# Mitigating the Scintillation Effect on GNSS Signals Using MP and ROTI
## 2 Materials and Methods
### Methodology  
Before conducting the experiments on scintillation mitigation, the convergence time of PPPH was estimated. Typically, a day without scintillation is used to evaluate the convergence time [33]. Thus, the data on 1 September 2017 at SAO0P station, 1 September 2017 at SJCU station and 29 May 2016 at SNAOP station was used for this purpose. The convergence was defined by [PERSON] et al. [33] as the positioning accuracy reaching a specific tolerance, which typically refers to 0.1 m for the Up component. Thus, this defintion of convergence was applied in this paper. Figure 2 shows the flowchart of the method used to mitigate scintillation effects. First, the data on the scintillation day was input, where the scintillation days could be determined with the method introduced by [PERSON] et al. [27]. All the data was applied with an elevation mask of 10\({}^{\circ}\). Then, the first strategy was conducted, where the satellite with the maximum value of each reference parameter was removed. As there were five parameters (MP1, MP2, ROTI, S4 and \(\sigma_{\phi}\)), this step was repeated five times in order to compare the effectiveness of different parameters. It should be noted that values of S4 are not high in the Antarctica station SNA0P, which is typical at high latitudes [34]. Thus, S4 was not used for the SNA0P station in the satellite and observation removal strategies. After that, the processed and original data was input into PPPH to obtain the height and 3D time series outputs. Based on the PPP outputs, RMSE of both original and processed data during the period affected by scintillation as well as the corresponding improvement rates could be calculated. If the scintillation occurs at the beginning of the day, the RMSE was calculated after the convergence period. When computing RMSE, a reference coordinate should be input. In this paper, the Natural Resources Canada's Canadian Spatial Reference System (CSRS) PPP was used to generate the reference coordinate by inputting the RINEX file on a day without scintillation [35]. Moreover, the geometric dilution of precision (GDOP) was generated to investigate the change of position and clock quality of satellites before and after satellites or observations were removed; this was calculated with the position of each visible satellite relative to that of the receiver and it started with a fraction of the design matrix [36]:  
\[\mathrm{G}= \begin{bmatrix}\left(\mathrm{x}_{0}-\mathrm{x}^{1}\right)/\rho_{0}^ {1}&\left(\mathrm{y}_{0}-\mathrm{y}^{1}/\rho_{0}^{1}\right)&\left(\mathrm{z}_ {0}-\mathrm{z}^{1}\right)/\rho_{0}^{1}&\mathrm{c}\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ \left(\mathrm{x}_{0}-\mathrm{x}^{\mathrm{g}}\right)/\rho_{0}^{\mathrm{g}}& \left(\mathrm{y}_{0}-\mathrm{y}^{\mathrm{g}}\right)/\rho_{0}^{\mathrm{g}}& \left(\mathrm{z}_{0}-\mathrm{z}^{\mathrm{g}}\right)/\rho_{0}^{\mathrm{g}}& \mathrm{c}\end{bmatrix}  \tag{4}\]  
where \(G\) is the fraction that contains the information of position and clock of satellites. Then, GDOP was calculated using the covariance of \(G\):  
\[\mathrm{GDOP}=\sqrt{\sigma_{\mathrm{x}}^{2}+\sigma_{\mathrm{y}}^{2}+\sigma_{ \mathrm{z}}^{2}+\sigma_{\mathrm{t}}^{2}}=\sqrt{\mathrm{trace}\big{(}\left( \mathrm{G}^{\mathrm{T}}\mathrm{G}\right)^{-1}\big{)}} \tag{5}\]  
where \(\sigma_{x}\), \(\sigma_{y}\), \(\sigma_{z}\) and \(\sigma_{t}\) are the RMSEs of the estimated receiver coordinates and clock, respectively, and trace is the sum of the matrix diagonal. When satellites are far apart, the geometry is regarded to be strong and low DOP values can be obtained, thus, with a higher accuracy. Typically, the geometric quality is reliable and acceptable with a DOP value less than 5 and 10, respectively [37]. To observe the variation in the small values of GDOP, GDOP values larger than 30 are set to 30. For the second strategy we removed outliers, defined as parameter values that exceeded a threshold. We compared the mild threshold (MT) and extreme threshold (ET) as thresholds for defining outliers.