## 5 The INS-Aided Acquisition Experiments with Different Grade INS
### Doppler Shift and Code Phase Estimation Errors Using Different Grade INS  
According to Equations (27) and (28), Doppler shift and code phase estimation errors exist due to the velocity error and positon error caused by the INS used. According to the ephemeris and the INS information of the 12 visible satellites, the Doppler shift and the code phase estimation of each satellite can be calculated by Equations (7) and (14). Then, the Doppler shift and code phase estimation errors of the 12 visible satellites are achieved by calculating the difference between the estimation and real value. The maximum Doppler shift estimation errors and the maximum code phase estimation errors are listed in Tables 5 and 6, respectively.  
The experimental results show that the Doppler shift and code phase estimation errors increase as the quality of the INS decreases. The Doppler shift estimation errors are less than the minimal frequency search space (\(\pm\)500 Hz) in 180 s. The code phase estimation errors are less than 1023 chips  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **MEMS Grade** & **Civil Grade** & **Tactical Grade** & **Inertial Grade** \\ \hline \multirow{6}{*}{BDS} & PRN 3 & 16.6109 & 2.3727 & 0.1767 & 0.0229 \\  & PRN 6 & 12.3420 & 1.6628 & 0.1198 & 0.0154 \\  & PRN 7 & 14.5754 & 2.0277 & 0.1488 & 0.0192 \\  & PRN 9 & 14.0123 & 1.8668 & 0.1423 & 0.0186 \\  & PRN 10 & 16.1468 & 2.2217 & 0.1707 & 0.0224 \\  & PRN 14 & 18.3990 & 2.6928 & 0.2032 & 0.0264 \\ \hline \multirow{6}{*}{GPS} & PRN 12 & 9.0416 & 1.2784 & 0.0988 & 0.0130 \\  & PRN 14 & 4.6490 & 0.5560 & 0.0408 & 0.0054 \\ \cline{1-1}  & PRN 22 & 5.0048 & 0.6440 & 0.0445 & 0.0057 \\ \cline{1-1}  & PRN 25 & 8.9826 & 1.1339 & 0.0998 & 0.0138 \\ \cline{1-1}  & PRN 31 & 9.4901 & 1.3072 & 0.1128 & 0.0154 \\ \cline{1-1}  & PRN 32 & 7.0746 & 1.1309 & 0.0714 & 0.0086 \\ \hline \end{tabular}
\end{table}
Table 6: Maximum code phase estimation errors of total satellites.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**Maximum Error**} & **MEMS Grade** & **Civil Grade** & **Tactical Grade** & **Inertial Grade** \\ \hline \multirow{6}{*}{Velocity (m/s)} & \(x\) axis & 11.14 & 1.88 & 0.22 & \(-\)0.016 \\  & \(y\) axis & \(-\)45.09 & \(-\)4.98 & 0.60 & \(-\)0.1085 \\  & \(z\) axis & 5.19 & 0.52 & 0.04 & \(-\)0.0183 \\ \hline \multirow{3}{*}{Position (m)} & \(x\) axis & 1115 & 265.5 & 11.33 & 0.99 \\  & \(y\) axis & \(-\)2737 & \(-\)328.6 & 34.66 & \(-\)5.23 \\ \cline{1-1}  & \(z\) axis & 725.2 & 73.2 & 4.18 & \(-\)0.48 \\ \hline \end{tabular}
\end{table}
Table 4: Maximum position and velocity errors of the different grade INS.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & & **MEMS Grade** & **Civil Grade** & **Tactical Grade** & **Inertial Grade** \\ \hline \multirow{6}{*}{BDS} & PRN 3 & 164.0205 & 19.8074 & 2.2807 & 0.3910 \\  & PRN 6 & 112.2213 & 13.1841 & 1.4684 & 0.2656 \\  & PRN 7 & 139.3393 & 16.5499 & 1.8787 & 0.3185 \\  & PRN 9 & 134.6166 & 15.6793 & 1.7725 & 0.3139 \\  & PRN 10 & 161.1931 &  
(for GPS) or 2046 chips (for BDS). Furthermore, by comparing Table 3 with Table 5, it can be seen that the Doppler shift estimation error is about 200 Hz when using a MEMS grade INS, and that if the INS accuracy increases by 10-fold, the estimation error of the Doppler frequency shift decreases by 10-fold. Similarly, the code phase estimation error decreases approximately 10-fold if the INS accuracy improves by 10-fold. Thus, the appropriate INS for the intended acquisition can be selected according to the required accuracy of the Doppler frequency shift and code phase.