# Autonomous Orbit Determination of LLO Satellite Using DRO-LLO Links and Lunar Laser Ranging
Astronauts on Apollo 11, 14, and 15 deployed CCRs on the lunar surface in July 1969, February 1971, and July 1971, respectively [23]. Table 1 details the information about the deployed CCRs on the Moon. By emitting laser signals from the ground and measuring the echo signals from the CCRs, the distance between the Earth and the Moon can be determined, which is known as lunar laser ranging (LLR) technology. On 12 December 2023, NASA's Lunar Reconnaissance Orbiter (LRO) directed a laser beam towards the Vikram lander located on the surface of the Moon. Subsequently, it received laser signals reflected back from the laser reflector array mounted on the lander. This achievement successfully demonstrated the ability to locate the reflector device on the lunar surface from lunar orbit, validating that spacecraft can accurately identify lunar objects using lunar laser ranging technology. In 2024, Chang'e-6 placed an Italian CCR on the far side of the Moon. This placement aimed to offer precise navigation services for lunar-orbiting satellites. It enabled these satellites to calculate distances accurately, assess their orbits, and enhance the precision of lunar landings. To satisfy the requirements of stable and fast high-precision autonomous orbit determination schemes for cislunar space LLO spacecraft, this paper presents an autonomous orbit determination scheme for an LLO satellite using DRO-LLO SST and lunar laser ranging. Figure 2 illustrates the autonomous orbit determination scenario. One satellite in the formation orbits around the DRO, while the other satellite orbits around the LLO. Both satellites carry high-performance transceivers for inter-satellite measurements. For the microwave link, deploying microwave equipment on the lunar surface is required. However, the lunar surface environment is extremely harsh, characterized by drastic temperature variations, prolonged lunar nights, and other challenges, which render it highly difficult to deploy microwave equipment capable of long-term stable operation. In contrast, laser CCRs are passive devices with excellent adaptability to the lunar environment, and their engineering applicability has been validated in practical missions. Therefore, the LLO satellite is additionally equipped with laser ranging equipment for laser ranging with the lunar corner reflectors. The inter-satellite and lunar laser ranging data are combined with orbital dynamics, and the orbit determination of the DRO and LLO satellites can be achieved using the EKF algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reflector Label** & **Deployment Time** & **Task** & **Position on the Moon** \\ \hline Apollo 11 & 1969 & Apollo 11 lunar landing mission & 0.67\({}^{\circ}\) N, 23.47\({}^{\circ}\) E \\ Apollo 14 & 1971 & Apollo 14 lunar landing mission & 3.67\({}^{\circ}\) S, 17.45\({}^{\circ}\) W \\ Apollo 15 & 1971 & Apollo 15 lunar landing mission & 26.13\({}^{\circ}\) N, 3.63\({}^{\circ}\) E \\ Lunakhod 1 & 1970 & Soviet luna 17 mission & 38.23\({}^{\circ}\) N, 35.00\({}^{\circ}\) W \\ Lunakhod 2 & 1973 & Soviet luna 21 mission & 25.58\({}^{\circ}\) N, 30.70\({}^{\circ}\) E \\ LRA & 2023 & Chandrayaan-3 lunar landing mission & 70.90\({}^{\circ}\) S, 32.90\({}^{\circ}\) E \\ INRRI & 2024 & Chang’e-6 lunar landing mission & South Pole-Aitken \\ LRA & 2025 & Blue Ghost lunar landing mission & Mons Latreille \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information on Corner Cube Reflectors deployed on the Moon [24].