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为了准确预报人造卫星的轨道,需要考虑复杂的动力学模型,并使用数值方法进行求解.虽然Runge-Kutta法和Adams-Cowell法等数值积分方法在轨道预报中已经取得了预期的效果,但是一般不考虑保辛,忽视了系统的固有特性.本文提出适用于轨道预报的乘法保辛摄动方法,将描述卫星运动的Hamilton正则方程分解为二体问题和摄动部分.二体问题采用解析解,摄动部分用区段矩阵近似求解.由于二体问题的状态转移矩阵必然为辛矩阵,故此过程保辛.本文考虑的摄动因素有地球非球形引力、日月引力、太阳光压和潮汐摄动,选取GPS卫星做数值仿真,以GPS卫星精密星历为参照得到轨道预报误差,并与Runge-Kutta法和Adams-Cowell法进行对比.结果表明:对PRN01号GPS卫星和PRN02号GPS卫星进行3 d的轨道预报,本文算法的误差分别为4.56和10.10 m,精度与Runge-Kutta法和Adams-Cowell法一致,而Runge-Kutta法与Adams-Cowell法的计算耗时分别是本文算法的237.7%与71.3%,因此本文算法效率明显高于Runge-Kutta法,但比Adams-Cowell法稍低.
In order to accurately predict the satellite orbit, complex dynamic models need to be considered and solved numerically.Although numerical integration methods such as Runge-Kutta method and Adams-Cowell method have achieved the expected results in orbit prediction, Ignoring the intrinsic properties of the system and neglecting the inherent properties of the system.This paper presents a multiplicative method of Xinxin perturbation for orbital prediction, which decomposes the Hamiltonian canonical equation describing the satellite motion into a two-body problem and a perturbed part.The two-body problem adopts an analytic solution , The perturbation part is approximated by the segment matrix. Since the state transition matrix of the two-body problem is bound to be a symplectic matrix, the process is Paulin. The perturbation factors considered in this paper are the non-spherical gravity of the earth, the gravitation of the sun and the moon, the solar pressure and the tide Perturbation, choose GPS satellite for numerical simulation, GPS orbit ephemeris is used as reference to get orbit prediction error, and compared with Runge-Kutta method and Adams-Cowell method.The results show that: PRN01 GPS satellite and PRN02 GPS satellite For the 3-day orbit prediction, the error of the proposed algorithm is 4.56 and 10.10 m, respectively. The accuracy is consistent with the Runge-Kutta method and Adams-Cowell method. The Runge-Kutta method and Adams-C The computation time of owell method is 237.7% and 71.3% respectively, so the efficiency of this algorithm is obviously higher than that of Runge-Kutta method, but slightly lower than that of Adams-Cowell method.