外部扰动引力逼近的最小二乘配置法研究

Research on the Least Squares Collocation Method for External Disturbance Gravity

本文给出了利用附加参数最小二乘配置方法计算局部空间扰动场元的公式与计算方法。文中采用不同范围的初始数据，计算了一定高度上的局部空间扰动引力垂直分量的格网值，并将其与模型计算值进行比较分析。在移去恢复低阶模型阶数分别为36阶、90阶、180阶、360阶和720阶的情况下，使用附加参数最小二乘配置方法计算了不同高度上的扰动引力垂直分量值。结果表明，当高度一定时，所求格网范围越小并越接近已知点中心，计算精度越高。其中，移去恢复720阶低阶模型得到的计算精度最高；在已知点附近的空间范围内，计算点的高度越低，得到的扰动引力垂直分量的精度越高。

The formula and calculation method of local space perturbation field elements are put forward using least squares collocation with extra parameters. Initial data of different ranges are used to calculate local spatial grid values of vertical compo- nent of disturbing gravity at certain height and are compared with model results. Under the conditions that the remove - restore degree of the low degree model are 36 degree, 90 degree, 180 degree, 360 degree and 720 degree, the vertical component values of disturbing gravity at different heights are calculated respectively using least squares collocation with extra parameters. The re- sults show that a higher calculation accuracy will be achieved as the grid range decreases and comes nearer to the center of unknown point. To be specific, the highest accuracy is obtained by the remove - restore low degree model of 720 degree, and around the known point, the lower the calculated point is, the higher accuracy will be achieved.