## 3 Instantaneous Multi-Constellation Relative Positioning: Methodology and Performance
### Performance Assessment of Precise Positioning with Focus on E14 and E18 Galileo Satellites
#### 3.2.3 Performance Assessment of Instantaneous Positioning
At this point we should recall that the residuals correspond to double-differenced observables. Figure 8: Scatter plots of coordinate residuals obtained on 3 October 2017 for tested scenarios. Grey and green dots represent float and fixed solutions, respectively. As an example, Figures 9 and 10 show L1/E1 and L2/E5a phase residuals obtained on 3 October 2017. For better distinction, these values were depicted with separate colours for GPS, Galileo, E14 and E18 signals. Moreover, Figure 11 presents L1/E1 phase residuals in the function of satellite elevation and Figure 12 depicts elevation angle of the E14 and E18 satellites. In general, the figures did not reveal important differences in DD observable residuals between GPS, Galileo, E14 and E18 satellites. We did not recognise the outliers in the signals from the FOC satellites with incorrect orbits. A more detailed analysis may be performed on the basis of residuals' histograms and selected statistical measures. The former are presented in Figure 13. The latter were given in Table 6.  
Table 6 summarises the results in the observation residuals domain obtained with scenario #3. Specifically, we give the values of the standard deviation of phase residuals obtained on the corresponding days of the positioning experiment. In addition, Figure 13 visualises the distribution of the phase residuals of the selected satellites and systems obtained on 3 October 2017. As we can see from Table 6, the standard deviation of the L1/E1 phase residuals, corresponding to GPS, Galileo, E14 and E18 signals, were at a comparable level, in the range of 6.5-8.7 mm. Slightly \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **GPS L1** & **GPS L2** & **Gal E1** & **E14 E1** & **E18 E1** & **Gal E5a** & **E14 E5a** & **E18 E5a** \\ \hline
3 October & 7.4 & 10.3 & 7.3 & 8.0 & 7.0 & 13.9 & 12.3 & 15.4 \\
4 October & 7.0 & 10.3 & 7.3 & 8.7 & 7.5 & 14.6 & 16.3 & 15.8 \\
5 October & 7.8 & 10.3 & 7.7 & 8.5 & 6.5 & 14.6 & 17.3 & 14.7 \\ \hline \end{tabular}
\end{table} 
Table 6: Empirical standard deviation of phase observable residuals based on multi-baseline single-epoch solution (in mm). Figure 11: L1 + E1 DD phase residuals in the function of satellite elevation angle on 3 October 2017. Figure 12: Elevation of the E14 and E18 satellites in the function of the satellite altitude on 3 October 2017. Figure 13: Histograms of phase residuals corresponding to L1/E1 and L2/E5a on 3 October 2017.  
higher values were recognised for residuals of double-differenced observables formed with the application of E14 satellites (up to 8.7 mm), whereas in the case of E18 signals these indicators were in the range of 6.5-7.5 mm. At the same time the _std_ for observables formed with Galileo satellites other than E14 & E18 were within 7.3-7.7 mm. According to this, we do not see important differences between residuals corresponding to signals of satellites with incorrect orbit and others. In the case of L2 and E5a frequencies, we found that the _std_ of phase residuals was at a higher level with respect to L1/E1. This may be explained in two ways. First, the weighting scheme distinguishes the observable weights between frequencies. Specifically, the weights are correlated to the ratio of applied frequencies with respect to L1/E1 [64]. Therefore, L2 and E5a signals are depicted with lower weights than L1/E1. This ratio is obviously more significant when E1 & E5a signals are used than in the case of L1 & L2. Moreover, we should note the lack of official antenna phase centre offsets and variations for E5a signals. In this case, corrections corresponding to L2 frequency are applied. For GPS signals the _std_ of L2 phase residuals equalled 10.3 mm, whereas this reached 14.6 mm in the case of Galileo satellite signals excluding E14 and E18. In the case of the latter satellites, the standard deviation of the E5a phase residuals of DD observables was in the range 12.3-17.3 mm. Judging on the basis of observable residuals, the FOC satellites with incorrect orbits did not stand out.