利用卫星引力梯度确定地球重力场的张量不变方法研究

应用张量不变理论对利用卫星重力梯度数据确定地球重力场的方法进行了研究，对张量不变观测方程的线性化处理、非全张量观测值的数据处理策略以及采用白噪声特性下的梯度观测值恢复地球重力场的精度等进行了数值分析。结果表明，张量不变解实现了不同观测值的联合求解，基于先验重力场模型的线性化方法在实现张量不变观测模型线性化处理的同时，提升了张量不变方法的模型解算精度，且初始参考模型的选择对解的收敛特性影响较小；在无噪声和白噪声条件下，利用先验位模型的球谐综合值代替低精度梯度分量实现非全张量梯度观测值的处理均是可行的，不会改变解的收敛速度和最终精度。

Tensor Invariant Method for Determining the Earth Gravity Field from Satellite Gravitational Gradient Data

  Objectives  The objective is to study the tensor invariant method for determining the Earth's gravity field with satellite gravitational gradient data.  Methods  The tensor invariant method does not depend on the acquisition of the spatial orientation information of the gradiometer, so it has a special advantage over the traditional methods in determining the earth gravity field. Numerical analyses are made for the linearization of tensor invariant observation equation, the processing of non-full tensor observation data, and the accuracy of gravity field recovery with the gradient data containing white noise.  Results  The results show that the tensor invariant solution realizes the combine processing of the different tensor components. The tailored linearization effectively achieves the linearization of the tensor invariant observation model while the accuracy of gravity field model determined using tensor invariants is significantly higher than that of the single tensor component solution. Also, the choice of initial reference model exerts minor influence on the total iterative process.  Conclusions  Due to the non-full tensor gradient observations, it is proposed to replace the low precision gradient component using the spherical harmonic synthesis of a priori gravity field model, which will not change the convergence and the accuracy of the solution even if the white noise exists in the observations because of the nadir-pointing characteristics of the gradiometer.