## 3 Results and Discussion
### Multi-Constellation Data Fusion  
An accuracy improvement on _Ne_ retrieval is found by combining both GPS and Galileo measurements. As shown in Figure 6a, the _Ne_ retrieved from selected GPS (L1 and L2) is combined with the Galileo (E1 and E5b) _Ne_ from a simulation using the 13 July 2018 almanac, when there were 13 operational Galileo satellites. After taking an average of those selected GPS and Galileo PRNs (with outlier-free _Ne_ measurements), a 0.01 Hz low pass filter was applied to plot the final values in black. The SR _Ne_ profile is plotted in red to represent the \"true\" values. The measurement errors (discrepancy between filtered _Ne_ and \"true\" value) are plotted in green. It is found that the mean and standard deviation of measurement errors were decreased by 32.83% and 46.12%, respectively, compared to just using the GPS constellation in this simulated scenario.  
As expected, an accuracy improvement can also be seen by simulating the GPS and Galileo almanac in a more recent time. As shown in Figure 6b, the _Ne_ retrieved from selected GPS (L1 and L2) is combined with the Galileo (E1 and E5b) _Ne_ from a simulation using a more recent 8 March 2019 almanac, where there were 22 operational Galileo satellites. It is found that the mean and standard deviation of measurement errors were decreased further by 43.34% and 49.92%, respectively, compared to using only the GPS data in the simulated scenario. This accuracy improvement is consistent with the growing number of Galileo satellites and indicates a benefit of applying multi-constellation GNSS SFF for ionospheric remote sensing. Adding a new constellation can improve the geometry and increase the number of line-of-sight measurements, which is beneficial to smooth out the bias in each measurement.  
Figure 5: Vertical _Ne_ retrieved from Galileo PRN 30 TEC: (**a**) E1 and E5a TEC (**b**) E1 and E5b TEC.  
Figure 6: Vertical _Ne_ retrieved from selected GPS (L1 and L2) plus Galileo (E1 and E5b) PRNs: (**a**) 13 July 2018 almanac (**b**) 8 March 2019 almanac.  
Wavenumber spectra of the _Ne_ measurements were generated to analyze the retrieval resolution on multiple spatial scales of ionospheric plasma structure, based on the 8 March 2019 Almanac and the SR _Ne_ profile. As shown in Figure 7, the wavenumber spectrum of the SR _Ne_ model is plotted in red, the wavenumber spectrum of _Ne_ measurements using L1 and L2 TEC from all visible GPS satellites is plotted in blue, and the wavenumber spectrum of _Ne_ measurements using TEC from all visible GPS satellites plus eight Galileo satellites is plotted in green. The wavenumber \(k\) is a function of spatial scale \(\lambda\) as \(k=2\pi/\lambda\). Ne(_k_) is the spatial Fourier transform of the _Ne_ profile. The three plasma bubbles can be clearly seen in the spectra at 0.1 \(<\) k \(<\) 0.2, which corresponds to 30 km \(<\lambda<\) 60 km. Compared to the blue spectrum, the green spectrum is closer to the red spectrum across the whole spatial range except a noisy spike near \(k\) = 6. This, once again, demonstrates an improvement of ionospheric electron density retrieval resolution using more satellites from multi-constellation GNSS.