# Clock Ensemble Algorithm Test in the Establishment of Space-Based Time Reference
## 1 Introduction  
Taking advantage of two rapidly developing technologies, e.g., optical frequency references and inter-satellite laser links [1, 2], a new concept of establishing a network of space-based synchronized references has been widely discussed for future GNSS systems. For instance, a future Galileo-like medium earth orbit (MEO) constellation, Kepler, has been proposed by the German Aerospace Center (DLR), which could be characterized by both MEO and LEO segments and the innovative key features of optical inter-satellite links delivering highly precise range measurements and of optical frequency references enabling a perfect time synchronization within the complete constellation [3, 4, 5].  
With the help of space-based time-synchronized references, GNSS can attain many benefits from the following aspects. Firstly, the broadcast of navigation signals could be synchronized to a level far superior to modern GNSSs. Secondly, a significant reduction or even the entire elimination of the satellite clock parameters could be achieved in the estimation process [3, 6]. Thirdly, a better separation of uncertainties in the spatial and time domains could be obtained to enhance orbit determination. Moreover, a relativistic navigation system could be realized so that the satellite orbits are determined through the dissemination of each satellite's proper time, and users estimate their own positionswithout the need to apply relativistic corrections. In addition, the synchronized signals also have potential impacts on the monitoring of the Earth's gravity field, the provision of terrestrial reference frames, atmosphere sensing applications, and GNSS reflectometry [4].  
In a space-based synchronized time reference, LEOs can be used as moving monitoring stations to achieve global tracking coverage of the MEOs. Thus, high-stability atomic clocks onboard and high precision time comparison between clocks is essential in the first place. Based on the time offsets of every individual clock, a proper composite clock algorithm is required to estimate a weighted average out of all ensemble clock readings, serving as the newly established system time. With the appropriate adjustment, the system time can keep coordinated with other standard time references similar to UTC or GNSS time. Finally, similar to the GNSS system, the space-based system time can provide users with ordinary time service and enable privileged users to build their time system by sharing detailed time comparison information.  
When building the terrestrial time scale, the commonly used composite clock algorithms are the ALGOS algorithm (used by BIPM [7]) and the AT1 algorithm (used by the National Institute of Standards and Technology (NIST) [8]). Alternatively, the Kalman filter algorithm was developed in the 1980s [9; 10], which allows for the addition or deletion of clocks at any time and provides automatic error detection and correction. With the continuous improvement of the algorithm, especially the reduction in the estimation error matrix [11; 12] and the improvement of the medium and short-term frequency stability of the timescale [13], the Kalman filter algorithm has become mature and is widely used in GNSS to satisfy the real-time requirement [14].  
What algorithm should be used for the space-based synchronized reference is still an important subject to be explored. In this work, we analyze the performance of three algorithms, namely the Natural Kalman clock ensemble algorithm (NKT) [15], the Reduced Kalman clock ensemble algorithm (RKT) [16], and the two-stage Kalman clock ensemble algorithm (TKT) [17], in establishing space-based time system in detail. In addition, simulation data have been used to compare and examine the timescale prediction accuracy of these three algorithms.