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Global navigation satellite systems broadcast signals for positioning estimation and time dissemination to end users. Current systems rely on ground-based observations and predictions. The Kepler system deviates from that by employing bidirectional optical inter-satellite links for time synchronization and orbit determination. This approach increases resilience, reduces ground infrastructure requirements and improves end-user accuracy. Optical two-way time transfer at sub-picosecond level and ranging at sub-millimeter precision are achieved by means of a chip rate of 12.8 Gcps and high-resolution optical correlation tracking. Our laboratory demonstrator verifies this concept. Two-way optical time transfer with a short-term stability below $$1.8\cdot 10^{-13}$$ was demonstrated over a 30 m free space range. The received optical signal power was scaled to emulate a medium earth orbit inter-satellite distance of over 50,000 km. The hardware is rather similar to the one used in coherent optical communications systems and thus of limited complexity. This confirms that a system architecture based on bidirectional optical free-space links can achieve the required precision in time synchronization and orbit estimation in future global navigation satellite systems.