AI 中文总结
本文针对卫星重力测量中微分方程的参数估计，综述相关数学方法，提出基于测量的摄动理论，推导离散跟踪数据下卫星运动微分方程的局域解，为高分辨率重力模型提供理论基础。
AI 中文摘要
卫星重力测量已成为地球科学诸多领域的重要技术，然而卫星重力模型在数百公里尺度上的分辨率仍较低，且尚无重力恢复方法能充分利用卫星跟踪测量前所未有的高精度。本文首先为卫星重力测量中的微分方程参数估计提供统一理论框架，随后简要综述从卫星跟踪数据计算地球重力场的数学方法，重点关注配点法（collocation method）、Kaula线性摄动、两点边值问题以及基于轨道能量的方法。数值积分法也被纳入本综述，尽管已证明该方法在数学上不正确且物理上不被允许，但它已成为从卫星跟踪数据常规生成全球重力模型的标准方法，且这些模型已广泛应用于地球科学的诸多不同领域。由于尚不明确其错误基础会如何影响卫星跟踪数据生成的重力产品，因此本文未综述这些产品的任何应用。接着，本文提出一种基于测量的摄动理论以估计地球重力场，该方法可充分利用任意长度的高精度卫星轨道以及卫星和星间跟踪的前所未有的高精度，在理论上不受建模误差影响，能够从卫星和星间跟踪数据中提取任何微小力，并为高精度高分辨率全球重力模型提供保障。最后，本文假设一个参考重力模型，针对离散跟踪数据推导卫星运动的牛顿非线性控制微分方程的局域解，该局域解在某些应用中仍具有重要意义。
英文摘要
Satellite gravimetry has become essential in many areas of earth science. However, the resolution of satellite gravitational models remains low at scales of a few hundreds km and no gravity recovery methods can take full advantages of unprecedented high accuracy of satellite tracking measurements. We first provide a unified theoretical framework of parameter estimation in differential equations for satellite gravimetry and then briefly review the mathematical methods to compute the gravity field of the Earth from satellite tracking. We focus on the collocation method, Kaula linear perturbations, two-point boundary value problems and orbit-energy-based methods. The numerical integration method is also included in this review, though it has been proved to be mathematically incorrect and physically not permitted. The reason is that it has become the standard method to routinely produce global gravitational models from satellite tracking data, which have been widely applied in many different areas of earth science. Because it is not clear how the incorrect foundation would affect gravity products from satellite tracking, we do not review any applications of these products. We then present a measurement-based perturbation theory to estimate the gravity field of the Earth, which can fully utilize both precise satellite orbits of arbitrary length and unprecedented high accuracy of satellite and inter-satellite tracking. The method is theoretically free of modeling errors, is capable of extracting any small forces from satellite and inter-satellite tracking data and provides a guarantee for high-precision and high-resolution global gravity models. Finally, we assume a reference gravity model and derive local solutions to the Newton's nonlinear governing differential equations of satellite motion for scattered tracking data that can still be important in some applications.
Comments28 pages, 2 figures
