*2.2. Constellation Visibility Analysis*

The visibility of GPS, GLONASS, and GPS+GLONASS in different latitude networks was analyzed and evaluated using the following criteria:


As the GLONASS constellation geometry repeats about every 8 sidereal days, we used observation data from 28 March 2021 (day of year (DOY) 087) to 4 April 2021 (DOY 094) to evaluate the observation quality. The elevation cutoff angle was set to 3◦. The study employed the same data set as the data quality check for visibility assessment.

#### *2.3. DD Network Processing Strategy*

The DD network processing was conducted using the Bernese GNSS Software, Version 5.2. The software is developed at the Astronomical Institute of the University of Bern (AIUB), Bern, Switzerland. A daily batch processing scheme is used for the data processing. The final precise orbits from CODE were adopted, containing consistent orbits for GPS and GLONASS. The different code biases (DCB) files and the Earth Rotation Parameters (ERP) of CODE were also used for consistency. The PCC model used was igs14.atx. The ocean tides model used was FES2004 (Finite Element Solutions). The elevation mask for data preprocessing was set to 3◦. The baselines were defined with the OBS-MAX strategy. An attempt to fix the GPS and GLONASS integer value ambiguities was attempted with the Quasi Ionospheric Free (QIF) strategy [22]. The VMF1 (Vienna Mapping Function) [23] grid file [24] and NET WET model were used for the tropospheric estimate. Zenith Tropospheric Delay (ZTD) parameter was estimated per hour. The datum definition was realized with the minimum-constraint solution by a set of reference stations of IGS14. The processing scheme is displayed in Figure 1.

**Figure 1.** DD network processing scheme.

#### *2.4. Static PPP Processing Strategy*

The static PPP processing was carried out by FUSING (FUSing IN GNSS) software [25], Version 2.0, developed by Wuhan University, Wuhan, China. The Ionosphere-free (IF) linear combination with L1 and L2 was employed. The elevation mask, the precise products, and the ocean tides model, as well as the PCC model, were the same as the DD processing strategy. The GPT2 (Global Pressure and Temperature) [26] model and VMF1 [23] model were used for the tropospheric estimate. PPP static in 24 h window was processed with a forward extended Kalman filter. The processing strategies of PPP are summarized in Table 1.

**Table 1.** The processing strategies of PPP.


DD network and static PPP processing were carried out for different positioning combination modes: GPS stand-alone positioning mode, GLONASS stand-alone positioning mode, and GPS+GLONASS combined positioning mode.

#### *2.5. Accuracy Assessment*

The station coordinates and ZTDs provided by the IGS were used as references to assess the accuracy of DD network solutions and PPP solutions. The Root Mean Square Error (RMSE) of daily coordinate estimates was used as the accuracy assessment indicator,

$$\text{RMSE}\_{\text{COORDINATE}} = \sqrt{\frac{\left(\text{COORDINATE}\_{\text{estimated}} - \text{COORDINATE}\_{\text{ICS}}\right)^2}{\mathbf{n}}} \tag{3}$$

where n is the total number of daily coordinate estimates.

The tropospheric products from IGS are sampled every 300 s, while, in this paper, the ZTDs estimated interval by DD strategy was one hour, and 30 s by PPP strategy. Thus, the tropospheric estimates or the IGS products needed to be resampled to match the sampling intervals. The current study resampled the IGS tropospheric products to 1 h and the PPP tropospheric to 300 s to coincide with IGS products. The RMSE of ZTD estimates is,

$$\text{RMSE}\_{\text{ZTD}} = \sqrt{\frac{\left(\frac{\text{ZTD}\_{\text{estimated}} - \text{ZTD}\_{\text{IGS}}\right)^2}{\mathbf{n}}} \tag{4}$$

where n is the total number of available ZTD estimates after resampling.

#### **3. Data Selection**

To comprehensively study the GLONASS performance, three networks located in high, middle, and low latitude regions were employed. In addition to the differences in latitude, the following three factors were also considered in the selection of the IGS station:



**Table 2.** The GNSS receivers and the antenna + radome types of the high latitude stations.

**Table 3.** The GNSS receivers and the antenna + radome types of the middle latitude stations.



**Table 4.** The GNSS receivers and the antenna + radome types of the low latitude stations.

According to the above station select criterion, 21 IGS stations were selected and formed 3 networks, distributed in high, middle, and low latitude regions, as shown in Figure 2. The high latitude network locates between 60◦N and the North Pole, the middle latitude network lies between 30◦N and 60◦N, and the low latitude network situates between the equator and 30◦S. The baseline lengths of the three networks are approximately 660 km, 880 km, and 778 km, respectively. The performance evaluation period was from 1 January 2021 (DOY 001) to 30 June 2021 (DOY 181). The GPS and GLONASS observations were downloaded from NASA CDDIS [30].

**Figure 2.** The IGS tracking stations of the high (red triangle), middle (green triangle), and low latitude networks (blue triangle).

#### **4. Results and Discussion**

The data quality of GPS and GLONASS, the constellation visibility of GPS, GLONASS, and GPS+GLONASS, and the performance of the DD network solutions and PPP solutions, are shown and discussed in this section.

#### *4.1. Data Quality*

The DI rate, MP1, MP2, SN1 (the SNR of L1), and SN2 (the SNR of L2) of GPS and GLONASS observations for each station are calculated and presented in Figure 3. The mean value of each indicator is listed in Table 5, where G and R denote GPS and GLONASS, respectively.

**Figure 3.** The results of the data quality check.

**Table 5.** The mean value of each data quality indicator in the three networks.


The data integrity rate of GLONASS in 21 stations of the 3 networks is lower than that of GPS, as is evident in Figure 3. As shown in Table 5, the calculated average data integrity rates of GLONASS in the three networks are 82.37%, 83.46%, and 81.33%, respectively, significantly lower than those of GPS with 94.33%, 96.11%, and 94.81%, respectively.

The MP1 and MP2 of GPS presented similar performance to that of GLONASS in the high latitude network. However, the MP1 and MP2 of GPS in the middle latitude network are smaller than those of GLONASS in most stations, except station HERT. By contrast, the MP1 and MP2 of GLONASS in the low latitude network are smaller than those of GPS. The calculated average value of MP1 and MP2 in Table 5 indicates similar results, but the differences in MP1 and MP2 between GPS and GLONASS are insignificant.

The difference in SN1 between GPS and GLONASS is minor in the three networks, except SOD3 and SVTL in the high latitude network and WARN in the middle latitude network. The SN2 of GLONASS is significantly better than that of GPS in the high and low latitude networks and similar to that of GPS in the middle latitude network.

Among the 21 tracking stations, however, the data quality of SALU in the low latitude network is significantly worse than other stations. The DI rate of SALU is 84.3% for GPS and 71.6% for GLONASS. The MP1 of SALU is up to 0.99 m and 0.89 m for GPS and GLONASS observations, respectively, much larger than those calculated average values, 0.39 m and 0.46 m for GPS and GLONASS. The MP2 of SALU presented similar results as that of MP1.
