# Autonomous Orbit Determination of LLO Satellite Using DRO-LLO Links and Lunar Laser Ranging  
[PERSON]  
1 University of Chinese Academy of Sciences, Beijing 100049, China; [EMAIL_ADDRESS] (S.C.); [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (Y.X. )1 University of Chinese Academy of Sciences, Beijing 100049, China; [EMAIL_ADDRESS] 1  
[PERSON]  
1 University of Chinese Academy of Sciences, Beijing 100049, China; [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (S.L. ); [EMAIL_ADDRESS] (Y.X. )1 University of Chinese Academy of Sciences, Beijing 100049, China; [EMAIL_ADDRESS]. Linked, Autonomous, Interplanetary Satellite Orbit Navigation (LiAISON) can utilize the asymmetry of the three-body gravity field to determine the absolute state of satellite orbits at both ends of the inter-satellite link [9]. The two-body gravity field is symmetric with respect to the Earth's center of mass. In the Earth-Moon Circular Restricted Three-Body Problem (CRTBP) model, due to the combined influence of the gravity fields of the Earth and the Moon, the gravity acceleration field is asymmetric [15]. The absolute state refers to the state parameters of the satellite relative to a fixed inertial reference frame, while the relative state is relative to another specific reference object (such as a satellite, a space station, a ground station, etc.). Domestic and foreign scholars have conducted relevant research on the application of the LiAISON autonomous navigation method in the cislunar space. [PERSON] [15] tested the LiAISON navigation method in libration point orbits and showed that the filter typically converges within approximately 1.5 orbital periods. [PERSON] et al. [16] studied the application of LiAISON in the navigation of manned spacecraft in the cislunar space. [PERSON] et al. [13] studied the application of LiAISON in autonomous navigation on the far side of the Moon. [PERSON] et al. [17] studied the application of LiAISON in the Distant Retrograde Orbit (the DRO is a group of large-scale, retrograde, periodic orbits around the Moon in the cislunar space) for autonomous navigation in the cislunar space. These studies indicate that the DRO is located in an area with strong asymmetry in the gravity field of the Earth-Moon three body system. An inter-satellite ranging link is established between one DRO satellite and one LLO satellite, then their absolute states can be determined using the LiAISON method. In addition, research on inter-satellite links conducted by foreign scholars has also contributed to autonomous navigation in cislunar space. [PERSON] [18] carried out an in-depth performance analysis of optical communication links within satellite formations which was vital, as reliable communication links are essential for data exchange in autonomous navigation systems. Concurrently, [PERSON] [19] analyzed the impact of adding extra nodes to satellite formations and found that expanding the network of interconnected satellites can enhance the robustness and accuracy of autonomous navigation. However, previous studies have shown that relying solely on LiAISON for autonomous orbit determination results in a longer convergence time and is susceptible to dynamic disturbances [20]. This highlights the necessity of further research and improvements to enhance the effectiveness of autonomous navigation in the cislunar space. The DRO has good orbital stability, and there is no need for frequent position maintenance [21]. The orbital period of the Moon is an integer ratio to the period of the spacecraft orbiting the Moon in the DRO, which is called the resonance ratio. Typical resonance ratios are 2:1, 3:1, and 4:1 [7]. The DRO with a resonance ratio of 2:1 is shown in Figure 1.  
Figure 1: DRO with a resonance ratio of 2:1 [22] (the track marked in red is DRO, the left figure shows the Earth–Moon rotating system, and the right figure shows the Earth-centered inertial system). Laser ranging (LR) is a technique employed for accurate distance measurement between a laser ground station and an optical target (Corner Cube Reflector).