# The Impact of Eclipsing GNSS Satellites on the Precise Point Positioning
## Materials and Methods
### The Multi-GNSS Precise Point Positioning and Its Strategy
Due to the neglect of the pseudorange IFBs, the value of \(\sigma_{0}\) for GLONASS pseudorange observables is enlarged by several times [26], such as 0.9 m. The phase IFBs of GLONASS can be absorbed by the GLONASS float ambiguities; therefore,the value of \(\sigma_{0}\) for GLONASS phase observables can be set as the same as that of GPS [26]. For BDS GEO satellites, because of the low accuracy of the orbit and clock products, the value of \(\sigma_{0}\) for GEO can be set as 1.2 m and 0.009 m for the raw pseudorange and phase observables [27; 28]. Due to the satellite-induced code variations for BDS IGSO and MEO satellites, the value of \(\sigma_{0}\) for IGSO/MEO can be set as 0.4 m after correcting the satellite-induced code errors using the linear interpolation model [29]. The phase observables of IGSO and MEO satellites are not influenced by these errors and the value of \(\sigma_{0}\) for IGSO/MEO phase observables can also be set as the same as that of GPS [27]. During the data pre-processing, data integrity, pseudorange gross errors [30] and cycle-slips [31] are checked and detected. When cycle slip occurs, new ambiguity parameters are introduced into the filter state rather than being repaired. However, the pre-processing is difficult to detect the small cycle-slips and code gross errors. To reduce the influence of the undetected cycle slips and gross errors, the robust Kalman filter using IGG (Institute of Geodesy and Geophysics) III function [32] based on the observation residuals is used to adjust the variance of the observations:  
\[\vec{\sigma}^{2}=\sigma^{2}/\gamma, \tag{13}\]  
\[\gamma=\left\{ \begin{array}{cc}1&|\vec{v}|\leq k_{0}\\ \frac{k_{0}}{|\vec{v}|}\left(\frac{k_{1}-|\vec{v}|}{k_{1}-k_{0}}\right)^{2}& k_{0}<|\vec{v}|\leq k_{1}\\ 0&|\vec{v}|{>k_{1}}\end{array} \right., \tag{14}\]  
where \(\vec{\sigma}^{2}\) is the equivalent variance and \(\gamma\) is the variance inflation factor; \(|\vec{v}|\) is the standardized residual; and \(k_{0}\) and \(k_{1}\) are the threshold, which are usually chosen as 1.5 and 3.0, respectively. For each iteration, only the satellite with the maximum standardized residual is selected to adjust its variance. When the standardized residual of phase observable is bigger than \(k_{1}\), the ambiguity of this satellite is reset as a new parameter, rather than setting its variance as a large value. The strategy of GNSS PPP is summarized in Table 3. Multi-GNSS precise orbit and clock products from GFZ/Wuhan University are used. Due to the small higher-order ionospheric delays, the higher-order corrections are ignored in all PPP schemes. Currently, the phase center corrections of receiver for GALILEO and BDS are still unavailable. Therefore, the corrections of receiver PCO and PCV (Phase Center Variations) for GALILEO and BDS are assumed the same as that of GPS. After fixing the orbit, clock and DCBs for all visible satellites, the estimable parameters for GNSS PPP are \(\left(\Delta x_{r},Z_{r},d\vec{t}_{r}^{G},\mathbf{A}_{r,if}^{s\text{ys},s},ISB_{r} ^{G\ast}\right)\). The process noise of the Kalman filter state is also shown in Table 3.