# LEO Precise Orbit Determination with Inter-satellite Links
## 5 Discussions  
As a high-precision ranging method between satellites, ISLs have been proven by many scholars to be used in the process of POD. Past researches focus on analyzing POD performance of MEO, GEO, and IGSO navigation satellites with ISLs. For the first time, we have made a comprehensive assessment of the POD performance of LEO satellites with ISLs. The results demonstrate the accuracy is considerable because of strong geometric constraint from ISL observations. Moreover, according to the numerical analysis, better link ranging accuracy and more numbers of links get better POD accuracy. This is because there are more observations and smaller observation errors during the adjustment process. Our study shows that future application of ISLs in the POD for LEO satellites is possible.  
Limited by the absence of real LEO onboard data, all our work is based on simulation. We only simulate dual-way observations which are used in the POD process. This simulation strategy circumvents the refinement preprocessing of raw observation data so the POD process is greatly simplified compared to the actual situation. Moreover, in the navigation constellations, the establishment of ISLs usually adopts the principle of time division multiple access (e.g., BDS-3). It means every satellite establishes links with other satellites according to the designed timeslot but at an exact time there is only one link per satellite. For simplicity, we assume that at one point in time, all satellites can be linked to multiple satellites to avoid epoch naturalization. For the above reasons, our simulated data is somewhat inconsistent with real data. Therefore, the high-precision orbit determination results in our study have not yet been tested in practical applications.  
The method that we used for POD is a simple kinematic orbit determination based on the whole network adjustment, but in common use reduced-dynamic orbit determination which take force models into consideration is mainly adopted for the LEO satellites. It is a pity that we can't find a  
Figure 12: 192-LEO constellation orbital errors in radial, along-track, cross-track and 3D under 20 cm ranging accuracy, in which satellite of PRN 1, 10, 19,..., 190 (divided at interval 9 of PRN number) are displayed.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Constellation**} & \multicolumn{4}{c}{**Orbital Errors/m**} \\ \cline{2-5}  & **Radial** & **Along-Track** & **Cross-Track** & **3D** \\ \hline
120-LEO & 0.005 & 0.002 & 0.008 & 0.010 \\
192-LEO & 0.003 & 0.001 & 0.005 & 0.006 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average orbital errors of 60- and 120-LEO constellations with references provided by navigation satellites.  
proper force model for simulated constellation so we refer to previous studies using a simpler orbit determination method. In the following study, we will improve our means of orbit determination.  
In general, we have carried out some preliminary research by focusing on demonstrating the feasibility of carrying out POD process for LEO satellites using ISLs. Subsequent study relies on the refinement of data processing methods and the acquisition of actual ISL data.