# Improving GNSS PPP Convergence: The Case of Atmospheric-Constrained, Multi-GNSS PPP-AR
## 4 Variations between Estimated Slant and GIM Delays  
A combination of the VTEC and a mapping function express the slant ionospheric delays generated in GIM. The differences between GIM and estimated slant ionospheric delays for particular satellites are depicted in Figure 3. As observed in Figure 3a-d, different satellites show metre-level variations between GIM and slant delays in PPP processing, especially within the first few minutes. These observed variations are not only due to different ionospheric estimates but there is the potential of unmodelled biases [40; 41]. These differences were observed to be consistent for all available GNSSs.  
Figure 3: _Cont._  
In comparing the GIM and estimated slant delays, a key question presents itself: considering PPP float and fixed solutions, how precise must the GIM be in order to notice significant improvement in atmospheric constrained solutions? Unfortunately, attempting an answer represents a meander rather than a straight trajectory. Aside from being multi-faceted, the answer is reliant on the method and models used in the GIM generation (product-wise), how the GIM is used in PPP processing (application-wise), and quality of other GNSS products and observations (quality check). However, there is a level of consistency in the general trend of convergence for both slant and GIM delays. The bordered colours represent the uncertainties of GIM and slant delays, depicting the accuracy of the delays. As expected, given the convergence of the uncertainties of GIM delays, PPP solutions tend to become more optimistic. In the first few minutes of typical processing, a GIM is beneficial in PPP ionospheric constraining while the noisy pseudorange measurements are the limiting factor in accurately estimating slant ionospheric delays.  
Shown in Figures 4 and 5 are correlations plots of GIM and estimated slant delays with their respective uncertainties. The correlation between the GIM delays and uncertainties range up to 8 m \(+/-1\) m with a correlation coefficient of 0.52. This performance is in contrast to the estimated slant delays which ranged up to 10 m \(+/-0.3\) m. while having a very weak correlation of 0.19.  
Figure 4: Correlation between GIM delays and their sigmas. Correlation coefficient equals 0.52. Each colour marker point represents a particular satellite. Delays are shown for DOY 253, 2018 for GMSD station, located in Japan.  
Figure 3: Magnitude of L1 GIM and estimated slant ionospheric delays for sample satellites with metre-level variations shown against satellite elevations. Delays are shown for DOY 253, 2018 for GMSD station, located in Japan. Bordered shaded colours represent the uncertainties.  
The pivotal message from these analyses is that the critical minutes during PPP initialization show GIM with realistic ionospheric delays but decimetre-level uncertainties in contrast to the centimetre-level uncertainties for estimated slant delays. The typical slant ionospheric delay is more precise but less accurate, whereas GIM is more accurate but less precise in the first few minutes. This phenomenon elicits the need for an adaptive approach when using either GIM or ZPD product in constraining. The realism of the estimates and uncertainties is key in constraining. Unrealistic estimates and uncertainties could result in either over or under constraining. The observed product/measurement/processing sensitivity prompts urgency for further investigation to achieve an adaptive approach, which will be fully dependent on the GNSS measurements and parameters of the station, rather than just the atmospheric delays and uncertainties.