# Distributed Orbit Determination for Global Navigation Satellite System with Inter-Satellite Link
## 1 Introduction  
For the global navigation satellite system (GNSS), the master control station (MCS) currently collects the satellite to monitor station measurement data, estimates the satellite ephemeris and clock offsets, and generates a time stream of navigation messages. The messages are then uploaded to satellites by ground antennas to broadcast to the user community [1]. However, the MCS as well as the other ground-based segments including monitor stations and ground antennas have the risk of destruction during a warfare or natural disaster. This is the case especially for the monitor stations which are distributed globally for increasing the accuracy of satellite orbit determination [2]. In order to enhance the viability of satellite navigation systems under the potentially fatal conditions, as early as in the 1980s, autonomous navigation techniques using inter-satellite link (ISL) measurements without support from the MCS were investigated for the global positioning system (GPS) [3]. If the ISL measurement was the only source for orbit determination and time synchronization, the datum mark would be insufficient [4]. This problem can be addressed by setting up a few ground anchorage stations (GASs) which provide a reference coordinate system and a time system [5]. Combining both the ISL and satellite-to-GAS measurements, the autonomous navigation system has several features: firstly, data processing will be completed by satellite onboard computers rather than the MCS; secondly,the GASs can be considered as pseudo-satellites; and finally, the globally allocated monitor stations can be replaced by a few domestic GASs [3].  
The centralized data processing technique, which is widely applied in the current autonomous navigation constellation, collects the ISL and satellite-to-GAS measurement data, combines all the satellite state vectors (including satellite orbit, clock error parameters, etc.) into one matrix, and computes the optimal state vector for each satellite by a central satellite on-board computer. As a result, the associated state vector covariance matrix could be very large and the method would require vast computation power [6]. It is worth mentioning that, in this case, every satellite is observed indirectly by other satellites.  
On the other hand, in the distributed data processing algorithm, computation is broken down and assigned to each satellite. Each satellite is required to deal with self-related ISL measurements and local state vectors. In this way, the number of measurement equations and dimension of the state vectors are reduced. As a result, the computational amount of the whole system is decreased considerably. Moreover, the accuracy of the orbit ephemeris and clock offsets calculated by the distributed data processing method could have the same level of accuracy as the results of centralized data processing.  
With the measurements from ISLs and satellite-to-GASs, the autonomous navigation constellation constitutes an extremely complex system. Each satellite has to finish the task of ISL measurement, data processing, and communicating. A practical algorithm for autonomous orbit determination is still under development. Based on the methods of the iterative cascade extended Kalman filter (ICEKF) and the increased measurement covariance extended Kalman filter (IMCEKF), a new distributed method, the balanced extended Kalman filter (BEKF), is proposed in this paper. Together with whole-constellation centralized extended Kalman filter (WCCEFK), four different autonomous navigation algorithms are conducted in simulations for comparisons of accuracy and computation loads.