## 2 Data and Processing Method  
The measurements of GNSS signal carrier phase were performed during 13 and 16 April 2021 with use of the multi-system multi-band navigation receiver Javad Delta-G3T connected to the RingAnt-G3T antenna (Kal  
We applied the following procedure for deviation frequency estimation. (1) The second order phase derivative was used to detect cycle slips and abnormal data in the carrier phase records. Cycle slip and anomalies in data yield sharp peaks of the phase derivative. All the carrier phase records that contain one or more events defined by Equation (1) were excluded from our analysis  
\[dMax\leq d2L_{j}=\frac{L_{i+2}-2L_{i+1}+L_{0}}{dt^{2}} \tag{1}\]  
where \(dMax\) is the threshold defined empirically as \(dMax=10d2L_{j-1}\); \(d2L_{j-1}\) is the second order derivative of the carrier phase at the previous step of calculation; and \(L_{i}\) is the carrier phase at \(i\)-th time point (in cycles). (2) Phase ambiguity was resolved by means of polynomial filtering. We used a 2-step algorithm to reduce the phase ambiguity. First, the main trend of the carrier phase was removed by means of linear interpolation as follows  
\[ \begin{array}{l}{IL_{i}=a_{0}+a_{1}t_{i}}\\ {dL_{i}=L_{i}-IL_{i}}\end{array}  \tag{2}\]  
Further, the second-order trends of the carrier phase were removed by means of the 5-th order polynomial interpolation:  
\[ \begin{array}{l}{PL_{i}=b_{0}+b_{1}t_{i}+b_{2}t_{i}^{2}+b_{3}t_{i}^{3}+b_{4} t_{i}^{4}+b_{5}t_{i}^{5}}\\ {LP_{i}=dL_{i}-PL_{i}}\end{array}  \tag{3}\] \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Navigation** & & & & & & & \\
**System** & & & & & & & \\ \hline GPS & LIC & & L1W & & L2W & & L2X & & L5X \\ GLONASS & & LIC & & L1P & & L2C & & L2P \\ Galileo & & & L1X & & & L5X & \\ SBAS & & LIC & & & L5I & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Considered GNSS signal components. Figure 1: Variations of SYM-H and Kp indices during 13 April (**upper left** panel) and 16 April 2021 (**upper right** panel). General picture of SYM-H and Kp variations during 1-30 April 2021 (**lower** panel). (3) The final de-trending of the carrier phase was performed by means of moving averaging window filter as follows  
\[ \begin{array}{l}SL_{i+\frac{N}{2}}=\frac{1}{N+1}\sum\limits_{k=0}^{N}LP_{i+k}\\ LS_{i}=LP_{i}-SL_{i}\end{array}  \tag{4}\]  
The parameter of the filter \(N\) defines the window width. Considering the results reported in [14], we chose the 5 min averaging window. According to [14], phase fluctuations caused by small-scale irregularities usually have a period of several seconds. Indeed, [PERSON] et al. [7] reported a period of \(\sim\)(2-13) s and [PERSON] and [PERSON] [22] reported \(\sim\)(0.4-5) s.  
After the data preprocessing, a fast Fourier transform was applied to the de-trended phase data series \(LS\) (4). We did not apply the Hanning window as in work [15], because of uncertainty of filter parameter choice under the unknown spread and behavior of deviation frequencies. The deviation frequency was determined at the logarithmic spectrum of phase variations as a \"break point\" at which the maximum decrease in the slope of the spectrum passes into near-zero decrease in a given frequency range. Figure 2 illustrates the example of deviation frequency identification from the logarithmic spectrum of phase variations for line-of-site to GPS satellite PRN07 on 13 April (panel a) and 16 April (panel b). When performing this analysis, the frequency range from 1 to 25 Hz in the spectrum was studied in which the deviation frequency was expected to vary. The \"break point\" defines the part of the phase variations spectrum where the expected power law character is shallowing towards white noise. Therefore, the carrier phase noise is a key issue to define the precise value of deviation frequency. That is why it is important to analyze the level of phase measurement noise for signals of different navigation systems, different frequencies and components.