## 6 The Effect of the IMU Quality on the Tracking Performances  
Based on the ultra-tight integration, the tracking performances of the receiver are enhanced by compensating the receiver antenna's dynamics and reducing the dynamic stress noise. The estimation accuracy of the dynamics is affected by the quality of the IMU. Therefore, the IMU quality becomes an impact factor in the tracking of the ultra-tightly integrated GNSS/INS receiver. The relation between the dynamic stress noise and the quality of the IMU, derived from Equations (12) and (13), is expressed for second-order PLL in the ultra-tightly integrated GNSS/INS receiver:  
\[\theta_{UT}=\frac{1}{3}\cdot K_{2}\,\frac{\overline{\
abla}+\overline{g}\cdot \overline{\alpha}\big{(}0\big{)}+\overline{g}\cdot\overline{\varepsilon}\cdot t _{d}}{\big{(}\,B_{PLL}\big{)}^{2}}\cdot\frac{360\cdot L_{c}}{c}\,\quad\big{(} ^{\circ}\big{)} \tag{15}\]  
The dynamic stress noises in four ultra-tightly integrated GNSS/INS receivers aided by different grade IMUs are compared to verify the effect of the IMU quality. Table 4 lists the IMUs selected.  
Since the correction frequency of the INS in the ultra-tight integration is usually 1 Hz, the drift time \(t_{d}\) is assumed to 1 s and initial misalignment is null. Figure 11 illustrates that the dynamic stress noise decreases as the IMU quality is enhanced. For a low quality IMU, such as the MEMS IMU and the automotive IMU, the IMU errors would have an effect on the loop noise and tracking performances of the PLL if a narrow bandwidth is selected in the ultra-tightly integrated GNSS/INS receiver. On the other hand, for a high quality IMU, such as the tactical IMU and the navigation IMU, the dynamic stress noise in the ultra-tightly integrated GNSS/INS receiver is far less than the tracking threshold and  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **MEMS IMU** & **Automotive IMU** & **Tactical IMU** & **Navigation IMU** \\ \hline Gyro bias & 300 \%h & 50 \%h & 1 \%h & 0.01 \%h \\ Accelerometer bias & 10 mg & 1 mg & 0.1 mg & 0.01 mg \\ \hline \end{tabular}
\end{table}
Table 4: IMUs selected in the comparisons.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Dynamics** & **0.1 g** & **0.5 g** & **1 g** & **1.5 g** \\ \hline Standard & Optimal Bandwidth & 14 Hz & 22 Hz & 28 Hz & 32 Hz \\  & Tracking Error of the PLL & 13 deg. & 15 deg. & 17 deg. & 18 deg. \\ Receiver & In Optimal Bandwidth & 13 deg. & 15 deg. & 17 deg. & 18 deg. \\  & Dynamic Stress Noise & 3\% & 14\% & 25\% & 33\% \\  & Proportion (B\({}_{PLL}=20\) Hz) & 3\% & 14\% & 25\% & 33\% \\ \hline Ultra- & Optimal Bandwidth & 9 Hz & 9 Hz & 9 Hz & 9 Hz \\ tightly & Tracking Error of the PLL & 12 deg. & 12 deg. & 12 deg. & 12 deg. \\ Integrated & in Optimal Bandwidth & 12 deg. & 12 deg. & 12 deg. & 12 deg. \\ GNSS/INS & Dynamic Stress Noise & \textless{}1\% & \textless{}1\% & \textless{}1\% & \textless{}1\% \\ Receiver & Proportion (B\({}_{PLL}=20\) Hz) & \textless{}1\% & \textless{}1\% & \textless{}1\% & \textless{}1\% \\ \hline \end{tabular}
\end{table}
Table 3: Tracking performance comparisons of two kinds of receiver with different dynamics (30 dB-Hz C/N0).  
can be neglected. Therefore, to get better tracking performances, a high quality IMU should be used in the ultra-tightly integrated GNSS/INS receiver.