# Mitigating the Scintillation Effect on GNSS Signals Using MP and ROTI
## 2 Materials and Methods
### Methodology
As different parameters may reflect different scintillation activities [20], the combination between parameters may cover more data influenced by scintillation. Thus, a series of permutations and combinations of parameters were used in observation removals so that the optimal combination could be determined. Standard (MP and ROTI) and scintillation (S4 and \(\sigma_{\Phi}\)) parameters were applied separately for comparison. Taking scintillation parameters as an example, there were 3 combinations: (1) S4; (2) \(\sigma_{\Phi}\); (3) S4 and \(\sigma_{\Phi}\). Since there might be outliers in \(\sigma_{\Phi}\) that were not in S4, the combination of S4 and \(\sigma_{\Phi}\) could cover more outliers, and more outlier removals might lead to more accurate results. Similarly, there were 7 combinations of standard parameters. It should be noted that the same idea was not applied to the satellite removal because excessive satellite removals might result in complete failure of the positioning algorithm when the number of tracked satellites was less than four. The same procedures as satellite removal were repeated for the observation removal strae  
Figure 2: Method flow chart. The three strategies: (1) satellite removal, (2) observation removal and (3) observation weighting strategy. An additional step in the third strategy was to calculate the IF combination of MP1 and MP2 (MPF) that was used to down-weight the multipath effect as proposed by [PERSON] [38]. Though the primary ionospheric error in MPF was mitigated through IF combination, the cycle slip and corresponding IF ambiguity caused by scintillation could still affect MPF. As suggested by [PERSON] [39], it is possible that only one of the carrier phase and pseudorange observations is affected by scintillation, where the carrier phase is more susceptible to scintillation [40]. On the contrary, the effect of multipath on pseudorange observations is considerably greater than that on carrier phase observations. Furthermore, MPF was used mainly to characterize multipath, but also to describe scintillation and ROTI was used mainly to characterize ionospheric activity. Based on these propositions, MPF was applied to weight the IF combination of pseudorange observation and ROTI was applied to weight the IF combination of carrier phase observation in PPP, which could achieve the best improvement as compared with other weighting strategies. In addition, S4 and \(\sigma_{\Phi}\) were, respectively, used to weight pseudorange and carrier phase as S4 was calculated based on signal intensity and \(\sigma_{\Phi}\) was obtained from signal carrier phase, which in turn were the influence factors, respectively. of pseudorange and carrier phase. In the Kalman filter (KF), the weights of observations were dependent on the measurement error covariance matrix \(R\) introduced in [32]. Assume that the numbers of pseudorange and carrier phase observations are both \(n\). Thus, \(R\) could be initiated with an \(2n\)-by-\(2n\) identity matrix as below [32]:  
\[\mathrm{R}= \begin{bmatrix}1&&\\ &\ddots&\\ &&1\end{bmatrix} _{\mathrm{2n}\times\mathrm{2n}} \tag{6}\]  
Then, an initial weight dependent on the a priori standard deviation (SD) of measurements was multiplied to each value on the diagonal of \(R\)[32]:  
\[\mathrm{R}= \begin{bmatrix}\mathrm{P}_{w,0}&&&&\\ &\mathrm{L}_{w,0}&&&\\ &&\ddots&&\\ &&&\mathrm{P}_{w,0}&\\ &&&\mathrm{L}_{w,0}\end{bmatrix} _{\mathrm{2n}\times\mathrm{2n}} \tag{7}\]  
\[\mathrm{P}_{w,0}=\mathrm{SD}_{0,P}^{2}\cdot\left(\frac{\mathrm{f}_{1}^{2}}{ \mathrm{f}_{1}^{2}-\mathrm{f}_{2}^{2}}\right)^{2} \tag{8}\]  
\[\mathrm{L}_{w,0}=\mathrm{SD}_{0,\mathrm{L}}^{2}\cdot\left(\frac{\mathrm{f}_{1} ^{2}}{\mathrm{f}_{1}^{2}-\mathrm{f}_{2}^{2}}\right)^{2} \tag{9}\]  
where \(SD_{0,P}\) and \(SD_{0,L}\) are the a priori SDs of code and phase measurements, respectively, typically 3 m and 0.03 m, respectively [32; 41]; \(P_{w,0}\) and \(L_{w,0}\) separately indicate the initial weight for code and phase measurements.