# A Survey of Precision Formation Relative State Measurement Technology for Distributed Spacecraft
## 2 Research Status of the Precision Formation of Distributed Spacecraft Project
### Trend Analysis of the Distributed Precise Spacecraft Formation Flying Project
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Project**} & \multicolumn{2}{c}{**Country/**} & \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Nodes**} & \multirow{2}{*}{**Measurement**} & \multirow{2}{*}{**Precision**} & \multirow{2}{*}{**Number**} & \multicolumn{1}{c}{**Whether**} \\  & \multicolumn{1}{c}{**Institution**} & & & & & & **Launch** \\ \hline Taiji & China & Laser & — & Interferometric & & & & \\  & & Interference & — & & & & & \\ \hline \multirow{5}{*}{XEUS} & \multirow{5}{*}{ESA} & \multirow{5}{*}{Laser GPS} & \multirow{5}{*}{—} & Z-direction distance & & & & \\  & & & & (40 cm + 1 m) & & & & \\  & & & X-Y surface & & 8′′11′′ & 2 & No launch \\  & & & & & Roll, pitch and & & & \\  & & & & yaw angle & & & \\ \hline \multirow{5}{*}{Gemini} & \multirow{5}{*}{Germany} & \multirow{5}{*}{Laser GPS} & \multirow{5}{*}{Rough mode} & Z-direction distance & & & & \\  & & & (>100 km) & & & & \\ \cline{1-1}  & & & Precision mode & & & & \\ \cline{1-1}  & & & & Precision mode & & & \\ \cline{1-1}  & & & & Ultra- & & & \\ \cline{1-1}  & & & precision mode & & & & \\ \cline{1-1}  & & & & & & & \\ \hline \multirow{5}{*}{Proba-3} & \multirow{5}{*}{ESA} & \multirow{5}{*}{RF GPS} & \multirow{5}{*}{Rough mode} & Z-direction distance & & & & \\  & & & (Perigee) & & & & \\  & & GPS & & & & & \\  & & Laser & & & (Apoge) & & & \\ \cline{1-1}  & & & & & Z-direction & & & \\ \cline{1-1}  & & & & & distance & & \\ \cline{1-1}  & & & Precision mode & & & & & \\ \cline{1-1}  & & & & mode & & & \\ \cline{1-1}  & & & & & offset & & & \\ \cline{1-1}  & & & & X-Y surface offset & & & & \\ \cline{1-1}  & & & & (\pm\)20.5 mm) & & & & \\ \hline Darwin & ESA & Laser & — & Inter-satellite & & & & \\  & & GPS & — & & baseline & & \\  & & & & measurements & & & \\ \hline LISA & USA & Laser & — & Interferometric & & & & \\  & (NASA) & Interference & — & & & & \\ \hline \multirow{5}{*}{IRASSI} & Germany & Laser & — & Interferometric & & & & \\  & (DLR) & GPS & — & & & & \\ \cline{1-1}  & & & & & & & \\ \cline{1-1}  & & & & & & & \\ \hline \multirow{5}{*}{FOXST} & \multirow{5}{*}{China} & \multirow{5}{*}{Vision GPS} & \multirow{5}{*}{—} & Distance measurement & & & & \\ \cline{1-1}  & & GPS & & & & & \\ \cline{1-1}  & & & & & & & \\ \cline{1-1} \cline{2-1}  & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._The project background for this paper is the Focusing Optics Hard X-ray Solar Telescope (FOXST). It utilizes the precise formation of two satellites to achieve high-quality imaging of the sun's hard X-rays. The primary satellite carries a swept-in imaging optical system to converge hard X-rays, while the slave satellite is equipped with a detector system to accomplish X-ray focal plane imaging. The mission formation baseline is one hundred meters, located in the heliocentric Earth-trailing orbit, to carry out tasks. The spacecraft altitude control accuracy is required to be 1\({}^{\circ}\); the relative distance control accuracy is required to be 0.1 m; measurement accuracy is required to be one order of magnitude higher than the control accuracy. The specific parameters are shown in Table 6. The Earth's trailing orbit belongs to deep space and cannot be stabilized with a GPS signal for formation. After a comprehensive investigation and analysis, combined with consideration of the future technical development direction, to control the quality of the spacecraft platform and the project budget we plan to use relatively simple visual sensors to complete the autonomous precision formation-flying task. This will be a great breakthrough in the field of deep space precision formation and is currently under study. Figure 14: Measurement scheme of the inter-satellite relative state at different orbital heights. Figure 13: Relative measurement accuracy of the distributed spacecraft precision formation flying projects.