## 4 Results and Discussion
### Static Field Test  
Although the baseband signal preprocessing model and the ultra-tight GPS/INS integration can both restrain noise better, the field test is carried out in an open-sky area (N : 39\({}^{\circ}\)57\({}^{\prime}\)36.16\({}^{\circ}\), E : 116\({}^{\circ}\)19\({}^{\prime}\)1.58\({}^{\prime}\), Hgt : 32.9m) and does not involve the weak signal problem. After collecting signals with a radio frequency front-end, seven satellites are chosen according to their high Carrier-to-Noise Ratio \((C/N_{0})\) listed in Table 1. The sky plot of these satellites is shown in Figure 3, and the elevation of each satellite is always greater than 10\({}^{\circ}\) during the test. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Satellite** & \(C/N_{0}\)**(dB** **Hz**)** & **Satellite** & \(C/N_{0}\)**(dB** **Hz**)** \\ \hline PRN22 & 48.881 & PRN14 & 45.612 \\ PRN31 & 48.025 & PRN32 & 45.693 \\ PRN25 & 45.987 & PRN12 & 45.202 \\ PRN18 & 48.086 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(C/N_{0}\) of selected satellites. Since weak signals are beyond the scope of this contribution, there is no need to employ INS to aid GPS tracking in static field tests. Hence this part just compares the performance of GPS receivers equipped with single pre-filter (pre-filter-S) and double pre-filters (pre-filter-D). First of all, in the tracking domain, the reference Doppler shifts can be provided by cubic spline fit interpolation. Then, taking PRN25 for example, Figure 4 shows the difference between Doppler shift tracking errors obtained by these two aforesaid methods. According to the statistical analysis, the Root Mean Square (RMS) value of the Doppler shift tracking errors corresponding to pre-filter-S is 0.487 Hz. For pre-filter-D, this value is 0.198 Hz. Obviously, pre-filter-S has a bad Doppler shift estimation outcome due to the influence of code phase error, while pre-filter-D achieves a significantly higher degree of precision. The decoupling between carrier tracking and code tracking proposes a 59.3 percent reduction in Doppler shift tracking error. Staying with the PRN25 example, Figure 5 shows the difference between the code phase tracking errors obtained by these two methods. It is observed that the new model proposed in this paper has slightly better performance. Specifically, the RMS values of code phase tracking errors corresponding to pre-filter-S and pre-filter-D are respectively 1.55 \(\times 10^{-2}\) chip and 1.43 \(\times 10^{-2}\) chip. The decoupling reduces the code phase tracking error by 7.7 percent. Figure 4: Doppler shift tracking error for PRN25 in field test. Figure 3: Satellites sky plot of the field test. To analyze the impact of tracking parameters on position and velocity detection, receiver implements navigation through Least Squares (LS). The position estimation errors in the ECEF coordinate system are shown in Figure 6, while their corresponding RMS values are listed in Table 2. It can be seen that pre-filter-D makes positioning more precise. Then, Figure 7 illustrates the velocity estimation errors in ECEF frame, and Table 3 lists their RMS values. Obviously, there are multiple glitch impulses in the velocity estimation result output by the receiver employing pre-filter-S, which is quite similar to the situation in Doppler shift tracking. Sometimes the velocity errors in the \(y\) and \(z\) direction are even close to 0.3 m/s. On the contrary, the other receiver achieves comparatively stable and accurate outcomes. The absolute maximum values of the velocity errors are smaller than 0.1, 0.13 and 0.12 m/s, respectively. Figure 5: Code phase tracking error for PRN25 in field test. Figure 6: Position estimation errors with field data. It can be drawn from the analysis above that, using the new preprocessing model based on dual-filter makes GPS receiver behave better in the static field tests.