# Summary of Lunar Constellation Navigation and Orbit Determination Technology
## 4 Constellation Navigation and Orbit Determination Technology
### LiAISON Autonomous Navigation Method  
In the three-body problem, the gravitational influence of the third body can indirectly provide information about the direction to that third body, and with it the absolute orientation of the orbits. In other words, a halo orbit near the Moon is influenced very strongly by both the Earth and the Moon and has a unique size and shape. Because of the strong asymmetry of the three-body force field, a halo orbit with that size and shape can only have a single orientation with respect to the Earth and Moon. This means that a spacecraft in a halo orbit can track a second spacecraft using crosslink range measurements and determine the absolute positions and velocities of both spacecraft simultaneously without any Earth-based tracking or mathematical constraints. In 2006, [PERSON] et al. first started from the asymmetry of satellite motion acceleration functions and pointed out that under the influence of the third body gravity of the Moon, halo orbiting satellites near points L1 and L2 in the Earth-Moon system are most likely to only use interstellar ranging observations to determine the orbit autonomously. They proposed the concept of Joint Autonomous Satellite Orbit Navigation (LiAISON) [92; 93]. [PERSON] et al. also demonstrated the observability of autonomous orbit determination for libration point orbit satellites based on inter-satellite ranging information through covariance analysis. By comparing the autonomous orbit determination results of satellites with different libration point orbits, it was found that the farther away from the lunar orbital plane and the shorter the period, the higher the accuracy of autonomous orbit determination for libration point orbits [94; 95][PERSON] By analyzing the evolution of random acceleration error over time and its influence on the autonomous orbit determination accuracy of the LiAISON method, [PERSON] conducted a systematic study on the autonomous navigation problem of manned exploration missions in the Earth-Moon space. [PERSON] et al. also studied the specific application of inter-satellite measurement navigation in the combination of satellites orbiting Lagrange points and other types of satellites [96; 97]. [PERSON] et al. analyzed the orbit optimization problem in inter-satellite measurement navigation and its applications [96; 98][PERSON] Starting from the correlation of the coefficient matrix, [PERSON] et al. pointed out the key role of the introduction of Earth-Moon system libration point orbit satellites in improving the positive definiteness of the orbit determination matrix. Taking the lunar low-orbit satellite-Halo orbit satellite constellation as an example, they demonstrated the feasibility of the autonomous orbit determination method based on inter-satellite ranging data under the CRTBP (Circular Restricted Three-Body Problem) model [99]. [PERSON] et al. studied the joint ranging autonomous orbit determination problem of the Earth-Moon system's libration point orbit and the large amplitude retrograde orbit with the lunar orbit, and pointed out that the Halo orbit with a larger vertical plane amplitude has better autonomous orbit determination accuracy and lunar coverage performance, while the large amplitude retrograde orbit has more advantages in stability than the Halo orbit [100]. [PERSON] et al. used a hybrid constellation composed of libration point probes, DRO probes and satellites as a typical scenario to analyze the autonomous orbit determination accuracy of the Earth-Moon space detector based on inter-satellite ranging, demonstrating the application of inter-satellite ranging technology on Earth. There is huge application potential in the construction of a lunar space navigation system [101].