## 6 Data Quality Analyze 5 (DQA5): Applicable Almanac Period  
Although almanac data can be used for a longer time, it still has a useful life. In this part, this research applies the SIS almanac data for over a month in an attempt to find the applicable almanac period for both systems. The schematic diagram of the applicable almanac period test is presented in Figure 16. The true satellite position is calculated from the latest ephemeris data. Before verifying the almanac useful period, the detection mechanism should be established first. The purpose of the almanac is to use the rough positioning result to determine which satellite is in view. Moreover, the almanac also computes a rough estimate of the satellite Doppler shift. With the rough estimate Doppler shift, acquisition can be processed more quickly, and the information from the satellite can be decoded in a shorter period of time. For a general GNSS signal, Equations (3) and (4) present the Doppler Effect for the signal. The \(f\) is the observed frequency; _f_\({}_{0}\) is the emitted frequency, and c is the speed of light. _v_\({}_{r}\) is the velocity of the receiver, which is positive if the receiver is moving towards the source. _v_\({}_{s}\) is the velocity of the source, which is positive if the source is moving away from the receiver. For Equation (4), if we redefine the _f_\({}_{0}\) as the observed frequency and \(f\) as the estimated frequency calculated from the almanac, then, the _\(\Delta\)f_ represents the error of the satellite Doppler shift estimate. For the same reason, if the _v_\({}_{s}\) and _v_\({}_{r}\) means the true satellite velocity and the velocity calculated from the almanac, the _\(\Delta\)v_ will be redefined as the velocity error between the truth and the value estimated from the almanac. The general case of the Doppler shift searching range is about 5000\(\sim\)10,000 Hz, for which this research sets the _\(\Delta\)f_ as 7500 Hz. The GPS _f_\({}_{0}\) is set at 1575.42 MHz and BDS _f_\({}_{0}\) is 1561.098 MHz. With these assumptions, we can \begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{5}{c}{**GEO**} \\ \hline PRN & 1 & 2 & 3 & 4 & 5 \\ Mean & 1904.1 & 2023.6 & 1879.2 & 2099.9 & 1897.7 \\ std & 774.4 & 940.1 & 765.9 & 866.1 & 828.0 \\ \hline \multicolumn{5}{c}{**IGSO**} \\ \hline PRN & 6 & 7 & 8 & 9 & 10 \\ Mean & 2124.6 & 1811.1 & 2126.3 & 1933.3 & 1689.7 \\ std & 906.3 & 729.0 & 1017.8 & 812.9 & 692.5 \\ \hline \multicolumn{5}{c}{**MEO**} \\ \hline PRN & 11 & 12 & 13 & 14 & X \\ Mean & 1361.4 & 1065.3 & 1560.9 & 1108.1 & X \\ std & 611.7 & 380.0 & 893.4 & 415.9 & X \\ \hline \end{tabular}
\end{table} 
Table 6: BDS DQA4 statistical results. Figure 16: Schematic diagram of DQA5. calculate the maximum velocity error for the GPS to be about 1427.203 m/s, and it is 1440.296 m/s for the BDS:  
\[f=\left(\frac{c+\
u_{r}}{c+\
u_{s}}\right)f_{0} \tag{3}\]  
\[\Delta f=\frac{\Delta v}{c}\,f_{0}\,\,\,\,where,\Delta f=f-f_{0},\Delta v=\
u_{ r}-\
u_{s} \tag{4}\]  
\[\Delta v=\frac{\Delta f}{f_{0}}\,c\,\,\,\,where,\Delta f=f-f_{0},\Delta v=\
u_{ r}-\
u_{s} \tag{5}\]  
Figure 17 presents the satellite positioning error for the same almanac use for one week. The true position is using the satellite position calculated from the ephemeris. This result requires a continuous true position. The BDS GEO satellites have been selected in this analysis due to the fact that users in Taiwan can continuously receive these satellite signals. The different colors represent the different BDS GEO satellites in Figure 17. The results show that all positioning errors grow with time, and the maximum position error after one week is more than 35,000 m. In this section, the satellite position error is not the only indicator. The elevation angle error and velocity error for each satellite also become analysis items. Figure 18 shows the all analysis indicators in the DQA5. The top figure demonstrates the velocity error, which relates to using the almanac to estimate the Doppler shift.