# Evaluation of Ionospheric Delay Effects on Multi-GNSS Positioning Performance
## 3 Data and Processing Strategy  
To evaluate the ionospheric delay effects on multi-GNSS combined positioning performances, datasets from 10 stations of the MGEX network for 1-30 September 2018 (day of year (DOY), from 244 to 273) were selected and utilized for numerical analysis. Figure 1 shows the geographical distribution of the selected MGEX stations. Figure 2 provides the F10.7 values and geomagnetic Kp index for 1-30 September 2018. All of the stations receive quad-system observations from GPS, Beidou, GLONASS and Galileo constellations. The quad-constellation satellite orbits and clock offsets are corrected by the broadcast ephemris provided by MGEX, which is available at [[ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/rinex3/2018/brdm/](ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/rinex3/2018/brdm/)]([ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/rinex3/2018/brdm/](ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/rinex3/2018/brdm/)), or the precise orbit and clock offset products provided by Deutsches GeoForschungsZentrum (GFZ). The sampling rate of orbit and clock products are 5 min and 30 s, respectively. The detailed data processing strategies for multi-GNSS positioning are shown in Table 1. When integrated multi-GNSS combined positioning is carried out, the additional system time difference is needed for each newly added GNSS system. To maintain the consistency of the pseudo-range and carrier phase observations of the quad constellation, we use b1 to denote observations on the first frequency, b2 to denote observations on the second frequency, and b3 to denote observations on the third frequency. The cut-off angle is set to 7\({}^{\circ}\) in this study. The stochastic models of the observations represented by a sinusoidal function and based on the elevation angle of the satellite are utilized to reduce the effect of these elevation angle related errors [21]. The GPS and GLONASS phase observation precision is set to 0.003 m and the GPS code observation precision is set to 0.3 m. To reduce the effect of the inter-frequency bias (IFB) in GLONASS, the GLONASS code observation precision is set to 0.9 m. The Beidou and Galileo code observation precision is set to 0.9 m and 0.4 m, respectively, and the phase observation precision is set to 0.004 m. The LS method is used for SPP data processing and the Kalman filter is utilized in the PPP process of parameter estimation. The tropospheric ZWD is estimated as a random walk process and the receiver clock is estimated as white noise. The time system difference parameters are estimated as constant. The ambiguities are estimated as constant for each epoch. The determination of the weight of virtual ionospheric parameters will affect the ionosphere-constrained PPP performances. In this study, we define the variance of virtual ionospheric parameters as:  
\[\sigma^{2}=(1+0.2\Delta t)\cdot\sigma_{lon}^{2}\cdot mf(z)^{2} \tag{20}\]  
\[mf(z)=\left[1-\sin^{2}z/(1+H_{ion}/R)^{2}\right]^{-1/2} \tag{21}\]  
where \(\Delta t\) denotes the epoch number in the filter processing. \(\sigma_{lon}^{2}\) is the mean VTEC spatial variance. \(H_{ion}\) is the height of the ionosphere single layer. \(R\) is the average radius of the Earth. Equation (20) indicates that the virtual ionospheric observations are weighed at a relatively larger weight at the beginning, and then the weight gradually decreases to get a better positioning accuracy after convergence [12]. The a priori variance of ionospheric delay is determined by the precision of the ionospheric models. Since the Klobuchar model in BIM can remove the ionospheric delay by more than 50%, the variance for BIM is uniformly set to the square of the corresponding BIM ionospheric correction value [3]. The variance of NTCM is set to 1.22 m\({}^{2}\) since the model has a root mean square (RMS) deviation of 7.5 TECU [5]. With regard to the GIM, a temporal and spatial correlation function is utilized, which can be expressed as in [22]. \[\sigma_{ion}^{2}=\left\{