A method of relativistic synchronization of moving atomic clocks and experimental verification thereof

We present results of the experiment on compensation of a relativistic shift in the timescale of a transportable hydrogen quantum clock with 3 $\times$ 10$^{-15}$ instability over its motion path. Calculation of the relativistic shift of the onboard timescale of the moving clock was based on continuous measurements of its current coordinates and velocity over the path with the aid of GLONASS/GPS navigation equipment. The experimental error of the proposed method does not exceed $\pm$1 ps.