## 2 Analysis of Signal Power and Noise
### Phase Measurement Noise  
The analysis of phase noise at a particular frequency is usually performed with zero or ultra-short baselines, which allows for elimination of short-term variations of atmospheric influence. However, the stations used in the given experiment belong to active reference networks and are distant from each other by a few tens of kilometres. In such a case the combined weighted phase noise can be derived from single-station data using triple-frequency combinations. In our case it was realised using the difference of two ionosphere-free combinations (DIF) according to the following equation [12; 45]:  
\[ \begin{array}{l}DIF\Big{(}\varphi_{k,f_{1}}^{i},\varphi_{k,f_{2}}^{i},\varphi _{k,f_{3}}^{i}\Big{)}=IF\Big{(}\varphi_{k,f_{1}}^{i},\varphi_{k,f_{2}}^{i} \Big{)}-IF\Big{(}\varphi_{k,f_{1}}^{i},\varphi_{k,f_{3}}^{i}\Big{)}\\ =\Big{(}\frac{f_{1}^{2}}{f_{1}^{2}-f_{2}^{2}}-\frac{f_{1}^{2}}{f_{1}^{2}-f_{3} ^{2}}\Big{)}\lambda_{f_{1}}\varphi_{k,f_{1}}^{i}-\frac{f_{2}^{2}}{f_{1}^{2}-f_{ 2}^{2}}\lambda_{f_{2}}\varphi_{k,f_{2}}^{i}+\frac{f_{3}^{2}}{f_{1}^{2}-f_{3}^ {2}}\lambda_{f_{3}}\varphi_{k,f_{3}}^{i}\end{array}  \tag{4}\]  
This triple-frequency combination theoretically eliminates all geometric factors and influence of the first-order term of ionospheric refraction. Thus, the right side of the equation should contain aggregated weighted phase noise, constant factor including ambiguity term, hardware delay and inter-frequency biases The last parameter was recognised and investigated in GLONASS (due to satellite individual frequencies) and GPS signals. However, it was reported in [12; 48] that for the latter system such data are affected by variations of inter-frequency bias, which have to be eliminated. In this work triple-frequency combinations were created taking advantage of L1, L2, L5 and E1, E5a, E5b signals of GPS and Galileo systems, respectively. The long-term variations associated with inter-frequency bias, also observed in our case, were removed using a fourth-order polynomial. The further algorithm of DIF combination data processing was analogous as in the case of multipath combinations. A summary of phase noise variations with elevation angle is presented in Figure 4.  
Looking at these results, it can be observed that DIF phase noise for E14 and E18 is slightly lower (up to 1 mm) than for the other Galileo satellites. On the other hand, this improvement is detectable only at selected elevations (mainly low) and is probably an effect of the lower multipath in these cases. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & \multicolumn{2}{c}{**GPS**} & \multicolumn{2}{c}{**Galileo**} & \multirow{2}{*}{**Galileo E14**} & \multirow{2}{*}{**Galileo E18**} \\  & & & **(Except \#14 and E18)** & & & & & \\ \cline{2-2} \cline{6-8}  & _MP1_ & _MP2_ & _MP1_ & _MP2_ & _MP1_ & _MP2_ & _MP1_ & _MP2_ \\ \hline BYCE & 0.20 & 0.21 & 0.16 & 0.14 & 0.16 & 0.13 & 0.16 & 0.13 \\ CHLE & 0.21 & 0.22 & 0.19 & 0.13 & 0.17 & 0.13 & 0.18 & 0.13 \\ IAWA & 0.22 & 0.23 & 0.18 & 0.15 & 0.20 & 0.16 & 0.19 & 0.17 \\ OLSZ & 0.13 & 0.19 & 0.08 & 0.07 & 0.07 & 0.08 & 0.07 & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMS of dual-frequency multipath combinations at zenith (m). Figure 4: Variation of phase noise and multipath (DIF) with elevation at stations IAWA (left panel) and OLSZ (right panel). At high elevations the differences do not exceed 0.3 mm and 0.1 mm at IAWA and OLSZ, respectively. The results from stations with better equipment prove that the level of phase noise for both analysed satellites is the same as for the others. The comparison of RMS values for IAWA and OLSZ sites confirms that applying a choke ring antenna reduces the phase multipath in the entire elevation angle domain. As a consequence, RMS of DIF combination declines from 2.3 mm and 8.8 mm to 1.6 mm and 5.0 mm at high and low elevations, respectively. Unfortunately, OLSZ station did not record the third GPS frequency, and thus the discussed results are given for IAWA station only.