combined with the previous study (Liu et al., 2021a), it is suggested to find a more suitable temporal 395 resolution for the generation of RT-GIM in sun-fixed reference frame.
In addition, the GEC evolution of UPC RT-GIM and IGS combined RT-GIM is close to the GEC evolution of IGS final combined GIM in post-processing mode, and has an obvious response to the geomagnetic storm during the low solar activity period. Future improvements might include: -To broadcast real-time RMS maps that can be useful for the positioning users.

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-To increase the accuracy of high temporal resolution RT-GIMs. In addition, higher maximum spherical harmonic degrees might be adopted to increase the accuracy and spatial resolution of RT-GIMs.
-Coinciding with a much larger number of RT-GNSS receivers in the future, the dSTEC weighting might be improved by replacing the "internal" by the "external" receivers, i.e. not used by any RT ::::::: real-time analysis centers. In this way the weighting would be sensitive as well to the interpolation/extrapolation error of the different RT ::::::: real-time ionospheric 405 GIMs to be combined. And the resulting combination might behave better.
Author contributions. QL wrote the manuscript. QL developed the updated combination software with contributions from DRD, HY and Q. Zhao and Q. Zhang provided the real-time GIMs of the corresponding IGS centers. AH, MS, GW and AS contributed in creating the framework of the real-time IGS service, the ionospheric message format and BNC open software updates. LA suggested the initial idea of this work. AK, SS, JF, AK, RGF and AGR contributed in the generation of rapid and final IGS GIMs used as additional reference in the manuscript.