Relativistic Modelling for Accurate Time Transfer via Optical Inter-Satellite Links

Abstract

The DLR Institute for Communication and Navigation is currently working on a new GNSS architecture that enables accurate autonomous inter-satellite synchronization at picosecond-level. Synchronization is achieved via time transfer techniques enabled by optical inter-satellite links (OISLs), paving the way for a system in which space (orbits) and time (synchronization) can be effectively separated, leading to a high level of synchronization throughout the constellation, which in turn greatly improves accurate orbit determination. This is possible provided that relativistic effects are adequately taken into account. This work focuses on a two-way time transfer scheme based on the exchange of time stamps via optical signals, which allows the synchronization of a GNSS satellite system with respect to a defined coordinate time with picosecond-level accuracy. We analyse the impact of relativistic effects in clock offset estimation between optically linked clocks: results show that to achieve synchronization at this level of accuracy it is necessary to account for terrestrial geopotential harmonics up to the third order while the gravitational influence of additional celestial bodies can be neglected. Relativistic delays in the propagation of electromagnetic waves through spacetime are also evaluated. It is shown that for a two-way synchronization method, the Euclidean expression for the propagation of light is sufficient to achieve picosecond synchronization, provided m-level orbit determination of both satellites is available, and the hardware delays are well calibrated to the targeted accuracy. Also, we show how to practically achieve autonomous synchronization via a sequence of pair-wise synchronizations across all satellites of the constellation.