# LEO Precise Orbit Determination with Inter-satellite Links
## 6 Conclusions  
We carry out research on LEO satellite POD using ISLs for the first time with designed constellations and simulated ISL observations. The experimental results evidence that POD with ISLs can achieve high precision for LEO satellites.  
There are two commonly used ISL link topologies: \"all-connected\" link topology with theoretically maximum numbers of links and \"4-connected\" link topology with constant four links per satellite. Rough orbit determination tests show the average 3D orbital errors are 0.112 m with \"4-connected\" link topology and 0.069 m with \"all-connected\" link topology in the 60-LEO constellation. POD performance can be better demonstrated with \"all-connected\" link topology.  
POD with center of gravity reference gets bad result when the ranging accuracy is poor and numbers of links are smaller. In the 60-LEO constellation, average 3D orbital error is 0.358 m with 40 cm ranging accuracy. The 20 cm ranging accuracy and the 10 cm ranging accuracy bring about 76.0% and 93.9% 3D orbital errors reductions compared to 40 cm ranging accuracy, respectively. Under the same 20 cm ranging accuracy, the average 3D orbital errors of 120- and 192-LEO constellations are 0.030 and 0.009 m, with 65.1% and 89.5% reductions compared to the 60-LEO constellation, respectively. Average 3D orbital errors are less than 10 cm for all constellations with 20 cm ranging accuracy. POD results with the center of gravity reference show the better link ranging accuracy and the more numbers of links bring the better orbit determination performance.  
With RAAN as the constraint, POD by using the reference provided by navigation satellites reaches an extremely high precision. Under 20 cm link accuracy, average orbital errors of 120-LEO constellation are 0.005 m in the radial, 0.002 m in the along-track, and 0.008 m in the cross-track and the 3D orbital error is 0.010 m. Average orbital errors of 192-LEO constellation are slightly better than 120-LEO constellation, with 0.003 m in the radial, 0.001 m in the along-track, 0.005 m in the cross-track, and 0.006 m in the 3D.  
In summary, high-precision dual-way ranging based on ISLs enables POD for LEO satellites. Generally, with better link ranging accuracy, more numbers of links, and better POD performance can be achieved.  
All authors contributed to the writing of this manuscript. [PERSON]. ([PERSON]), [PERSON] and [PERSON] conceived and designed the experiments. [PERSON] and [PERSON] processed the data, drew the pictures, and investigated the results. [PERSON], [PERSON] and [PERSON]. ([PERSON]) validated the data.  
This study is financially supported by the National Natural Science Foundation of China (Grant No. 41774030), the Hubei Province Natural Science Foundation of China (Grant No. 2018 CFA081), the Wuhan Science and Technology Project (Grant No. 2018010401011270), and the National Youth Thousand Talents Program.  
We are very grateful to the reviewers and the editors for their helpful remarks for improving the manuscript. Meanwhile, we would also like to express our gratitude to [PERSON] from Shanghai Astronomical Observatory, Chinese Academy of Sciences. She enthusiastically provided guidance for our study, bringing great help to the early research. In addition, our codes for the research have adopted several functions from open source library RTKLIB. We sincerely thank the code founder [PERSON] as well as other people who have contributed to improving RTKLIB.  
The authors declare no conflict of interest.