# The First Result of Relative Positioning and Velocity Estimation Based on CAPS
## 3 Experiment Result and Analysis
### Analysis of the Measurement Noises  
The noise of the code and carrier-phase measurement can generally be assessed using the data from the static zero-baseline experiment with a common antenna [2; 17]. The residual of the double-differenced observations on the inter-station and inter-satellite, in which the errors of the orbit, the bias resulting from the virtual clock offset model, ionospheric error, tropospheric error, receiver hardware delay and clock offset have been eliminated, is able to indicate the noise of the raw un-differenced code and carrier-phase measurement. We carried out the zero-baseline experiment tracking the CAPS navigation signal for more than four hours on 1 August 2017, with a 4-Hz sampling frequency, and the number of total epochs was over 70,000. Since CAPS are still in the development and testing phase, there is no commercial CAPS receiver yet. Two receivers developed by ourselves from scratch were used in this zero-baseline experiment. The basic structure of the self-developed receivers is almost like a GPS receiver. The largest difference is that the frequency of the coming signal is the C-band which means the carrier replicated by the CAPS receiver while acquisition and tracking is the C-band. There is no anti-multipath processing inside the current receiver. Those two receivers are connected to the same antenna via a power splitter. The antenna in our experiment was installed on the roof of the Academy of Opto-Electronics (AOE) in Beijing, China, and the CAPS navigation signals from the 4 GEO satellites and 1 IGSO satellite were tracked by our receivers during the experiment period. Since the observation environment is very open (see Figure 5), the multipath error can be considered at a relatively low level. For a receiver located in Beijing, the 4 GEO satellites are always visible while the IGSO satellite is visible for about 10 h every day. During the experiment, the visible time in Beijing is about 6:00 to 16:00 local time, and it cannot be seen during the rest of the time, which makes the three-dimensional solution impossible. The data in the experiments was collected from 9:00 to 14:00. During this time, the elevation angle of the IGSO was relatively high, which made the geometric configuration relatively good.  
As an example, the series of double-differenced residuals between the two CAPS satellites S1 and S2 are shown in Figure 6. The standard deviation (STD) of the residual from all pairs of CAPS satellites are illustrated in Table 1. The STD of the residuals of the double-differenced code measurements ranges from 0.42 to 0.57 m, while the STD of the residuals of the double-differenced carrier-phase measurements varies between 0.13 and 0.34 cm. Providing that the STDs of the un-differenced measurements are identical for different CAPS satellites and that they are independent from each other, we can infer that the noise of the code measurements is about 0.25 m, and that the noise of the carrier-phase measurement ranges from 0.07 to 0.17 cm. The high accuracy of the carrier-phase measurement is advantageous for further improving the CAPS precise positioning.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measurement Satellite Pairs** & **S1–S2** & **S3–S2** & **S4–S2** & **S5–S2** \\ \hline Code (m) & 0.56 & 0.49 & 0.48 & 0.42 \\ Carrier-phase (cm) & 0.34 & 0.24 & 0.13 & 0.22 \\ \hline \hline \end{tabular}
\end{table}
Table 1: STD of the residuals of the double differenced code and carrier-phase measurements between the two CAPS satellites.  
Figure 5: Surrounding environment of the antenna installed on the roof of the Academy of Opto-Electronics for the zero-baseline experiment.  
Figure 6: Time series of the residuals of the double-differenced code (**left**) and carrier-phase (**right**) measurements between the CAPS satellites S1 and S2 with a sampling rate of 4 Hz.