# RTK with the Assistance of an IMU-Based Pedestrian Navigation Algorithm for Smartphones
## 3 Results
### RTK Performances Based on the Xiaomi Mi 8
#### 3.1.2 RTK Performances in Dynamic Mode
Figure 8a shows the performance of RTK with only L1 measurements of GPS. The positioning results fluctuated drastically when the rover was located in the southeast of the sports ground because of the building nearby. This building blocked the signal and exacerbated the multipath effect, which could cause a big positioning error. RTKLIB ignored a satellite if the difference between its pseudorange and carrier phase exceeded the threshold, which was caused by the multipath effect and noise. If we only utilized the GPS, the number of valid satellites was likely to be less than four, which led to the absence of positioning results at some moments. As a result, Figure 8a shows that RTK with only L1 measurements did not provide positioning results in the southeast of the sports ground at some moments. Figure 8a also shows that the positioning results suffered from fluctuations and biases when the rover was located in the north of the sports ground at the beginning of the test, which reflected that RTK spent a few seconds converging to provide precise positioning results. Figure 8b shows the performance of RTK with L1 measurements and L5 measurements of GPS. The introduction of L5 measurements helped flatten the fluctuations caused by the blocking of signals and multipath effects. The positioning results given by RTK with L1 measurements and L5 measurements of GPS were also closer to the reference than those given by RTK with L1 measurements in Figure 8a, which meant more accuracy. However, the introduction of L5 signals could not increase the number of visible satellites. As a result, RTK still could not provide positioning results at some moments in the southeast of the sports ground. The introduction of L5 signals did not reduce the convergence time at the beginning, either. Figure 7 shows that there was only one valid L5 signal at the beginning of the test, which limited the advantages of dual-frequency RTK. Figure 8c shows the performance of RTK with L1 measurements of GPS and E1 measurements of Galileo. The introduction of another constellation meant more visible satellites. These additional Galileo satellites ensured the number of visible satellites when some GPS signals were blocked by the building, which helped to keep providing positioning results in the southeast of the sports ground. The introduction of Galileo also helped reduce the fluctuations and the convergence time at the beginning thanks to the improvement of the spatial distribution. Figure 8d shows the performance of RTK with L1/L5 measurements of GPS and E1/E5a measurements of Galileo. The positioning results given by RTK with L1/L5 measurements of GPS and E1/E5a measurements of Galileo were very close to the reference, as the introduction of Galileo helped increase the number of visible satellites, and dual frequency helped flatten the fluctuations and reduce the convergence time. Figure 7: Signals tracked by the Xiaomi Mi 8. (**a**) Visible signals and satellites; (**b**) number of signals. However, Figure 8d shows that dual frequency could not help increase the fixed rate of ambiguity resolution for RTK on the Xiaomi Mi 8 in dynamic mode. This phenomenon was caused by the poor quality of signals because of the poor performance of the antenna. The statistics of positioning error in the ECEF coordinate are shown in Table 1. Table 1 also shows that dual-frequency RTK could provide positioning results with smaller biases and fluctuations. Figure 8: RTK performances on the sports ground. (**a**) GPS(L1); (**b**) GPS(L1 + L5); (**c**) GPS(L1) + Galileo(E1); (**d**) GPS(L1 + L5) + Galileo(E1 + E5a). We changed the Xiaomi Mi 8's attitude to test the performance of the Madgwick algorithm with a three-axis turntable. The turntable could provide an accurate attitude with an error of smaller than four seconds. We initiated the turntable, setting the pitch, roll, and yaw to zero. Then, we changed the pitch, roll, and yaw of the turntable simultaneously. We set the pitch and roll to 45\({}^{\circ}\), while we set yaw to 325\({}^{\circ}\).