## 5 Data Quality Analysis 4 (DQA4): Satellite Position Difference between Almanac and Ephemeris  
Unlike the ephemeris data, almanac data is not very precise for calculating satellite position. However, it can be used for several months. Almanac data is used when a GPS receiver is just turned on. It helps with regard to the time required for a GPS receiver to acquire satellite signals and navigation data and calculates a position solution. The approximate almanac position result is enough to decide which satellite needs to do the search. The almanac data helps a user to spend less time obtaining the first positioning result, which is also called time to first fix (TTFF). The almanac data includes all satellite orbital parameters. The total satellite orbit parameters can be received from one satellite. However, if the user wants to use the complete almanac data, it takes 12.5 min to download the complete navigational message. In this section, we verify the satellite position difference using the almanac and ephemeris, as shown in Figure 13.  
The GPS almanac update rate is close to one day. Figure 14 shows the GPS satellite position difference between almanac and ephemeris, and GPS DQA4 statistical results are summarized in Table 5. The difference value was calculated when the new almanac received. The true satellite  
Figure 14: GPS DQA4: Satellite Position Difference between Almanac and Ephemeris.  
Figure 13: Schematic diagram of DQA4.  
position is calculated from the ephemeris at the same time. Compare with the true satellite position, the mean value for all GPS satellite is 1537.8 m, the maximum is 4982.2 m and the standard deviation is 716.4 m.  
The BDS almanac update rate is almost every hour. However, the almanac data is not synchronized for all BDS satellites. Sometimes the BDS MEO was broadcasting the old almanac. The time of almanac (TOA) is a reference time for users to calculate the satellite position. TOA usually is increased with the time during a one week period. The BDS TOA cannot provide a stable growing TOA. Sometimes, the user receives new almanac data, but the TOA is incorrectly tagged as occurring in the previous week. However, the entire BDS almanac still can provide adequate accuracy for the user. The results are presented in Figure 15. Table 6 shows the BDS DQA4 statistical results. The maximum position error for the BDS almanac data is 4448.9 m. The mean and standard deviation for the whole constellation is 1756.1 and 759.6 m, respectively. As a result, the BDS almanac data has almost the same accuracy as that of the GPS.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**PRN** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline
**Mean** & 1680.7 & 2364.1 & 1748.9 & 2189.5 & 1955.2 & 1497.1 & 1032.5 & 1007.1 \\ \hline
**std** & 980.3 & 877.3 & 743.7 & 953.7 & 785.1 & 753.6 & 849.9 & 631.5 \\ \hline
**PRN** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** \\ \hline
**Mean** & 1405.5 & 2451.0 & 1728.8 & 1079.2 & 1283.3 & 1487.9 & 1476.6 & 1222.7 \\ \hline
**std** & 1076.1 & 1130.4 & 1145.4 & 380.1 & 557.4 & 791.3 & 548.9 & 549.4 \\ \hline
**PRN** & **17** & **18** & **19** & **20** & **21** & **22** & **23** & **24** \\ \hline
**Mean** & 1984.2 & 2121.2 & 1448.7 & 1478.6 & 1738.5 & 1597.6 & 1730.8 & 1040.6 \\ \hline
**std** & 644.0 & 1120.9 & 657.7 & 529.9 & 611.0 & 633.3 & 619.9 & 363.2 \\ \hline
**PRN** & **25** & **26** & **27** & **28** & **29** & **30** & **31** & **32** \\ \hline
**Mean** & 1459.3 & 1566.9 & 1477.5 & 1442.5 & 1711.4 & X & 1265.0 & 1535.8 \\ \hline
**std** & 750.4 & 748.6 & 758.1 & 771.9 & 869.6 & X & 594.5 & 498.3 \\ \hline \end{tabular}
\end{table}
Table 5: GPS DQA4 statistical results.  
Figure 15: BDS DQA4: Satellite Position Difference between Almanac and Ephemeris.