GRACE重力反演中的轨道数值积分方法分析

Analysis of Orbit Numerical Integration Methods in Earth's Gravitational Field Recovery by GRACE

首先,对比分析Runge-Kutta积分法、Adams-Cowell联合并行积分法、Gauss-Jackson积分法以及天体力学中常用的外插积分法用于GRACE卫星轨道积分及变分方程解算时的优缺点,得出Gauss-Jackson算法优于其它算法并推荐了相对较优的阶数和步长,从算法的推导过程中分析出了Gauss-Jackson算法优于其它算法的原因。其次,对比不同积分方法抵抗误差的能力,结果表明这些方法都不能有效抵抗误差的干扰;并分析初始状态向量误差和摄动力误差对轨道积分的影响,结果表明,卫星初始状态向量中的速度误差(0.1 mm/s)对轨道积分的影响大于位置误差(10 mm)对轨道积分的影响,摄动力中的随机误差对轨道积分的影响较大且无规律可循。针对GaussJackson算法中的不足,提出基于移动窗口的多项式内插算法和Gauss-Jackson算法相结合的组合方法(改进GaussJackson算法),通过模拟和实测数据的计算表明该方法在保证积分精度的前提下不仅提高了积分效率而且可以得到任意时刻的积分值。

This paper assesses the existing numerical integration methods including the Runge-Kutta methods,the Adams-Cowell methods,the Gauss-Jackson methods and the extrapolation methods in the computation of the GRACE satellite orbits and state transition matrix.According to the results,we recommend the Gauss-Jackson methods with optimal parameters to integral orbit and also analyze the advantages of the Gauss-Jackson methods relative to the other methods.Then the resistance capacity of the random errors which are included in the satellite initial state for those methods is analyzed,and the numerical results indicate that all methods show the similar little resistance capacity.The integral orbits are more sensitive to the satellite initial state velocity errors（0.1 mm/s） than the initial state position errors（10 mm）.Compared to the errors in the satellite initial state,the perturbation force model errors have a significant impact on the orbit integral precision.Finally,we proposes a modified method which combines the Gauss-Jackson algorithm and the movingwindow polynomial interpolation algorithm to overcome the shortage of the large step size of the Gauss-Jackson method.The simulated and actual results show that the modified method can give the satellite position and state transition matrix at any time and has a significant improvement in computing efficiency while possessing high accuracy.