利用短弧积分法和GOCE轨道数据确定地球重力场模型

Gravity field modeling by using the short-arc integral approach and GOCE orbits

基于牛顿运动方程的短弧积分法是将卫星轨道表示成Fredholm积分方程形式的边值问题,该方法不需要任何初始值或参考模型,观测方程是线性的并且不包含速度向量.GOCE卫星采用无阻尼推进补偿掉了大部分非保守力加速度,对残余加速度采用经验函数加以吸收,并将残余加速度的偏差、振幅参数和弧段边界轨道改正向量作为局部参数,与位系数统一进行求解.利用GOCE卫星2009-11-01至2010-01-31共92天的精密轨道数据,基于短弧长积分法恢复了120阶次和130阶次两组重力场模型GOCE-SAIA01S和GOCESAIA02S.结果表明:当插值多项式的阶数超过9阶时,多项式的阶数增加对恢复的重力场模型的精度改善越来越小;相对于GOCE卫星约90min的运行周期,采用15min弧长恢复的重力场模型精度最好.在120阶次的大地水准面误差约为±4.3cm,在6-120阶次内GOCE-SAIA01S的精度优于EIGENCHAMP03S.由于极空白的影响,所恢复的重力场模型位系数的带谐项精度偏低.

The short-arc integral approach which based on Newton＇s equation of motion formulates the satellite orbit as a boundary value problem in the form of the Fredholm type integral equation,this approach does not require any initial values of unknown parameters and reference gravity models,and the observation equation is linear and does not contain the velocity vector.The non-conservative force of GOCE satellite is largely compensated by the drag-free control and the residual acceleration is absorbed by the empirical acceleration.Spherical harmonic coefficients is resolved with local parameters which contains bias and amplitude parameters of the residual acceleration and boundary arc correction vectors.Two gravity field models, which named GOCE-SAIA01S and GOCESAIA02S,are recovered based on GOCE precision orbits of 92-days from 2009-11-01 to 2010-01-31 with the short-arc integral approach.The results show that the accuracy of the recovered gravity field model is of non-significance for its improvement when the order of the polynomial interpolation exceeds 9;the gravity field model with the best accuracy is recovered by 20 min arc length which is compared with 90 min cycle of the GOCE satellite.The geoid error of the model GOCE-SAIA01S is ±4.3 cm with degree and order 120,the accuracy of the model GOCE-ECP01S is higher than the model ITG-CHAMP05S with degree and order 6 to 120,and the precision of zonal coefficients is low due to the polar gap.