# The First Result of Relative Positioning and Velocity Estimation Based on CAPS
## 3 Experiment Result and Analysis
### Real-Time Experiment  
In addition to the post-processing experiment, we also carried out a real-time kinematic experiment based on the carrier-phase in order to validate the performance of the CAPS in cm-level positioning. The reference antenna was installed on the roof of AOE at the same location as that shown in Figure 5, and its position was precisely determined by GPS using the RTK approach described in Section 3.2. Based on the raw measurements from the reference receiver, the corrections of the code and carrier-phase and their variation rate could be calculated using the known position of the reference antenna, before being broadcast to the user via radio. The rover received these corrections and used them to correct the error of observation during the positioning estimation. The maximum distance between the reference station and rover was around 8.2 km. During our test, the sampling rate of the reference receiver and rover receiver was 4 Hz, and the differential correction from the reference station was broadcast at 1 Hz. The experiment was carried out on the morning of 24 August 2017, and the 4 GEO and 1 IGSO satellites could be tracked by our self-developed receiver in Beijing, China. Moreover, the velocity was also measured during the real-time experiment. The experiment was divided into two parts: first, the test vehicle was parked off the road for about 15 min after the initial ambiguities were fixed and began to move on the road for about 25 min with a speed of 40-60 km/h. The NovAtel GPS/BDS RTK and INS integrated terminal was installed with a common antenna with the user receiver in order to obtain the 'true' coordinates and velocity to validate the accuracy of the relative positioning. The nominal accuracy of the 'true' coordinates and velocity generated by the NovAtel terminal are 1-2 cm and 0.02 m/s, respectively. It should be noted that the true velocity for the rover during the static period was selected to be zero for the validation rather than the result from the NovAtel terminal. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**RMS** & **Components** & **East-West** & **North-South** & **Vertical** \\ \hline Relative positioning & Code (m) & 0.66 & 1.07 & 1.80 \\ \hline Velocity estimation (cm/s) & 1.35 & 1.70 & 3.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Root Mean Square (RMS) of the CAPS relative positioning and the velocity estimation during the experiment period for three components. Figure 9: Time series of the error in the east (**left**), north (**middle**) and up (**right**) components for the CAPS velocity estimation based on the doppler measurement with a sampling rate of 4 Hz. The time series of the positioning error in the three components during the static period is illustrated in Figure 10, and the corresponding result during the kinematic period is shown in Figure 11. Compared with the post-processing result, we can find that the CAPS static relative positioning based on the carrier-phase becomes a little poor in these three components. Moreover, the real-time kinematic positioning performance of CAPS in the horizontal and vertical components is much poorer. The RMS of the static differential CAPS positioning based on the carrier-phase is about 2.83, 4.37 and 10.41 cm in the east-west, north-south and vertical components, while they are about 3.33, 5.36 and 10.78 cm for the kinematic mode. It can be seen from Figures 10 and 11 that the position result shows some periodic feature, while the post-processing result doesn't. A spectral analysis of the east positioning error in static and dynamic modes with FFT was shown in Figure 12. The largest magnitude was located at 0.08 Hz in static mode, which means a period of about 12.5 s. A similar result was obtained from the positioning errors of other components. In dynamic mode, the largest magnitude was located at 0.066 Hz, which means a period of about 15 s. The reason for this may lie in the error model of the corrections, in the truncation error or in the errors related to the time delay of the broadcast.