# Centimeter-Level Precise Orbit Determination for the Luojia-1A Satellite Using BeiDou Observations
## 5 Luojia-1A Satellite POD Results and Discussion
### Precise Orbit Determination with BeiDou Observations
The panel (a) presents the overlapped orbit residuals for the all satellite equally weighted cases. The figure shows that orbit presents systematical biases for the whole arc and significant fluctuation presence, especially at the end of the arc. As the weight of the GEO satellites is reduced to 1/25, the fluctuation of orbit error series is dramatically mitigated, but the constant bias on the cross-track direction is still present. Further reducing the weight of the GEO satellites can reduce the constant bias in the cross-track direction. A weight of 1/900 for the GEO satellites is considered as the optimal choice for the Luojia-1A satellite since the orbit error is noticeably reduced and without significant fluctuation. The analysis also indicates that the GEO satellite orbit error may introduce fluctuations and constant bias in the LEO orbit determination. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scheme ID** & **A** & **B** & **C** & **D** & **E** & **F** \\ \hline Weighting Strategy & 1 & 1/25 & 1/49 & 1/100 & 1/900 & 1/2500 \\ \hline \end{tabular}
\end{table} 
Table 4: The weight setting for GEO satellite observations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Weight** & **Radial** & **Along-Track** & **Cross-Track** & **3D** & **Improvement** \\ \hline
1 & 2.02 & 3.32 & 5.00 & 6.333 & / \\
1/25 & 1.50 & 2.29 & 4.37 & 5.157 & 18.57\% \\
1/49 & 1.28 & 2.20 & 2.45 & 3.533 & 44.21\% \\
1/100 & 1.11 & 2.00 & 1.98 & 3.025 & 52.23\% \\
1/900 & 0.94 & 1.75 & 1.19 & 2.316 & 63.43\% \\
1/2500 & 0.94 & 1.73 & 1.23 & 2.322 & 63.43\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The precision of Luojia-1A precise orbit results with different GEO weighted strategies (Unit: cm). The ionosphere-free carrier phase residuals of Luojia-1A satellite orbit determination under different weight strategy is also analyzed, and the results are presented in Figure 10. In this analysis, the C12 satellite is excluded in the orbit determine procedure due to the absence of precise orbit products. The figure indicates that for the equal weight strategy, the residuals of GEO satellites achieve a minimum while the IGSO and MEO satellites yield larger residuals. By adopting the re-weighting strategy, the residuals of GEO satellites are slightly increased, which is reasonable since the GEO satellite orbit errors are assimilated into the residuals. Meanwhile, the residuals of IGSO and MEO satellites are decreased to less than 10 mm. Different weighting strategies did not lead to dramatic variation of the carrier phase residuals. The residuals of observations reflect the consistency of the reduce-dynamic model and the observation model, which can approach noise level if only the reduce-dynamic model can represent the  
Figure 10: The RMS of different satellite residuals, (**a**) C01–C05, (**b**) C06–C14. Figure 9: Orbit error of Luojia-1A in different scenarios. motion of the LEO satellites appropriately. According to experiments, the precise orbit of the Luojia-1A satellite can obtain the best result with the condition that the weight of GEO satellite observations is set 1/900. The left panel of Figure 11 reflects the relationship between the carrier phase residuals and the elevation angle of the optimal results of the Luojia-1A satellite, which indicates that the residuals are elevation-dependent. For the high elevation angle case, the carrier phase residuals are generally less than 3 cm, while the carrier phase residuals with lower elevation angle are generally smaller than 9 cm. The figure also concludes that the residuals are fairly small in most cases. The carrier phase residuals are smaller than 2 cm in most cases; hence, the overall RMS of residuals is 1.49 cm. According to the right panel, it is apparent that over 70% residuals are smaller than 1 cm and over 93.01% residuals are smaller than 3 cm.