## 4 Tracking Loops Error in the Ultra-Tightly Integrated GNSS/INS Receiver
dynamic stress noise proportion is less than 1% in the ultra-tightly integrated GNSS/INS receiver when the other noises are same as those in the standard receiver. Hence, we can conclude that the reduction of the loop error in the ultra-tightly integrated GNSS/INS receiver is brought by the compensation of the receiver antenna's dynamics. Since the phase error of the PLL is reduced, the ultra-tightly integrated GNSS/INS receiver can keep tracking in lower C/N0. It can acquire and track the weaker signal than the standard receiver. Comparing Figure 8 with Figure 3, it can be derived that the ultra-tight integration can reduce the minimum PLL bandwidth to keep the loop in lock since the receiver antenna's dynamics is estimated and compensated. According to Equation (1), the thermal noise would decrease once the PLL bandwidth is reduced. Hence, not only the dynamic stress noise but also the thermal noise would decrease in the ultra-tightly integrated GNSS/INS receiver since the less PLL bandwidth can be selected. In this case, the Allan deviation noise and vibration-induced noise becomes the major error sources. It is consistent with the distributions in \[\delta\overline{f}_{IMU}=\overline{\
abla}+\overline{g}\cdot\overline{\alpha }\left(0\right)+\overline{g}\cdot\overline{\varepsilon}\cdot t_{d} \tag{12}\]3  
Based on Figures 3-10, the tracking performances of the two kinds of receiver with different C/N0 are compared and listed in \[\delta\overline{f}_{IMU}=\overline{\
abla}+\overline{g}\cdot\overline{\alpha }\left(0\right)+\overline{g}\cdot\overline{\varepsilon}\cdot t_{d} \tag{12}\]4 The optimal PLL bandwidth of the ultra-tightly integrated GNSS/INS receiver is less than that of the standard receiver. The narrow bandwidth can reduce tracking phase noise, so the ultra-tightly integrated GNSS/INS receiver has better tracking performances than the standard receiver in GNSS-challenged environments. Furthermore, due to the reduction of the dynamic stress noise, the phase error of the PLL in the ultra-tightly integrated GNSS/INS receiver can decrease by 1-8 degree in different C/N0 scenarios. In this case, the PLLs of the ultra-tightly integrated GNSS/INS receiver are easier to be locked. Moreover, the dynamic stress noise is not considered as a crucial error source in the ultra-tightly integrated GNSS/INS receiver as its proportion decreases. The biggest advantage of the ultra-tightly integrated GNSS/INS receiver is that it can perform in a highly dynamic scenario. Assumed that the C/N0 is 30 dB-Hz, Table 3 compares the tracking performances of two kinds of receiver with different dynamics based on Figures 5 and 6, Figures 8 and 9. In the standard receiver, the optimal bandwidth, the tracking error and dynamic stress noise proportion \begin{table}
\begin{tabular}{c c c c c c} \hline  & **C/N0** & **25 dB-Hz** & **30 dB-Hz** & **35 dB-Hz** & **40 dB-Hz** \\ \hline \multirow{4}{*}{Standard Receiver} & Optimal Bandwidth & 15 Hz & 22 Hz & 28 Hz & 35 Hz \\  & Tracking Error of the PLL & & & & \\  & in Optimal Bandwidth & 28 deg. & 15 deg. & 9 deg. & 7 deg. \\  & Dynamic Stress Noise & & & & \\  & Proportion (BPLL = 20 Hz) & 8\% & 14\% & 21\% & 28\% \\ \hline \multirow{4}{*}{Ultra- tightly Integrated GNSS/INS Receiver} & Optimal Bandwidth & 7 Hz & 9 Hz & 13 Hz & 25 Hz \\  & Tracking Error of the PLL & & & & \\  & in Optimal Bandwidth & 20 deg. & 12 deg. & 8 deg. & 6 deg. \\ \cline{1-1}  & Dynamic Stress Noise & & & & \\  & Proportion (BPLL = 20 Hz) & \(<\)1\% & \(<\)1\% & \(<\)1\% & \(<\)1\% \\ \hline \end{tabular}
\end{table} 
Table 2: Tracking performance comparisons of two kinds of receiver with different C/N0 (0.5 g LOS acceleration). gradually increase as the receiver antenna's dynamics raise. But, the ultra-tightly integrated receiver has good tracking performances all the time and is not influenced by the receiver antenna's dynamics.