# Analysis of BDS/GPS Signals' Characteristics and Navigation Accuracy for a Geostationary Satellite
## 4 Navigation Performance
### Single-Point Position Accuracy  
The single-epoch least square solutions are recalculated at 20 s intervals using flight observations and broadcast ephemerides. Comparisons between the solutions using only GPS observations and GPS + BDS observations combination at weights of 1:2, 1:1, 2:1, 4:1 and the precision orbit determination solutions are reported in Table 3. The accuracy of these solutions is related to measurement errors and the PDOP. Because the PDOP of the combined GPS+BDS satellites improves (see in Section 3.2), remarkable improvements in position and velocity accuracy are made with the combined GPS and BDS observations. When GPS observations combined with BDS observations at the weight of 1:1, the RMS of the position accuracy can improve from 32.1 m to 16.5 m and the corresponding velocity accuracy can improve from 0.238 m/s to 0.165 m/s. When BDS observations are involved, the accuracy of position and velocity in the x-axis direction is improved obviously. The x-axis direction is basically consistent with the radial direction of the orbit of the receiver, according to the location of the receiver. The position error in radial direction will be significantly higher than that in the other two directions, because there is a weak constraint in this direction [22]. According to the results in Table 3, except that the velocity differences is larger than others at weight coefficients 1:2, there is no big difference on the navigation accuracy with four different weight coefficients.  
In order to evaluate the improvement obtained with BDS MEO or BDS GEO/IGSO satellites, we use GPS + BDS MEO and GPS + BDS GEO/IGSO observations combinations to calculate single-epoch least square solutions respectively. When we use GPS + BDS pseudorange combinations, one more unknown parameter (BDS clock offset) becomes available. At least two BDS satellites pseudorange combinations should be used to make sense of the BDS pseudorange contribution to the solutions. Therefore, one set of position and velocity solutions using GPS + BDS GEO/IGSO combinations are calculated when the number of BDS GEO and IGSO satellites tracked is more than or equal to two. Another set of solutions are also given using only GPS pseudorange with the same epoch as the previous set. Comparing the two sets of solutions with the reference of the precision orbit determination solutions, the position and velocity differences are reported in Table 4. In this case, using additional BDS GEO and IGSO observations reduces the position error from 28.9 m to 15.9 m and the velocity error from 0.218 m/s to 0.184 m/s.  
Figure 8: Standard deviation of the pseudorange noises and carrier phase noises for GPS and BDS in different C/N\({}_{0}\) range over two days.  
We use the same method to give the solutions using GPS + BDS MEO observations combinations and only GPS observations. We compare these solutions with the reference of the precision orbit determination solutions, as shown in Table 5. When using additional BDS MEO observations, the accuracy improvement in position is small and the accuracy improvement in velocity is even worse. It is further confirmed that the improvement of the position and velocity accuracy comes from combinations with BDS GEO and IGSO.