## 1 Introduction  
Spacecraft formation flying (SFF) has attracted a great deal of attention, since it can perform space missions with more reliability, adaptability, and low life-cycle cost, compared with traditional monolithic spacecraft [1]. Several SFF missions have successfully been deployed in low Earth orbit (LEO), such as the Gravity Recovery and Climate Experiment (GRACE) mission for precise Earth gravity field measurement [2], EO-1/LandSat 7 for Earth observation [3], the TanDEM-X mission for the generation of high-precision digital elevation models by using a high-resolution interferometric synthetic-aperture radar [4, 5], and PRISMA, for the on-orbit demonstration of millimeter-level SFF technology [6]. With the development of space technologies in recent decades, scientists have attempted to explore outer space far beyond Earth, which has turned their eyes toward highly elliptical orbit (HEO) SFF technologies. The most famous examples include the Magnetospheric Multiscale mission (MMS)launched by the National Aeronautics and Space Administration (NASA), a Solar Terrestrial Probes mission that studies the Earth's magnetosphere [7]. The Cluster II mission directed by the European Space Agency (ESA) is aimed towards space physics observation [8]. These two HEO SFF missions are comprised of four instrumented spacecraft operating in an adjustable pyramid-like constellation, with verified guidance, navigation, and control (GNC) technology on orbit. The realization of precise SFF GNC technologies requires the development of actuators, metrologies, and algorithms, where the metrologies system conducts the baseline of GNC, since it provides the direct relative-states measurement between the spacecrafts in formation. Typically, the metrologies system will cover both radio frequency (RF) and optical metrologies. The RF terminal receives signals from other spacecraft, and processes time-of-flight spread-spectrum code and carrier phase that allow for the retrieval of distance and line-of-sight (LOS) measurement with an accuracy of 1 cm (distance) and 1\({}^{\circ}\) (LOS). The optical metrologies can be conducted using geometric and interferometric concepts, achieving different ranges and accuracies. Optical position metrology for XEUS is reported as a coarse and fine sensor, which achieves accuracy of tens of microns, with a maximum relative distance of 120 m [9; 10]. The dual-wavelength interferometer (DWI) was chosen as a fine longitudinal sensor for the DARWIN mission, with a ranging accuracy of about 10 \(\upmu\)m within 250 m distance [11; 12]. China's space agency has recently approved an HEO SFF mission, called the Highly Elliptical Formation Flying Demonstration (HEFFD) mission, consisting of two spacecraft for science observation, quite similar to the Proba-3 mission [13; 14]. The two formation spacecrafts are preliminarily designed in different formation configurations with a relative distance of several meters to hundreds of kilometers, according to the real task on orbit. Besides the original observation data obtained, the most anticipated reward of this mission is the design and development of technologies that enable future HEO SFF missions, especially for the on-orbit demonstration of high-precision GNC technology. The primary ranging payload is designed based on optical metrology, which delivers micron-level relative lateral/longitudinal ranging between spacecraft during the science observation period in apogee. Moreover, a K-band microwave ranging (MWR) payload is developed particularly for this HEO formation mission for the following reasons:  
* In addition to optical metrology, (a) MWR can provide precise ranging results as backup equipment, during the science observation period around apogee; and (b) can avoid sunlight disturbance which occurs in the optical spectrum, for specific space science missions such as solar corona observation.