GOCE卫星径向重力梯度一阶、二阶径向偏导数标准差的近似解析公式  

Approximate Analytical Formula for Standard Deviation of the First and Second Radial Derivatives of GOCE Satellite Radial Gravity Gradient

作　　者：徐天河[1,2] 贺凯飞[3] 

机构地区：[1]武汉大学测绘学院,湖北武汉430079 [2]西安测绘研究所,陕西西安710054 [3]长安大学地测学院,陕西西安710054

出　　处：《测绘学报》2011年第4期416-420,441,共6页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(40604003);全国优秀博士学位论文作者专项资金

摘　　要：基于Kaula准则,推导卫星重力梯度径向分量Tzz一阶、二阶径向偏导数T.zz、Tzz标准差的近似解析表达式,给出GOCE卫星.Tzz、Tzz标准差的近似估计值,由此分析Tzz延拓处理中可忽略的延拓误差最大高度。解析公式表明:T.zz、Tzz标准差的计算公式可近似表示成若干伽玛函数线性组合的开方,GOCE卫星.Tzz、Tzz标准差近似解析估值分别为1.269×10-15s-2m-1和1.109×10-20s-2m-2,由此若得到满足1 mE的精度要求,可忽略的延拓误差最大高度对于T.zz应小于0.8km,而对于Tzz应小于13.4km,延拓中重力场模型阶次应不低于200。最后基于模拟的GOCE卫星轨道,利用严格公式计算出的T.zz、Tzz标准差,验证近似解析表达式估算结果的正确性,解析结果与严格公式计算结果的相对误差小于2%。Approximate analytical formula for standard deviation of the first and second radial derivatives T·zz and T¨zz of GOCE radial gravity gradient Tzz are derived based on Kaula＇s rule.From the derived formula,the maximum height to be ignored for the continuation of GOCE Tzz is estimated.It shows that the formula of the standard deviation of T·zz and T¨zzcan be expressed approximately by square root of linear combination of a series of Γ functions,the estimated standard deviations are about 1.269×10^-15 s^-2m^-1 and 1.109×10^-20 s^-2m^-2 respectively for GOCE satellite.To meet the precision requirement of 1 mE,the maximum heights to be ignored for GOCE T·zz and T¨zz are less than 0.8 km and 7.6 km respectively.A numerical calculation by using strict formula for the standard deviation of T·zz and T¨zz from simulated GOCE orbits is performed.The results show the proposed approximate analytical formula can reasonably evaluate standard deviations of GOCE T·zz and T¨zz,and their relative errors are all less than 2%,which proves their validation and correctness.

关 键 词：解析公式 卫星重力梯度 相对误差 Kaula准则 

分 类 号：P207[天文地球—测绘科学与技术]