# Summary of Lunar Constellation Navigation and Orbit Determination Technology
## 1 Introduction  
Since the 21 st century, lunar exploration has once again become a research hotspot. Countries around the world have launched lunar probes more than one hundred times. Space powers such as the United States and Europe have successively planned several unmanned/manned lunar exploration missions, including the Artemis program [1,2] and the Moon Village project [3], etc., with a view to ultimately realizing long-term residence on the Moon as well as the development and utilization of resources. With the successful implementation of China's Chang'e-5 mission [4], the three-step plan of 'orbiting, landing and returning' of the lunar exploration project was successfully completed. The lunar south pole exploration, lunar far side sampling return, and the construction of the international lunar research station have become the next direction for China's lunar exploration. With the gradual launches of large-scale lunar exploration missions, the demand for high-precision navigation and positioning of lunar probes has become increasingly urgent. At present, the main methods of precise orbit determination for Earth-lunar space probes are via ground-based measurements, including radio ranging, velocity measurement, and interferometry. As the quantity of in-orbit lunar probes increases, ground measurement and control are facing daily increasing pressure, and are barely meeting the needs of long-term orbit determination for a large number of lunar probes. At the same time, for long-distance lunar probes, ground measurement and control have characteristics such as long time delays, weak signals, and the influence of unfavorable factors such as the problem that the far side of the Moon cannot communicate directly with the Earth due to blocking. It is difficult to achieve continuous, real-time and accurate navigation and positioning solely by relying on ground systems. Referring to the orbit determination capabilities of China's current lunar exploration projects, the orbit prediction accuracy of lunar probes is generallyin the order of several hundred meters, which cannot meet the orbit determination accuracy requirements of future lunar navigation constellations. Meanwhile, in addition to the above-mentioned methods, the current lunar probe orbit determination methods also include satellite-ground laser measurement, GNSS signal measurement, astronomical navigation, etc. Among them, satellite-to-ground laser ranging has a high accuracy, but also has high requirements on the Earth's atmospheric environment and limited usage time. GNSS can achieve real-time positioning. In [5], the estimated orbit is validated with SLR as the satellite is equipped with a laser retroreflector array (LRA). A 3D RMS of about 0.3 m accuracy levels is obtained for POD using SLR. Using a real-time onboard navigation filter, 1.1 m accuracy in 3D RMS was achieved while post-processing on the ground with flight data offered 0.7 m accuracy in 3D RMS. In [6], a POD solution based on the Schmidt-Kalman filter performed better in terms of accuracy than the standard Kalman filter using single-frequency GPS receiver data. POD accuracy is improved by about 6 cm compared to the standard Kalman filter. In [7], a consider Kalman filter (CKF)-based reduced-dynamic orbit determination (RDOD), or CKF-RDOD, approach was used. The results showed a satisfactory POD with approximately 1.5 m level of three-dimensional RMS error with the CKF-RDOD approach using GPS data and broadcast messages in real-time scenarios. For satellites on LEO orbits, [PERSON] et al. used a combined GPS/Galileo receiver to achieve precise orbit determination [8]. Ref. [9] used the Kalman filter algorithm for real-time POD, providing seven different solutions using the onboard and simulated data. At those distances, decimeter-level onboard orbit determination can be achieved. For deep space applications, GNSS faces challenges such as weak side-lobe signals, poor visibility and limited positioning accuracy.