## 4 Discussion
[52] showed that NeQuick overperforms the Klobuchar model in 98% of TEC estimates. However, in the positioning domain, the improvement is not so high--only 4-5%. In this current research, small differences in the positioning domain are, therefore, not surprising. However, they are statistically significant at \(\alpha<0.001\) due to the huge data set. [PERSON] et al. [53] validated NeQuick2 during 2008-2021. They found an increase in TEC RMSE under solar maxima and mean TEC bias at \(\sim\!-1.5\) TECU. That agrees with our results of TEC bias at \(\sim\!-1.22\) and overall mean absolute TEC error increase in both solar maxima. [PERSON] [54] showed that NeQuickG yields lower RMS of the precise point positioning error than the Klobuchar model: 20% and 11% for the horizontal and vertical components, respectively. The GIM significantly overperformed both models: 37 and 27% in the horizontal and vertical navigation error components, respectively. In the precise point positioning domain [54], NeQuickG RMS of positioning error is 50 cm less than of the Klobuchar model. Our results did not show such a big difference in the positioning domain between NeQuickG and Klobuchar models but did show it in the TEC domain. The probable reason is the noises due to non-smoothed pseudo ranges. Single-frequency PPP showed that GIM provides \(\sim\)1.5-2.5 better positioning than IRI-2016 and NeQuick [55]. In general, IRI-2016 and NeQuick2 showed similar statistical results [55]. However, our results show that NeQuick2 has a smaller TEC bias than IRI-2016. [PERSON] et al. [19] estimated BDGIM coefficients (which should be broadcast) for 2010-2017 (BeiDou broadcasts coefficients from 2015). They found that BDGIM performs similarly to the NeQuickG model and about 5% better than the empirical IRI-2016 model. Our results for the TEC domain showed that BDGIM overperformed other operational models (up to 20%) and had significantly less TEC bias. We should note that in our research, the GLONASS model was not used as an operational model because the broadcast model coefficients were not available. We used _F10.7_ and _Ap_ indexes instead for their effective analogues, which are implied for the model. So, the quite poor results obtained are most probably due to a non-optimal use of driving parameters. Our results surprisingly revealed that the empirical median NeQuick2 model tends to perform slightly better than NeQuickG (which implied corrections based on actual data), both in positioning and TEC domain. This demonstrates the importance of the background models used in correction procedures based on the limited amount of experimental data. Probably modifying the Galileo model via injecting NeQuick2 as a background model would provide even better results, but this requires additional studies that are beyond the scope of this current paper. BDGIM uses the most sophisticated methodology to use broadcast coefficients compared with NeQuickG. One of the differences is that BDGIM uses a background model and disturbance to it, while NeQuickG changes whole the model based on the broadcast coefficients. Our comparison indirectly shows that the first approach could be more effective than the second one. Finally, TEC updating procedure can improve the quality of ionospheric models (including IRI and NeQuick) [56]. Probably in the future, all the models will provide TEC updating capabilities (such as IRI-Plas) that will improve their operational effectiveness. Another way to improve ionospheric modeling is through machine learning techniques, whose usage is continuously increasing for global ionosphere modeling [37]. Such models now overperform classical models (such as IRI) [57]. These two ways seem to be the ionospheric modeling future.