以扰动重力为边值条件确定外部扰动重力场

Determining the external disturbing gravity field by applying gravity disturbance as boundary value condition

惯性导航系统的精确导航离不开地球重力场信息的支持,然而目前利用扰动重力求解地球外部空间扰动重力场的研究相对较少。针对地球外部空间扰动重力场求解问题,推导了以实际地形面为边界面的利用扰动重力与格林积分公式推求外部扰动重力三分量的公式,给出了利用扰动重力与豪汀积分公式计算扰动重力三分量的表达式。通过数值实验对格林积分法、豪汀积分法与点质量模型法进行了对比分析,结果表明:三种方法均可以在3 km处以优于2 mGal的精度逼近扰动重力三分量。所提出的方法对于地球外部扰动重力场的确定具有一定的借鉴与参考意义。

Accurate navigation of inertial navigation systems needs the support of the Earth’s gravity field information. However, there are few studies on the use of gravity disturbances to calculate the gravity disturbance vectors of the Earth’s external space. Aiming at the calculation of these gravity disturbance vectors, the formula for calculating the gravity disturbance vectors by using gravity disturbances and the Green integral with real terrain surface is deduced, and the formula for calculating the gravity disturbance vector by using gravity disturbances and the Hotine integral is given. Comparative analysis on Green integral method, Hotine integral method and point mass model method are conducted by numerical experiments, and the results show that all the three methods can approximate the disturbance gravity vectors at an accuracy of better than 2 mgal at 3 km altitude. The proposed methods can provide references for determining the gravity disturbance vectors of the Earth’s external space.