## 1 Introduction
Japan's Shiraito-R, which successfully entered lunar orbit at the end of March 2023, carried the UAE's first lunar rover and a small Japanese robot into the northern Atlas Crater on the lunar front at the end of April to study the movement of lunar soil, rock and dust, and plasma conditions on the lunar surface [26]. ESA has likewise launched plans to establish a network of navigation and communication satellites in orbit around the Moon [27; 28]. In addition, several commercial space companies around the world have announced plans to apply jump robots to survey the lunar surface [29]. More lunar exploration missions are underway, with the general hope of obtaining rich lunar information and painting a delicate \"portrait of the moon goddess\" to lay a solid foundation for lunar resource exploration and development, lunar base construction, and long-term human presence on the Moon [30]. A schematic diagram of the relevant range in cislunar space is shown in Figure 1 (the figure contains the ground-based Connected Element Interferometry (CEI) observation array as well as non-cooperative spacecraft at significant cislunar orbital altitudes). Given this, cislunar space has become an important base and destination for deep space explorations, which is also the main starting point of this study. The motivation and existing challenges of this research will be summarized as follows. As future lunar exploration activities will place higher requirements on lunar probe orbiting accuracy, real-time and applicable scenarios such as Positioning, Navigation, and Timing (PNT) of cislunar space explorations [31; 32] and the high-precision measurement, orbiting, and positioning of non-cooperative spacecraft in cislunar space will thus become a fundamental and cutting-edge research work. Nevertheless, the current means of determining its orbit still relies on ground-based measurements [33], including ground-based radar and optical telescopes, which are greatly restricted by geographical location and weather conditions around the stations, ground-based radio ranging, and velocimetry and interferometry, which requires rather long tracking time, especially for the transfer orbit between Earth and Moon [34]. Recently, the adoption of the short-time alternating differential measurement mode of radio source (Delta Differential One way Ranging, \(\Delta DOR\)) has greatly improved the measurement accuracy of deep space probes and has been successfully applied in international deep space exploration missions [35]. The China VLBI Network (CVN) [36], led by the Shanghai Observatory of the Chinese Academy of Sciences (SOAS), has been successfully applied in China's lunar exploration missions to support the high-precision orbit determination of lunar probes [37]. SOAS has also carried out the same beam interferometry observations of the two spinlets Rstar and Vstar of the Japanese lunar satellite SELENE and obtained differential phase time delays of _ps_ magnitude to achieve ultra-high precision interferometry between lunar probes [38]. Futhermore, the farther the probe is from Earth, the worse geometry of ground-based measurement will become, thus limiting the orbiting accuracy and applicability of merely ground-based methods. With the development of cislunar space exploration, space-based measurement technology has emerged [39], including interplanetary ranging technology [40] and satellite-based GNSS leakage signal technology [41], which have been applied in the current Earth satellite navigation system and will undoubtedly be extended to cislunar space. In this field, a series of frontier explorations have been carried out, including the research of autonomous orbiting of constellations based on lunar leveling point orbit [42], the joint autonomous orbiting technology of leveling point detector and Earth navigation satellite [43], the autonomous orbiting of detector of cislunar triangle  
Figure 1: Schematic diagram of the relevant range in cislunar space.