Accuracy and stability study of two-way time transfer in Cis-lunar space

The realization of clock synchronization and syntonization via inter-satellite link is of vital importance for navigation, space-based Very Long Baseline Interferometry (VLBI) experiments and precision tests of fundamental physics. We study the accuracy and stability of time and frequency transfer via inter-satellite link in Cis-lunar space. A relativistic time transfer model using microwave dual one-way ranging (DOWR) is developed. Taking the distant retrograde orbit (DRO)-low Earth orbit (LEO) inter-satellite link as an instance, sub-nanoseconds level accuracy is achieved. We analyze the error in orbit determination of LEO satellite and DRO satellite. With the models of relative velocity correction, relativistic frequency shift and Shapiro delay, the stability of time transfer is studied. The result shows the DOWR microwave link would support clock synchronization with a time stability of better than 14.3 ps over 1000 s, better than 100.5 ps over one day, with the accuracy constraints on the orbit determination of the LEO satellite 10 cm and DRO satellite 50 m in position. If the longer time stability of hardware delay reaches ps level, the performance of DOWR time transfer link can be further improved to support the distribution of the time–frequency scale established by an active hydrogen maser with a frequency stability of over one day. We estimated that high-performance DRO-LEO time and frequency comparisons may support the gravitational redshift tests at a 10−6 level and the space-based VLBI experiments to improve the orbit determination of deep-space probes by one to two orders of magnitude.