Objectives  With the ultra-high precision time and frequency signals provided by space high precision time and frequency system, series of space-to-ground time and frequency transfer and fundamental physics experiments can be carried out to support high precision validation of relativity and related theories.

  Methods  First, theoretical derivation and simulation analysis are conducted on the time and frequency transfer algorithm of space laser links. Theoretical formula of space-to-ground laser two way time transfer are reviewed, and the advantages and disadvantages of X-type and Lambda-type approaches are compared and analyzed. Then, the impact of relativistic effects on the conversion between proper time and coordinate time is discussed for the specific orbital height of China space station. Finally, the impact of space-to-ground time and frequency transfer discontinuity on the stability evaluation of high-precision atomic clocks onboard space stations is discussed.

  Results  The results show that: (1) Lambda-type two-way time transfer based on satellite laser ranging can make up the distance difference of first-order Doppler effect on the uplink and downlink, and increase of Sagnac effect can be ignored. (2) The relativistic effect of the conversion between proper time and coordinate time for satellite ground time transfer makes high demands on the velocity accuracy of space station positions, in order to achieve 1×10^－18 frequency transfer accuracy, geocentric distance accuracy of 1 dm and speed accuracy of 0.1 mm/s of space station is required; (3) Influenced by the visibility of space stations to the ground, it is not possible to evaluate the medium term stability of atomic clocks with only the observation data of domestic stations satellite for space-to-ground links.

  Conclusions  High precision navigation solution is important to ensure high-precision time and frequency transfer between space and ground. How to optimize navigation algorithms and use various payloads onboard to achieve high-precision position and velocity solution is a key issue that needs to be studied.