## 4 Results
### Influence of the Change of Satellite Elevation  
Firstly, we analyze the influence of the satellite's high elevation on the ranging accuracy of a single frequency point. As mentioned above, the BDS-3 satellite of PRN 37 is an MEO satellite, which satellite elevation changes greatly. We use the SDR of the B2a frequency point to process the raw IF data of PRN 37. The selected processing period is 13:09-17:23 (Beijing time). During this period, the satellite elevation gradually increased from 30\({}^{\circ}\) to the maximum, and then gradually decreased back to 30 degrees. According to Section 4.1, the code signal path differences of B2a and the satellite elevation time series change diagram can be seen in Figure 6.  
It should be noted that the time starting point and length of the data processing period selected at each frequency point is different. As described in Section 4.1, this is to meet the requirements of satellite elevation similarity. In addition, the processing speed of SDR is slow. Choosing 1-3 h instead of the whole range of data for processing can improve the processing efficiency and ensure the accuracy of the results. It should be noted that there are certain data interruptions in Figure 6, which are empty data records caused by loose data connection ports. It can be preliminarily seen from the Figure 6 that the absolute value of the code signal path differences remains within 0.5 m during the observation period. The code signal path differences converge towards 0 m in the state of high satellite elevation, and they are relatively discrete in the state of low satellite elevation. Standard deviation (STD) can be used to quantitatively describe the degree of data dispersion, which is an indicator of ranging accuracy. In the process of processing, since 19 code signal path differences will be recorded in one second, the STD of these 19 data in one second can reflect the dispersion of the code signal path differences in that second. The same processing is performed on the data in the selected period to obtain \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**PRN**} & **GPS LSC** & **BDS B2a** & **BDS BIC** \\ \cline{2-5}  & **4** & **37** & **39** & **39** \\ \hline RMS(m) & 0.1603 & 0.1526 & 0.1527 & 0.2674 \\ STD(m) & 0.1585 & 0.1309 & 0.1485 & 0.1779 \\ Mean(m) & \(-\)0.0234 & \(-\)0.0785 & \(-\)0.0358 & 0.1996 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical characteristics of code delay. Figure 6: Time distribution of B2a PRN 37 satellite code signal path differences and satellite elevation. all the STD distribution data at the 1 s interval. STD data with satellite elevation are plotted as shown in Figure 7.  
In Figure 7, with the increase in satellite elevation, it can be seen that the STD value has a very obvious downward trend. It is noted that there are many data points recorded at high satellite elevation, which is caused by the slow change in satellite elevation, and a large number of data points are recorded when the satellite operates at high elevation. The relationship between STD and satellite elevation will be described quantitatively. According to the data in Figure 7, the data correlation analysis can be carried out. The Pearson correlation coefficient matrix is used to describe this quantitative correlation. The STD value and satellite elevation can be regarded as two variables, and the relationship between them can be described by a two-dimensional matrix P:  
\[\text{P}= \begin{bmatrix}1&-0.308\\ -0.308&1\end{bmatrix}  \tag{11}\]  
In this matrix P, the main diagonal element represents the correlation coefficient of the two variables; that is, 1 represents a complete correlation. The sub-diagonal represents the Pearson correlation coefficient between STD value and satellite elevation. The closer the absolute value of the Pearson correlation coefficient is to 1, the stronger the correlation between the two variables they have. The Pearson correlation coefficient between STD and satellite elevation is \(-0.308\).