Analytical error analysis for satellite gravity field determination based on two-dimensional Fourier method
Analytical error analysis for satellite gravity field determination based on two-dimensional Fourier method
复制标题
基于二维傅立叶法的卫星重力场测定解析误差分析
DOI：
10.1007/s00190-013-0615-6
复制
发表时间：
2013-05-01
影响因子：
4.4
通讯作者：
Luo, Jun
中科院分区：
文献类型：
--
作者：
Cai, Lin;Zhou, Zebing;Luo, Jun
卫星重力测量任务的数据处理和误差分析一般采用时向和空向两种方法。但这两种方法都是基于最小二乘方法，解决了测量误差的整体影响，主要是从数值角度估计重力场模型的分辨率。此外，对重力场模型精度和分辨率的要求也增加了计算的难度，产生了严重的数值不稳定性。基于二维傅里叶描述，导出了卫星重力测量功率谱密度与地球引力模型球谐系数之间的直接解析表达式。该方法提供了对任务参数、仪器参数和重力场参数之间关系的物理认识。相反，最小二乘法主要基于数学观点。利用解析表达式，对任务参数估计和误差分析具有高效、清晰的特点。以卫星梯度仪恢复任务为例，从分析关系中不难得出低频噪声对重力场恢复的影响程度不同，这与以往数值误差分析方法的研究结果一致。
The time-wise and space-wise approaches are generally applied to data processing and error analysis for satellite gravimetry missions. But both the approaches, which are based on least-squares method, address the whole effect of measurement errors and estimate the resolution of gravity field models mainly from a numerical point of view. Moreover, requirement for higher accuracy and resolution gravity field models could make the computation more difficult, and serious numerical instabilities arise. A direct analytical expression between power spectral density of the satellite gravimetry measurements and spherical harmonic coefficients of the Earth’s gravity model is derived based on two-dimensional Fourier description. This method provides a physical insight into the relation between mission parameters, instrument parameters and gravity field parameters. In contrast, the least-squares method is mainly based on a mathematical viewpoint. By taking advantage of the analytical expression, it is efficient and distinct for parameter estimation and error analysis of missions. It is easy to obtain from the analytical relationship that the low-frequency noise affects the gravity field recovery in all degrees for the instance of satellite gradiometer recovery mission, which agrees with the work before by the numerical error analysis methods.