# Summary of Lunar Constellation Navigation and Orbit Determination Technology
## 5 Outlook on Key Technologies for Lunar Constellation Navigation and Orbit Determination  
### Moon Reference Frames and Time Scales  
In the cislunar space environment, due to the lack of clear geographical references, the traditional Earth coordinate often cannot meet the needs of precise positioning. The purpose of establishing the lunar reference frame is consistent with the purpose of establishing the Earth's reference frame, mainly to describe the position of the probe relative to the Moon. In addition to revolving around the Earth, the Moon also rotates. The intersection points of its rotation axis and the lunar surface are the Moon's north and south poles, respectively. The great circle that is perpendicular to the rotation axis and intersects the lunar surface through the center of the Moon is the lunar equator. This is the basis for defining the Moon-fixed coordinate system. There are two commonly used definitions of the Moon-fixed coordinate system. One is the mean pole frame recommended by IAU, and the other is the principal axes frame defined by JPL; the origin of both is the Moon's center of mass. In the lunar gravity field, laser lunar data analysis and other dynamic research work, the principal axes frame is mainly used, but the analysis results such as the coordinates of the lunar surface retroreflector are often given in the mean pole frame. The orbit determination of the lunar probe and the orbit determination of the near-Earth spacecraft are consistent in principle. They are both based on satellite tracking observations containing errors, and use an approximate observation model to optimally estimate the initial state of the satellite. However, the central gravitational field of the lunar probe will change when it is flying in orbit. Therefore, the orbit determination process of the lunar probe involves more spatiotemporal reference frames, and the conversion between different coordinate systems and time systems is also more complicated. Regarding the scale of the lunar reference frame, it is conceptually defined as the scale of a local lunar frame in the sense of gravitational relativity. In practice, it can usually be determined by the speed of light \(c\), the lunar gravitational constant \(GM\) and the relativistic correction model used in data processing. Unified Moon reference frames will provide the necessary spatial benchmark for deep space exploration activities, allowing for more accurate data comparison and analysis between different missions. Therefore, the urgency of constructing different means such as protocol inertial reference frames, lunar and planetary ephemerides and Earth satellite dynamic reference frames to ensure that they can be easily implemented and realized in lunar exploration missions has become increasingly prominent. Specifically, it includes the use of VLBI, LLR (Lunar Laser Ranging), GNSS and other technologies to jointly monitor the lunar ephemeris and its rotation balance. In this way, the connection and conversion of three types of celestial reference frames can be realized with high precision under the framework of the general relativity gravity theory, providing a new, unified celestial reference frame support for human social activities within the Earth-Moon space. Commonly used time scales can be divided into two categories: one is defined based on the rotation of the Earth, including sidereal time, solar time, etc. The second category is based on the International System of Units--atomic time seconds, including international atomic time (TAI) for practical applications, geocentric coordinate time (TCG) for theoretical research, and center of mass coordinate time (TCB). Geocentric ephemeris time (TT) and barycentric dynamical time (TDB) are related to this. When the lunar probe flies in the Earth-Moon transfer orbit or the lunar orbit, its coordinate time is defined in the solar system center of mass reference frame, that is, TDB. TDB and TT can be calculated by means of the following approximate formula [103]:  
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