# Summary of Lunar Constellation Navigation and Orbit Determination Technology
## 3 Overview of Single-Satellite Navigation and Orbit Determination Methods  
### Radio Measurement Orbit Determination Technology  
At present, ground-based measurement and orbit determination technology is the main precise orbit determination method for Earth-lunar space probes, including ground-based radio ranging, velocity measurement and interferometry. 1. Radio velocity measurement  
According to the location of the oscillation source, Doppler velocity measurement is divided into one-way Doppler velocity measurement and two-way Doppler velocity measurement. In unidirectional Doppler velocimetry, the oscillation source is mounted on the spacecraft. The downlink transmission signal is generated by the oscillation source on the spacecraft, and is received by the ground receiver after propagation and delay in space. The ground station calculated the spacecraft's radial velocity by measuring the frequency difference of the received signal relative to the nominal downlink transmitted signal. Therefore, the single velocity measurement equipment is simple and does not require uplink signals, so it is widely used in satellite navigation and positioning. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Project Name**} & **Leading Institution** & **Project Objectives** & **Navigation Communication Criteria** & **Orbit** \\ \hline \hline \multirow{7}{*}{Queqiao} & \multirow{7}{*}{China} & \multicolumn{3}{c}{In view of the communication and navigation capability requirements of the fourth phase of lunar exploration, the International Lunar Research Station and subsequent lunar exploration missions will carry out research on the lunar communication and navigation satellite system, complete critical technologies such as lunar relay navigation satellite constellation planning, relay navigation network architecture and navigation algorithms, and establish an interoperable lunar relay navigation constellation to provide general relay communication and navigation services for targets on the lunar surface.  
\end{table} 
Table 1: _Cont._The oscillation sources of the two-way Doppler velocity measurement are configured at the ground measurement and control station. The system consists of a ground transmitter, a ground receiver, a transmitting antenna, a receiving antenna and a transponder on the spacecraft. It is also called interrogational velocity measurement. The ground control station transmits a highly stable frequency signal to the spacecraft, which is forwarded or reflected back to the ground observation point through the spacecraft's transponder. Comparing the return signal with the reference signal can determine the Doppler frequency shift (a change of two times) in the round trip of the signal, thereby obtaining the relative radial velocity of the spacecraft. Since a ground-based frequency standard is used as the reference signal for uplink and downlink signals for two-way Doppler velocity measurement, and the stability of the frequency source used by the ground station can reach an extremely high level, it can obtain much higher accuracy than one-way velocity measurement. Doppler velocity measurement adopts an integral model. The relationship between the velocity measurement observation value and the receiving frequency is as follows [19]:  
\[\dot{\rho}=\left(1-\frac{f_{R}}{Mf_{T}}\right)c \tag{1}\]  
In the formula, \(\dot{\rho}\) represents the radial velocity of the probe. \(f_{R}\) is the receiving frequency and the measurement quantity. \(f_{T}\) is the transmission frequency, which is generally known. \(c\) is the speed of light. The parameter \(M\) is the spacecraft transponder turnaround ratio, which is the ratio of the transmitted down-leg frequency at the spacecraft to the received up-leg frequency at the spacecraft. Note that these two frequencies are phase-coherent. The turnaround ratio \(M\) is a function of the uplink band at the transmitting station on Earth and the downlink band for the data point. Both of these bands are obtained from the data record for the data point on the OD file.