# Initial Positioning Assessment of BDS New Satellites and New Signals
## 4 SPP Performance
### Data Setup and Processing Strategy  
As a volunteer association, the International GNSS Service (IGS) continuously provides multi-GNSS data and products [31]. For the validation of positioning, 54 globally distributed IGS stations are selected, as shown in Figure 5. These stations are equipped with JAVAD or SEPTENTRIO receivers, which are able to receive BDS signals B1I, B2I and B3I. Among JAVAD receivers, some firmware versions of JAVAD TRE_3 and JAVAD TRE_3 DELTA are able to receive new B1c and B2a BDS signals. For a statistical result, one-week of data at a sampling of 30 s from DOY 13 to 19 in 2019 are collected at these stations. For the processing of SPP, broadcast orbits and clocks are used. As the BDS broadcast clock refers to B3 frequency, TGD should be corrected when observations of other frequencies or frequency combinations are used. The cut-off elevation is set as 10\({}^{\circ}\), and observations with a PDOP value higher than 6 are rejected. Troposphere delay is corrected by GPT2w and the VMF model [32], ionosphere delay is corrected by the broadcast model. Hence, the estimated parameters are station coordinates and the receiver clock. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **BDS-2** & **BDS-3** & **BDS-2+BDS-3** \\ \hline TGD correction & 0.96 & 0.71 & 0.83 \\ DCB correction & 0.90 & 0.57 & 0.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average SISRE of BDS-2 and BDS-3 from DOY 010 to 070 in 2019 (in m). Figure 4: SISRE of BDS-2 (**upper**) and BDS-3 (**lower**) satellites on B1I/B3I ionosphere-free combination frequency, satellite clock difference is corrected by TGD or DCB. The stochastic model of the observations in SPP is composed by:  
\[\sigma^{2}=\sigma_{SISRE}^{2}+\sigma_{Trop}^{2}+\sigma_{Iono}^{2}+\sigma_{Code}^{2} \tag{2}\]  
where \(\sigma\) is the variance of code observation, while \(\sigma_{SISRE}\), \(\sigma_{Trop}\), \(\sigma_{Iono}\), \(\sigma_{Code}\) stand for the SISRE of satellites, troposphere error after model correction, ionosphere error after model correction and code measurement noise, respectively. According to the analysis of SISRE in the previous section, \(\sigma_{SISRE}\) can be set as 1.0 m for BDS-2 satellites and 0.7 m for BDS-3 satellites. As for \(\sigma_{Trop}\), it can be described by:  
\[\sigma_{Trop}=\sigma_{Trop\_Z}\cdot mf_{Trop} \tag{3}\]  
where \(\sigma_{Trop\_Z}\) is the zenith accuracy of the troposphere model and \(mf_{Trop}\) is a troposphere mapping function. According to [PERSON] et al. (2016), the accuracy of the zenith GPT2w model is at about 0.05 m.  
Similarly, \(\sigma_{Iono}\) can be expressed as:  
\[\sigma_{Iono}=\sigma_{Iono\_V}\cdot mf_{Iono} \tag{4}\]  
where \(\sigma_{Iono\_V}\) is the vertical precision of the ionosphere model correction and \(mf_{Iono}\) is the mapping function at the pierce point. \(\sigma_{Code}\) is determined by an elevation dependent model (Sanchez-Sanchez  
From Table 3 we can conclude that current BDS can provide a global positioning accuracy of 1.1 m and 2.2 m in horizontal and vertical, respectively. For the 95% accumulated error, it is at 2.2 m and 3.9 m in horizontal and vertical, which meets the BDS positioning accuracy standard goal [8]. Accordingly, the positioning performance of BDS shows a competitive performance when compared with GPS. The horizontal error of BDS seems slightly worse than GPS in RMS and 95% probability, while vertical error is almost at the same level. It can be observed from Figure 6 that the horizontal RMS is well below 1 m in the Asia-Pacific region, while it would be worse than 1 m around the Americas, which is consistent with the PDOP performance. However, it is interesting to find that the vertical RMS in the Southern Hemisphere is worse than the Northern Hemisphere in general. This may result from the inaccurate model of ionosphere correction in the Southern Hemisphere, which needs further analysis.