# A Survey of Precision Formation Relative State Measurement Technology for Distributed Spacecraft
## 3 Analysis of the Characteristics of Relative State Measurement Technology
### Radio-Based Autonomous Measurement Technology  
Radio-ranging is an important means of measuring the relative state of formation spacecraft, also known as radio frequency ranging or GPS-like measurement technology [48]. Radio measurement offers strong continuity and high coverage. It has both communication and measurement functions in a spatial range that GNSS signals cannot cover. In addition, it supports the simultaneous communication of multiple links and can realize the functional integration design of information exchange, time synchronization, and relative state measurement. As shown in Figure 21, RF measurements make relative state measurements by deploying receivers with multiple transmit or receive antennas on the spacecraft [49].  
Many devices for time synchronization and inter-satellite measurements have been developed internationally. The FFRF that was developed in the PRISMA project has a range measurement accuracy at centimeter-level and a visual angle measurement accuracy of \(1^{\circ}\)[50]; the AFF (autonomous formation-flying sensor) of the StarLight mission has a measurement accuracy of 2 cm and a relative altitude measurement accuracy of 0.025\({}^{\circ}\); the KBR ranging system developed by the GRACE project is a dual-channel microwave ranging system [51]. This dual-band ranging system can eliminate the influence of the ionosphere and improve measurement accuracy. The KBR system is composed of a K-band RF-ranging sensor, a high-precision GPS receiver, a local oscillator, and a mixer for composite relative measurement, as shown in Figure 22[52]. The satellite mixes the K/Ka signal with the local oscillation frequency, obtains the frequency difference signal for sampling and inputs it into the digital signal processing component in the GPS receiver. The corresponding channel digital phase-locked loop is used to track and solve the phase information of the frequency difference signal and transmit it to the ground for processing. The 24 GHz and 32 GHz frequencies of K/KA are used to effectively eliminate ionospheric errors [53].  
Figure 21: Principles diagram of radio state measurement.  
Figure 20: The VisNav sensor’s relative navigation schematic.  
RF technology is relatively mature, and the current accuracy can reach the centimeter level. Its advantage is that it does not depend on external information and can be used in any orbital space. The radio frequency measurement technology adopts two-way and pseudo-code ranging. As shown in Figure 21, the transmitting and receiving antennas are configured on the master satellites and the slave satellites, and the distance from the transmitting end to the receiving end is calculated using pseudo-code and phase measurement. The master satellite is equipped with 4 receiving antennas to form a goniometer; furthermore, it uses the phase comparison method to obtain the baseline pointing of the master and slave satellites [54]. At present, the L-band radio-ranging scheme can obtain centimeter-level ranging accuracy and 0.1\({}^{\circ}\)-level angle-measuring accuracy. The current direction of radio-based detection methods for accuracy improvement includes the optimization of antenna distribution configuration [55] and filtering algorithm optimization [56].