# Autonomous Orbit Determination of LLO Satellite Using DRO-LLO Links and Lunar Laser Ranging
## 4 Autonomous Orbit Determination Simulation  
### Simulation Setting  
The simulation uses the DRO (resonance ratio 2:1) at a distance of about 400,000 km from Earth and 70,000-100,000 km from the Moon, and the LLO at a distance of 300 km from the Moon's surface. The initial states of the DRO and the LLO are shown in Tables 2 and 3. The simulation lasts for 30 days, starting at 0:00 UTC on 1 January 2023 and ending at 0:00 UTC on 31 January 2023.  
Each simulation experiment is divided into four control groups: the first group only uses the DRO-LLO inter-satellite link data for the LiAISON navigation simulation; the second, third, and fourth groups have LLO lunar laser ranging schemes added based on the DRO-LLO inter-satellite link, with two (A5, A6), six (A5, A6, A11, A12, A15, A16), and  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline X/m & 54,774,713.693578 \\ Y/m & \(-\)57,499,627.371271 \\ Z/m & \(-\)38,544,286.402333 \\ Vx/(m/s) & \(-\)82.605557567 \\ Vy/(m/s) & \(-\)80.770436984 \\ Vz/(m/s) & \(-\)82.290358322 \\ Orbital period around the Earth/day & 13.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Initial states of the DRO (represented in the lunar center inertial coordinate system).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Orbital Elements** & **Values** \\ \hline Semi-major axis/m & 2,030,057.452 \\ Eccentricity & 0.001016503424 \\ Inclination/deg & 90.000974 \\ Longitude of ascending node/deg & 45.000001 \\ Argument of periapsis/deg & 45.286051 \\ True anomaly/deg & 44.713484 \\ Orbital period around the Moon/h & 2.3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Initial states of the LLO (represented in the lunar center inertial coordinate system).  
ten (A5, A6, A11-A18) lunar corner reflectors, respectively. During the orbit determination process, the satellite does not perform any maneuvers. When obtaining the observation data, the line-of-sight visibility between the satellites is taken into account, that is, whether they will be obscured by the Earth or the Moon.  
The latitude and longitude of the lunar corner reflectors are shown in Table 4. In the experiment, the effective reflection angle of the corner reflector is set to 45 degrees. Only when the angle between the laser link and the corner reflector is not larger than this angle can the LLO satellite obtain laser ranging data. The measurement duration of the LLO satellite and lunar corner reflectors is shown in Figure 5. The average measurement interval between the LLO satellite and the two corner reflectors A5 and A6 is 132 min, and the average measurement time is 6 min. The measurement intervals between the LLO satellite and A11-A18 corner reflectors also follow a periodic distribution.  
The dynamic model and integrator parameter settings for generating the reference satellite orbit are shown in Table 5, and the specific simulation conditions are shown in Table 6.  
\begin{table}
\begin{tabular}{c c c} \hline
**Corner Reflector Label** & **Longitude (deg)** & **Latitude (deg)** \\ \hline A5 & 0 & \(-90\) \\ A6 & 0 & \(90\) \\ A11 & \(23.63\) & \(0.71\) \\ A12 & \(91.77\) & \(66.36\) \\ A13 & \(-30.77\) & \(20.16\) \\ A14 & \(7.43\) & \(-63.68\) \\ A15 & \(97.43\) & \(-63.68\) \\ A16 & \(-120.55\) & \(-72.14\) \\ A17 & \(-125.66\) & \(53.76\) \\ A18 & \(-74.49\) & \(-8.97\) \\ \hline \end{tabular}
\end{table}
Table 4: Latitude and longitude of the lunar corner reflectors in the lunar fixed coordinate.  
Figure 5: Measurement duration of the LLO satellite and lunar corner reflectors.