The comparison model of satellite-earth time based on special relativity and its accuracy analysis

Abstract

The functions of navigation satellite include positioning and timing, which are based on high-precision time comparison. Most of the existing studies ignore the relativistic effect of the satellite-earth time comparison, or study some delay based on general relativity alone. There is no complete calculation model of the satellite-earth time comparison based on special relativity. In this paper, the satellite-earth time alignment model based on special relativity is derived and the space-time diagram of special relativity is established. In order to improve the accuracy of the satellite-earth time alignment, the uplink Sagnac effect delay and the special relativity effect delay are derived based on the relative motion of the satellite-earth. By calibrating the model of the satellite-earth alignment of the special relativity theory with the above two dealy terms, the alignment accuracy is improved. The experimental results show that the satellite-earth time comparison model derived in this paper is correct. After correction and optimization of the uplink Sagnac effect delay and special relativity delay, the maximum accuracy improvement and the average accuracy improvement are 0.022% and 0.014% to GPS. The highest accuracy improvement was 0.079%, and the average improvement was 0.012% to GLONASS . It can be seen that the accuracy of the satellite-earth time comparison model under the relativity theory is higher than that of the un-optimized satellite-earth time comparison model.