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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%。 更多还原

【Abstract】 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... 更多还原