相对论体系下卫星原时及星间钟差机理建模  

Mechanism Modeling of Satellite Proper Time and Inter-satellite Clock Difference in Relativistic System

作　　者：贾前 李青[3] 刘磊[1,2] JIA Qian;LI Qing;LIU Lei(School of Astronautics,Northwestern Polytechnical University,Xi’an 710072,China;Shaanxi Aerospace Flight Vehicle Design Key Laboratory,Xi’an 710072,China;School of Aerospace Engineering,Tsinghua University,Beijing 100084,China)

机构地区：[1]西北工业大学航天学院,西安710072 [2]陕西省空天飞行器设计重点实验室,西安710072 [3]清华大学航天航空学院,北京100084

出　　处：《宇航学报》2024年第3期366-375,共10页Journal of Astronautics

基　　金：国家自然科学基金(52075446,52305117)。

摘　　要：面向新一代导航卫星对高精度自主时间基准的需求,针对皮秒级星间钟差机理不清晰问题,在广义相对论体系下提出一种卫星原时以及星间皮秒钟差模型,该模型可基于卫星状态计算星载原子钟相对参考时钟的偏差以及星间钟差。首先从地心参考坐标系的度规张量出发,利用广义相对论建立了卫星的运动模型;然后,根据时空间隔的不变性,提出考虑地球非球形J2摄动项的卫星原时模型,并进一步给出了包含J2项修正的星间钟差模型。最后以北斗卫星导航系统和GPS为研究对象对建立的模型进行了仿真分析,为新一代导航系统的时间校准和同步提供了一种可行的建模方法。仿真结果表明,卫星原时模型与星间钟差模型的精度都在皮秒量级,能够准确地计算星载原子钟在引力场中的原时偏差以及星间钟差。To meet the demand for high-precision autonomous time reference of new generation navigation satellites,and addressing the unclear mechanism of picosecond level inter-satellite clock difference,the proper time and inter-satellite picosecond clock difference models are proposed using general relativity theory.The models utilize the satellite state to compute the on-board atomic clock deviation relative to the reference clock and inter-satellite clock difference.Firstly,beginning with the metric tensor in geocentric coordinate reference system,the satellite motion equations are derived using general relativity theory.Then,according to the invariance of space-time interval,the proper time model considering the non-spherical J2 perturbation is established and the inter-satellite clock difference model with J2 correction is further given.Finally,the simulation is conducted by taking BeiDou Navigation Satellite System and GPS constellations for examples,providing a feasible modeling solution for time correction and synchronization in new generation navigation systems.The simulation results demonstrate the accuracy of satellite proper time and inter-satellite clock difference models is in the order of picoseconds,which can accurately calculate the proper time deviation of the on-board atomic clock in the gravitational field and inter-satellite clock difference.

关 键 词：导航卫星 星间钟差 时间校准与同步 广义相对论 北斗卫星导航系统 

分 类 号：V412[航空宇航科学与技术—航空宇航推进理论与工程]