Analysis of the J2 relativistic effect on the performance of on-board atomic clocks

The GNSS satellite atomic clock is subjected to appreciable relativistic effects during its in-orbit operation. These effects include drift due to the gravitational redshift and time dilation due to the relative velocity, the periodic effects of the orbital eccentricity, the oblateness of the Earth's gravity field, and the tidal potential of the Sun, Moon and other planets. The accuracy of navigation, positioning and timing of satellite navigation systems is thus affected. The small terms, including those relating to the Earth's oblateness and the tidal potential of other planets, are usually neglected to estimate satellite clock. Inevitably, residual relativistic errors are introduced into the final solutions. Therefore, we comprehensively analyze the characteristics of relativistic effects on satellite clocks of the Beidou navigation satellite system, Galileo and Global Positioning System, including the combined relativistic effect, periodic relativistic effect, J2 relativistic effect and the tidal potential of other planets. The characteristics and performance of the satellite clock before and after the correction for J2 relativistic effect are evaluated. It is found that the amplitude of the satellite clock half-orbital periodic term is reduced by the correction, and the fitting residuals reduce by 6%. The Hadamard variance sequence tends to be stable. Meanwhile, J2 effect correction is applied to satellite clock prediction and improving the accuracy of the quadratic polynomial model by 9% and stability by 11%. Additionally, the results of using the spectral analysis model with and without adding the J2 period are improved.