基于B spline和正则化算法的低轨卫星轨道平滑

本文提出了一个利用纯几何轨道和力模型的新算法来计算精确且相对平滑的卫星轨道. 该法将一个纯几何轨道表达为一个B spline的线性组合，线性组合的系数可以由最小二乘法估计获得. 力模型通过计算加速度来附加约束. 为了平衡几何轨道的点位误差和加速度的不精确，一个基于“广义交互确认（GCV，generalized cross validation）”的正则化算法运用其中. 由于B spline的本地控制性，该方法的计算效率相当高. 本文的数值分析表明了该法的有效性. 模拟计算的结论是：带加速度约束较不带加速度约束的平滑效果好. 力模型越精确，平滑的轨道就越精确. 三个月的CHAMP实测轨道数据处理结果表明，平滑后的轨道改进了重力场模型.

Smoothing a satellite orbit on the basis of B-spline and regularization

A new algorithm is developed to compute a smooth and accurate satellite orbit on the basis of a kinematic orbit and a force model. Such a smoothed orbit is needed e.g. in the gravity field modeling procedure that is based on satellite accelerations. The procedure makes use of residual satellite accelerations defined as the difference between the observed accelerations and the reference ones. Computation of the reference accelerations requires an accurately determined set of satellite positions, which can be taken over from the smoothed orbit. The algorithm for computing the smoothed orbit is based on B splines. A component of the orbit (i.e. a set of X , Y , or Z coordinates in an inertial frame) is parameterized as a linear combination of B spline functions with corresponding coefficients. These coefficients are determined by means of a least square adjustment scheme. A force model is exploited to compute satellite accelerations, which are used as additional constraints. In order to find the balance between errors in the positions and unaccuracies of the computed accelerations, the generalized cross validation technique is implemented. Thanks to the property of a local support of B splines, the procedure is very efficient numerically.A numerical example demonstrates a performance of the proposed procedure. Furthermore, it shows that the solution with acceleration constraints is better than the solution based on the kinematic orbit only. The more precise the force model is, the more accurate smoothed orbit is obtained. Finally, a set of real CHAMP data is considered in the context of gravity field modeling. Smoothed orbits, which are computed both with and without acceleration constraints, as well as the original kinematic orbit are employed for calculating reference accelerations. The “Delft approach" is applied to recover gravity field models, which are compared with the EIGEN CG01C model. The results show that usage of the smoothed orbitobviously improves the gravity field model, especially if the smoothed orbit is computed with acceleration constraints.