# LEO Precise Orbit Determination with Inter-satellite Links
## 1 Introduction  
The precise orbit determination (POD) of satellite refers to the process of obtaining the accurate state vectors of satellites in a certain epoch by handling satellite orbital measurements with the estimation strategies like least squares or Kalman filtering [1; 2]. The measurement technique exploits a decisive role in the accuracy of the POD process, and the selection of the POD method should be adapted to the orbit measuring technology, combined with the actual situation of the satellites and the users' needs [3]. For global navigation satellite system (GNSS), which usually employs medium Earth orbit (MEO, altitude of 2000-20,000 km), geostationary Earth orbit (GEO, altitude of 35,786 km), and inclined geosynchronous orbit (IGSO, altitude of 35,786 km), the main source of orbit measurements are pseudo-range and carrier phase observations of ground-based monitoring stations. With the refinement of force model as well as the improvement of data processing strategy, POD for GNSS satellites can reach an accuracy of centimeter level [4; 5]. However, POD for GNSS satellites relies heavily on groundmeasurements. Once ground receivers lose communication with the satellites because of crisis situation like equipment downtime, orbit determination becomes a problem. In order to solve the above problems and further improve the accuracy of orbit determination, some scholars [6; 7; 8] have proposed the use of inter-satellite link (ISL) for POD of GNSS satellites. The ISL is a link used for communication between satellites and has a function of ranging. It is a wireless link that can be implemented using a laser link or a microwave link. The microwave link can reach centimeter-class ranging accuracy while the laser link can even reduce the ranging errors to sub-millimeter [9]. Though more precise in ranging, the laser link has higher power consumption as well as longer link acquisition time, so the microwave link is generally used in the constellation. The development trend of microwave ISLs is to use higher frequency bands, because it can reduce the weight and volume of the equipment, and the high frequency has not been occupied in a large amount, which benefits the frequency application and has strong anti-interference performance [10]. The bands that can be used for the ISL are very high frequency (VHF, 30-300 MHz), ultrahigh frequency (UHF, 300-3000 MHz), L (1-2 GHz), S (2-4 GHz), and K-above (Ka, 26.5-40 GHz) bands, while the L-band and S-band are already occupied by the satellite-ground links, so the ISL band is generally selected from the VHF, UHF, and Ka bands [11; 12; 13]. Since the ISL technology can obtain high-precision ranging values between satellites, it can be used as an auxiliary means of orbit observing and serve for POD. The American Global Positioning System (GPS) is the first constellation to successfully use the ISLs to achieve autonomous navigation [14]. In 1998, the United States launched the first Block IIR satellite using the UHF band. Since 2010, the Block IIF series launched into the sky, improving the link structure and function. Currently, the GPS system is preparing to increase the Ka-band ISL equipped on the GPS III satellites. In this way, the master station only needs to establish contact with a satellite to control the entire constellation [15]. The first ISL POD experiment has been carried out when Block IIR satellites carrying ISL payloads entered the orbit and the user ranging error (URE) of the autonomous determined orbits within 75 days is less than 3 m [16]. In order to comprehensively analyze the performance of ISL POD, further researches have been conducted. Data analysis shows that after adding the Block IIR ISL, the 180-day autonomous POD URE is less than 6 m and after adding the Block IIF ISL, the reduction of the original system URE is improved from 40 to 55% [17]. because of the critical technology to be solved, the launch plan of GPS III satellites was postponed until 2017 [18].