# An Approach to Speed up Single-Frequency PPP Convergence with Quad-Constellation GNSS and GIM
## 3 GIM and DCB Products  
The IGS ionosphere working group has started to produce the ionosphere vertical TEC maps since June 1998. Four IGS ionosphere associate analysis centers (IAACs) have released global TEC maps in agreement with the IONosphere map EXchange (IONEX) format [20], also referred as so-called GIM. The four IAACs are CODE (Center for Orbit Determination in Europe, Switzerland), ESOC (European Space Operations Center, Germany), JPL (Jet Propulsion Laboratory, USA) and UPC (Technical University of Catalonia, Spain). As a byproduct of these TEC maps, DCB values from both satellite and tracking receiver ends are estimated and provided as well. Each IAAC computes the rapid and final TEC maps independently using different approaches. The GIM products from CODE and JPL are combined to form IGS GIM products.  
GIM contains TEC values along the zenith direction, i.e., vertical TEC (VTEC), in a globally-distributed grid. In latitude, grid points range from +87.5\({}^{\circ}\) to -87.5\({}^{\circ}\) with a spatial resolution of 2.5\({}^{\circ}\). In longitude, grid points are arranged from \(-\)180\({}^{\circ}\) to +180\({}^{\circ}\) with a resolution of 5\({}^{\circ}\). The TEC map is updated at an interval of one or two hours. According to the IONEX format [20], the GIM is provided in an Earth-centered-Earth-fixed (ECEF) reference frame in spherical coordinates rather than the geographical coordinates.  
The multi-GNSS DCB can be determined by using a priori ionospheric models or jointly estimating the DCB bias and ionosphere delay [22]. Currently, two analysis centers, namely, Deutsches Zentrum fur Luft- und Raumfahrt (DLR) and the Chinese Academy of Sciences (CAS), provide the multi-GNSS DCB products, covering GPS, GLONASS, BDS and Galileo multi-frequency signals. The two DCB products exhibit a consistency of about 0.2 ns and 0.4 ns for Galileo and BDS, respectively [23]. In comparison with GPS and GLONASS DCB products generated by CODE, the multi-GNSS products exhibit RMS (root mean square) differences of approximately 0.2 ns and 0.6 ns, respectively. Monthly repeatabilities of the multi-GNSS DCBs are at the level of 0.1 ns for GPS and Galileo and 0.2 ns for BDS and GLONASS [23].  
In order to compare the GIM products generated from different agencies, the TEC along the line of sight at each ionospheric pierce point of satellite signals are computed using datasets at station PFRR on 4 September 2016 by applying Equations (6) and (7). Figure 1 shows the derived slant TEC (STEC) for all visible satellites from different constellations. It can be seen that there exist obvious offsets for GIM products provided by different agencies, although their varying trend is quite consistent. The largest TEC discrepancy is up to 10.5 TECU for GIM products provided by JPL and ESOC. In order to assess the GIM products, the dual-frequency observations from four constellations are utilized to derive the line-of-sight TEC of each satellite as references. The DCBs at both satellite and receiver ends are corrected using the multi-GNSS DCB products to obtain absolute TEC values. For further comparison, the CAS and DLR quad-constellation DCB products are employed, respectively. Figure 2 shows the RMS statistical values of the slant TEC derived from different agencies' GIM and DCB products. As seen from the two figures, the CODE GIM products achieve the highest accuracy in terms of the RMS values. Comparing the white bars and the color bars for each constellation, it is explicit that the DLR DCB products slightly outperforms the CAS DCB products. Based on this analysis, the CODE GIM products and the DLR multi-GNSS DCB products are, therefore, adopted in our study.