# Distributed Orbit Determination for Global Navigation Satellite System with Inter-Satellite Link
## 2 Overview of Orbit Determination Algorithms  
[PERSON] [7] proposed the framework of an autonomous navigation system without a MCS for the first time and validated the system by simulations. [PERSON] [3] introduced various autonomous navigation algorithms and presented preliminary on-orbit experiment results. In the designing of the GPS Block IIR, the ISLs, programmable microprocessors, and redundant management were carried out. The following two major features are critical to ensure high precision autonomous navigation [3; 7]:  
* the ISL communications and measurements in ultra high frequency (UHF) band;
* a high-precision autonomous navigation algorithm which is adapted to the computing capacity of the satellite on-board computers. A time division multiple access (TDMA) system, which has two frames, was employed for ranging and data transmission. In a ranging frame, each satellite is assigned a 1.5-s slot to make pseudo-range (PR) measurements with the visible satellites. Two frequencies were used in the measurement for ionospheric delay corrections. In a data frame, a 1.5-s slot was appointed to each satellite to transmit data that includes the PR measurements, the estimated satellite state vector, and the associated covariance matrix to all visible satellites. The GPS Block IIF follows the design of the GPS Block IIR and improved the performance of ISL measurements and on-board data processing. Without contacting with the ground system, Block IIF can operate about 60 days in the autonomous navigation mode and provides navigation messages which are corrected by ISL measurements with a 3-m user range error (URE) (URE is a root mean square value and does not consider the impact of the polar motion and UT1). However, it is difficult to establish a precise prediction system because of the irregular polar motion and uncertain UT1. Therefore, in autonomous navigation mode, the URE is far greater than 3 m after a 60-day duration [8]. For GPS III, each satellite in the constellation will have the ability of ISL measurements and communications. It is designed that once there are enough satellites in the orbit, the GPS constellation will be able to operate autonomously in wartimes, but currently it is still under investigation [9]. Galileo navigation system is also planned to employ an autonomous navigation algorithm based on ISLs [10]. The spatial orientation problem is solved by the combination of the ISL and satellite-to-ground measurements. The simulation for the Galileo system showed that URE is on the level of decimeters [10], which is better than that of GPS. For the distributed navigation algorithms, several techniques including the iterative cascade extended Kalman filter (ICEKF), increased measurement covariance EKF (IMCEKF), and Schmidt-Kalman Filter (SKF) are discussed by [PERSON], [PERSON], and [PERSON] [11; 12; 13]. The ICEKF is employed to processes a large number of space-borne GPS measurement data and a small quantity of ISL measurement data for low-Earth orbit formation flying satellites. In this method, the computation process will iterate for 3 to 4 times for convergence, and a good orbit accuracy is presented. For the method of IMCEKF, amendments are made based on ICEKF and it presents a better performance. On the other hand, the SKF yields results with less accuracy compared to IMCEKF while processing the GNSS ISL measurement data [4]. Recently, the International Association of Geodesy (IAG) initiated a GPS Dancer project which develops a distributed data processing algorithm to analyze the precision of GPS [14]. In China, distributed orbit determination and time synchronization algorithms based on ISL measurements were studied [15; 16; 17; 18; 19; 20; 21]. Distributed autonomous ephemeris updating was discussed for navigation satellites [22]. There are also many studies on developing higher precision orbit determination methods for new BeiDou (BDS-3) experimental satellites in the literature [23; 24; 25; 26].