## 4 Experimental Results and Discussion
### Real Experimentation  
The real experimental results are presented to validate the performance of the proposed algorithm. A ProPak6 GNSS Receiver was used as a base station and placed on the rooftop of the Weiqing Building, Tsinghua University, Beijing, China. It provided double-frequency pseudorange, Doppler, and carrier-phase measurements at 1 Hz. The dataset of the rover station was collected by a moving vehicle equipped with NovAtel SPAN-CPT, which was composed of a GNSS receiver and an Inertial Measurement Unit (IMU). The experimental equipment for data collection is shown in Figure 13. GNSS measurements were also output at 1 Hz, and inertial information including the specific force and angular rate measurements were collected at 100 Hz. The vehicle was driven around the Tsinghua campus with a maximum speed of 57.18 km/h. The baseline was less than 2 km. Since the ground truth is unknown, we select a segment with better satellite conditions and use the result of the post-processing software Inertial Explorer [19] as the reference trajectory to compare with the ARPD-RTK/INS algorithm. The reference trajectory is marked by a set of yellow points in  
Figure 11: Error distribution in ECEF-XYZ axis. Figure 12: **(a)** Error distribution in Earth-Centered Earth-Fixed (ECEF)-XYZ axis for different algorithms; **(b)** Error distribution in ECEF-Y axis; **(c)** Error distribution in ECEF-Z axis. Figure 14, and the selected segment is marked by green points. During the 200-s data, the satellite visibility is indicated in the left part of Figure 15. The red points represent invisible satellites, while the black points represent the available satellites in Figure 15a. Therefore, we can see that the satellite observations are in good condition, except for the periods around the 40 th and 121 st s.  
In order to compare the performance of the different positioning algorithms, we add cycle slips and large pseudorange noises under the existing observations artificially. Different scenes are designed as follows:  
* Scene F: The original real dataset. * Scene G: Frequent satellite changes are added to the original dataset. * Scene H: Large pseudorange noise are added to the original dataset. The standard deviation of the additional noise is 3 m. Meanwhile, the number of visible satellites is reduced, and only the BDS observations are preserved. * Scene I: Frequent satellite changes are added to the Scene H. At the same time, low-elevation satellites are removed. The satellite visibility of scene F and G is shown in Figure 15. The position errors of different tightly coupled RTK/INS algorithms in the ECEF frame are shown in Figure 16. Similarly, the satellite visibility of scene H and I is shown in Figure 17, and its corresponding position errors are shown in Figure 18. Tables 5 and 6 compare the accuracy and fix rate of these algorithms numerically. Figure 14: The entire path obtained by Inertial Explorer as a reference (from Google Earth). Figure 15: (**a**) The satellite visibility of the 200-s real data for Scene F; (**b**) The satellite visibility for Scene G; (**c**) The number of satellites in Scene F; (**d**) The number of satellites in Scene G.  
Figure 16: **(a)** Error distribution in the ECEF-X axis for Scene F; **(b)** Error distribution in the ECEF-Y axis for Scene F; **(c)** Error distribution in the ECEF-Z axis for Scene F; **(d)** Error distribution in the ECEF-X axis for Scene G; **(e)** Error distribution in the ECEF-Y axis for Scene G; **(f)** Error distribution in the ECEF-Z axis for Scene G.  
Figure 11:0 **(a)** The satellite visibility of the 200-s real data for Scene H; **(b)** The satellite visibility for Scene I; **(c)** The number of satellites in Scene H; **(d)** The number of satellites in Scene I. The conclusions obtained from the real datasets are basically consistent with those from the simulation datasets.