# Estimation of Inter-System Biases between BDS-3/GPS/Galileo and Its Application in RTK Positioning
## 3 Datasets and Experiments
### Stability of ISBs
#### 3.3.2 Long-Term ISB  
Having assessed the short-term stability of ISB, it was reasonable to regard the ISB between identical types of receivers as a constant with continuous observations. However, we also needed to determine whether the ISB remains as stable in the long term as it does in the short term. In addition, by assessing the long-term ISB, we further analyzed its distribution characteristics through its PDF and QQ of normal distribution. The time-series, PDF, and QQ plot of both phase and code ISBs between BDS-3 and GPS/Galileo are shown in Figure 5 for B1C/L1/E1 and B2a/L5/E5a. The results from DOY 29 to 70, 2021 were considered to validate the stability of ISBs. The relationship between the distribution characteristics of ISBs and the normal distribution was discussed. The figure shows that the level of the long-term ISB stability remains as low as it does in the short term. In addition, per both the PDF and QQ plot, the distribution of ISB fits a normal distribution well. This means that we can consider the ISB between identical types of receivers as random noise. Despite the higher noise appearing in the code ISB \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency Pair**} & \multicolumn{2}{c}{**Phase ISB (Cycle)**} & \multicolumn{2}{c}{**Code ISB (m)**} \\ \cline{2-5}  & **Expectation** & **STD** & **Expectation** & **STD** \\ \hline B1C/L1 & \(-\)0.002 & 0.010 & 0.034 & 0.183 \\ B2a/L5 & \(-\)0.002 & 0.010 & \(-\)0.052 & 0.098 \\ B1C/E1 & 0.000 & 0.009 & \(-\)0.009 & 0.176 \\ B2a/E5a & 0.000 & 0.009 & \(-\)0.004 & 0.077 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean value and Standard Deviation (STD) of short-term ISB. Figure 4: Inter-system bias (ISB) time series of both phase and code observations between BDS-3 and GPS/Galileo for the overlapping frequencies BIC/L1/E1 and B2a/L5/E5a. From the left to the right, BIC/L1, B2a/L5, BIC/E1, and B2a/E5a observations on DOY 120, 2021 were applied to assess the ISBs. The text in magenta describes the statistics of the ISBs. in B1C/L1/E1, the noise level of ISB between B1C/L1/E1 and B2a/L5/E5a is within the accuracy of the code observations. For the phase ISB, all the noise of phase ISB is about 0.01 cycles, which is also within the accuracy of phase observations. All the results prove that the ISBs between identical types of receivers have similar characteristics: zero-mean random noise and the noise level is similar to observation noise. Thus, the ISBs can be regarded as a constant even in the long term. The noise level of ISB varies in different periods, which is mainly influenced by the number of visible satellites, the elevation of the satellites in the pivot system, the environment, the receiver firmware, etc. Thus, an analysis on the statistics of ISBs within one day or one month was is necessary to validate the long-term ISB stability. Figure 6 shows the mean value by day, STD by day, and box plot by month of both phase and code ISBs with the overlapping frequency between BDS-3/GPS/Galileo from DOY 29 to 70, 2021. The mean value of phase ISB is close to zero during the period, while that of code ISB varies within 10 cm. In addition, the STDs of all the phase ISB are around 0.01 cycles for various days, whereas that of code ISB is within 0.2 m for B1C/L1/E1 and 0.12 m for B2a/L5/E5a. The box plots reflect the discrete values of ISBs in the statistics. In the box plots, the quartile of each month remains at a level lower than 0.01 cycles for phase ISB and 0.2 m for code ISB. Even the outliers remain lower than 0.06 cycles for phase ISB and 1.6 m for code ISB. All the results indicate that the ISBs between identical types of receivers are quite stable even in the long term, and they fit a normal distribution well. Thus, if an overlapping frequency inter-system DD is performed, we can ignore the influence of ISBs when identical types of receivers are applied.