# Analysis of BDS/GPS Signals' Characteristics and Navigation Accuracy for a Geostationary Satellite
## 3 BDS/GPS Signal Characteristics
### Observations Distribution and Accuracy  
C/N\({}_{0}\) is an important indicator about the signals power, which is related to the accuracy of observations. Figure 7 gives the distribution of GPS and BDS observations with respect to C/N\({}_{0}\). Most of the GPS, BDS-2 IGSO, and BDS-2 MEO observations are in C/N\({}_{0}\) range of above 30 dB-Hz and below 35 dB-Hz. However, for BDS-3 MEO satellites, the number of observations in C/N\({}_{0}\) above 40 is more than that in other C/N\({}_{0}\) range. This indicates that most of the observations was observed from the main-lobe signals of BDS-3 MEO antenna.  
The pseudorange \(P_{u}^{i}\) and carrier phase \(L_{u}^{i}\), respectively, are [22]  
\[\left\{\begin{array}{c}P_{u}^{i}=\rho+c\delta t_{u}-c\delta t^{s}+\delta \rho_{trop}+\delta\rho_{iono}+\epsilon_{p}^{i}\\ L_{u}^{i}=\rho+c\delta t_{u}-c\delta t^{s}+\delta\rho_{trop}-\delta\rho_{iono}+ \lambda N_{u}^{i}+\epsilon_{L}^{i}\end{array}\right. \tag{3}\]  
where \(\rho\) is the geometric range between the receiver and the navigation satellite; \(\delta t^{s}\) and \(\delta t_{u}\) are navigation satellite clock offset and receiver clock offset, respectively; and c is the speed of light. \(\delta\rho_{trop}\) and \(\delta\rho_{iono}\) represent the troposphere and ionosphere delay errors, respectively. The parameter \(\lambda N_{u}^{i}\) denotes the ambiguity of the carrier phase measurements. \(\epsilon_{p}^{i}\) and \(\epsilon_{L}^{i}\) are the measurement noises, for the pseudorange and the carrier phase, respectively. We use epoch difference arithmetics to analyze carrier phase measurement noise [22; 29]. In general, only random noise remains when using triple difference, which is described as follows:  
\[\begin{array}{c}\Delta\epsilon_{P}=P_{u}^{i}-P_{u}^{i-1}-\left(P_{u}^{i-1}-P _{u}^{i-2}\right)-\left(P_{u}^{i-1}-P_{u}^{i-2}-P_{u}^{i-2}+P_{u}^{i-3}\right) \\ \hskip 14.226378 pt=P_{u}^{i}-3P_{u}^{i-1}+3P_{u}^{i-2}-P_{u}^{i-3}\end{array} \tag{4}\]  
\[\begin{array}{c}\Delta\epsilon_{L}=L_{u}^{i}-L_{u}^{i-1}-\left(L_{u}^{i-1}-L _{u}^{i-2}\right)-\left(L_{u}^{i-1}-L_{u}^{i-2}-L_{u}^{i-2}+L_{u}^{i-3}\right) \\ \hskip 14.226378 pt=L_{u}^{i}-3L_{u}^{i-1}+3L_{u}^{i-2}-L_{u}^{i-3}\end{array} \tag{5}\]  
Therefore, we use \(\Delta\epsilon_{p}/\sqrt{2}\) and \(\Delta\epsilon_{L}/\sqrt{20}\) as the pseudorange and carrier phase noise statistics. The standard deviation of the pseudorange and carrier phase noises are shown in Figure 8. The pseudorange measurement noises are less than 4 m, and the carrier measurement noises are mostly less than 8 mm. The pseudorange and carrier phase noises of BDS measurements are lower than those of GPS measurements. Especially the pseudorange noises of BDS measurements are mostly less than 2 m in term of C/N\({}_{0}\) bellow 30, which are obvious lower than those of GPS measurements. According to accuracy estimation method of the code tracking errors as described in [27], the thermal noise jitter of code delay locked loop (DLL) is related to code chipping rate. Therefore, the pseudorange accuracy of BDS measurements is higher than that of GPS measurements, because the BDS B1I code chipping rate of 2046 Kbps is higher than the GPS C/A code chipping rate of 1023 Kbps.  
Figure 7: Distribution of observations with respect to C/N\({}_{0}\) over two days.