# LEO Precise Orbit Determination with Inter-satellite Links
## 1 Introduction
Therefore, there are currently no public data on the Ka-band ISL and it is impossible to evaluate its orbit determination performance. In addition to the GPS, the European Galileo and Russian Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLObal NAvigation Satellite System, GLONASS) are also equipped with ISL payloads. The Galileo system has designed two link schemes of GNSS+ and ADVISE which establish inter-satellite and satellite-to-earth links using transmit/receive antennas with the same frequency band [19]. Through experimental demonstration, when the GNSS+ scheme is adopted in the autonomous POD mode, the numbers of ground stations can be reduced to six while reaching an accuracy of meter level in 14 days. And when using the ADVISE scheme, the orbital accuracy can be improved by 67% [20]. In the future, the Galileo system will introduce the so-called optical-quantum link scheme based on frontier quantum communication technology in substitution of microwave links [21]. In order to solve the limitation of regional monitoring and tracking for GLONASS constellation, Russia has installed the S-band ISL transceiver on the GLONASS-M satellites to verify the function of ISLs [22]. Since the test results were promising, the laser links were used on the newly launched GLONASS-K satellites, and the POD error is less than 50 cm in the radial direction and less than 110 cm in the along-track direction [23]. Chinese new-generation BeiDou Navigation Satellite System (BDS), so-called BDS-3, are equipped with ISL payloads, which are capable of communications between satellites with Ka-band single-frequency pseudo-code ranging measurements [24]. Based on the whole network adjustment algorithm, a centralized kinematics POD algorithm using BDS-3 ISLs has been proposed by [PERSON] et al. [25]. With the simulated full operational capacity (FOC) BDS-3 ISLs data, the average POD errors obtained under 40 cm measurement noise are 0.80, 1.15, and 1.17 m in radial, along-track, and cross-track directions, respectively. [PERSON] et al. have proposed the joint POD model of ground observations, LEO satellite observations, and BDS-3 (including 3 GEO satellites, 3 IGSO satellites and 24 MEO satellites) ISL measurements based on simulation [26]. Under the ISL accuracy of 10 cm, the average orbital errors of BDS-3 constellation in the radial, along-track, and cross-track directions are 0.003, 0.254, and 0.200 m, respectively. Moreover, the introduction of BDS-3 ISLs shows more improvement in the orbital accuracies than the introduction of LEO satellites, compared to the traditional ground-based POD strategy. With the BDS-3 ISL data being accessible, more scientific researches have been carried out, which are concentrated on BDS-3 autonomous navigation and joint POD of ground observation and ISL data. [PERSON] et al. have compared and analyzed POD results of four experimental BDS-3 satellites with only ISL measurements in 4 days and the prior orbits have been used as constraints and the POD precision with two, three, and four ISLs is better than 6, 3, and 2 m, respectively [27]. [PERSON] et al. have investigated the centralized autonomous orbit determination using ISL observations with the support of ground anchor stations [28]. The results show that the radial overlap differences and satellite laser ranging (SLR) residuals are both less than 15 cm. [PERSON] et al. have evaluated the POD performance of BDS-3 satellites with satellite-ground and inter-satellite observation data [29]. Considering the regional distribution of the BDS-3 ground stations, only six stations within the Chinese border are used and the statistical results show after adding the BDS-3 ISL observations, the 3-dimensional (3D) RMS value of orbit overlap differences is reduced from 85.4 to 14.8 cm with great improvement of 83%. In summary, the ISL can provide high-precision orbit observation data and can be applied to POD, however, current researches on ISL POD are limited to GNSS satellites.