近地空间扰动引力梯度张量的高精度逼近理论与方法

The Earth’s external distrubing gravity gradient tensor is essential to gravity-aided navigation. To research the modeling theory and method of the Earth’s external disturbing gravity gradient tensor, the project concentrates on three aspects of the approximation of the external disturbing gravity gradient tensor. Firstly, with geoid and actual terrain surface as boundary surface respectively, the Boudary Value Problem (BVP) of external disturbing gravity are to be invesigated, from which the theory and method for the precise determination of local external disturbing potential as well as its second-order gradient could be established. Secondly, Bjerhammar problem with least square collocation method on a sphere using the combination of multiple gravity field observations including newly added vertical gravity gradients, thus determining the external disturbing potential as well as its second-order gradient. Thirdly, aiming at regions with rich gravity data, a stable and fast method for constructing the point mass model is to be probed; and for regions with sparse gravity data, a flexible method for determing the number and position of point mass based on data variablity and distribution is to be researched. And the determination as well as accuracy assessment of external disturbing potential with frequency-wise residuals of gravity anomalies will be discussed. The research of the project can further improve the theory and methods of the disturbing gravity as well as its gradients modeling within the earth’s external gravity field.

地球外部扰动引力梯度张量信息对于重力场辅助导航来说具有极其重要的应用价值。本项目围绕地球外部扰动引力张量高精度逼近的理论和方法，着重研究三个方面的内容：一是分别依据地面边值条件和大地水准面边值条件，求解外部扰动位的边值问题，从而确立外部扰动引力梯度张量精确逼近的理论和方法；二是依据现有的地面重力信息，联合增测的地面重力垂直梯度等多种重力场观测信息，通过球面最小二乘配置的方法求解Bjerhammar问题，从而确定外部扰动位及其二阶梯度；三是针对不同数据密度的地区，分别研究设计点质量模型的稳定快速求解方法和依据数据本身特征灵活确定点质量数量和位置的方法，并引入分频余差方法对外部扰动引力梯度张量进行分频段确定和精度估计。本项目的研究将完善地球外部扰动引力及其梯度场的建模理论与方法。

地球外部扰动引力梯度张量信息对于重力场辅助导航来说具有极其重要的应用价值。本项目围绕地球外部扰动引力梯度张量高精度逼近的理论和方法进行研究，获得了三个方面的研究成果：一是分别依据地面边值条件和大地水准面边值条件，求解外部扰动位的边值问题，从而确立外部扰动引力梯度张量精确逼近的理论和方法；二是依据现有的地面重力信息，联合增测的地面重力垂直梯度等多种重力场观测信息，通过球面最小二乘配置的方法求解Bjerhammar问题，从而确定外部扰动位及其二阶梯度；三是针对不同数据密度的地区，分别研究设计点质量模型的稳定快速求解方法和依据数据本身特征灵活确定点质量数量和位置的方法，并引入分频余差方法对外部扰动引力梯度张量进行分频段确定和精度估计，在其中对全国的重力异常数据、地形高程数据和中长波重力场模型进行了全面的评估。本项目的研究成果完善了地球外部扰动引力及其梯度场的建模理论与方法。