三次样条在卫星轨道插值中的应用研究

发布时间：2018-09-11 13:21

【摘要】：针对在卫星轨道插值中三次样条插值法的端点约束条件不易获得的问题,提出两种获得端点一阶导数的计算方法:差分法代替导数法;利用位置、速度和加速度之间的导数关系,求解坐标和速度的一阶导数。通过算例仿真表明,两种方法的坐标插值误差达毫米级以上,速度插值误差达厘米级以上,它们的插值精度均不受分段弧长影响,且比7阶Lagrange插值精度要高,但它们的运算时间比7阶拉格朗日插值法略大。其中,方法一优于方法二,因前者的速度插值误差比后者小,且后者的插值结果存在周期性抖动现象,其抖动周期与抽样频率有关。文中方法具有插值精度高,插值精度不受分段弧长影响,运算量不大的优点,是一种实用的卫星轨道和速度插值方法。
[Abstract]:In order to solve the problem that the constraint conditions of cubic spline interpolation are difficult to obtain in satellite orbit interpolation, two calculation methods for obtaining the first derivative of the terminal point are proposed: the difference method replaces the derivative method, the position, the position, The derivative relation between velocity and acceleration to solve the first derivative of coordinate and velocity. The simulation results show that the coordinate interpolation error of the two methods is more than millimeter and the velocity interpolation error is more than centimeter. The interpolation accuracy of the two methods is not affected by the segmental arc length and is higher than that of the seventh order Lagrange interpolation. However, their computational time is slightly larger than that of Lagrange interpolation of order 7. The first method is better than the second, because the velocity interpolation error of the former is smaller than that of the latter, and the result of the latter has the phenomenon of periodic jitter, and the jitter period is related to the sampling frequency. The proposed method has the advantages of high interpolation accuracy, no influence of segment arc length, and less computation, so it is a practical interpolation method for satellite orbit and velocity.
【作者单位】：广西大学计算机与电子信息学院;广西多媒体通信与网络技术重点实验室培育基地;广西高校卫星导航与位置感知重点实验室;
【基金】：国家自然科学基金项目(61563004) 南宁市科技攻关项目(20141033) 广西教育厅重点项目(ZD2014003)
【分类号】：P228

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