利用经验正交函数分解的大气密度模式校准方法

热层大气密度产生的阻力是作用在低轨航天器上最大的非引力摄动，现有大气密度模式存在15%~20%的偏差，难以满足空间任务应用需要。采用NRLMSISE-00模式作为密度参考标准，通过修正Jacchia-Roberts经验大气模式温度参数校准密度，建立温度修正量与密度的参数方程。针对部分区域修正量迭代计算发散问题，采用改进高斯牛顿迭代法求解方程。选择经验正交函数（EOF）分解方法分析修正量的时空特征，并与传统球谐（SH）分析的结果进行比较。结果表明，前4阶EOF基函数与前9项球谐基函数分别可提取温度修正量超过85%与80%的变化特征，EOF分解方法对温度修正量的表示效率高于球谐分析方法。第1阶EOF基函数反映了温度参数的整体偏差，第2~4阶EOF基函数对应的时间系数表明温度修正量的变化具有天周期性，且球谐分析得到的时间系数同样具有天周期性的特点。利用前4阶EOF基函数和前9项球谐基函数重构的温度修正量校准Jacchia-Roberts模式，校准后的模式密度偏差分别下降了9.06%与5.37%，表明EOF分解方法与传统球谐分析方法相比，能够更有效地修正温度参数，改进模式精度。

Atmospheric density model calibration using empirical orthogonal function

The force produced by thermospheric density is the largest non-gravitational perturbation acting on low orbit space-crafts. It is difficult for existing atmospheric density models to satisfy space mission requirements because of the 15%-20% deviations in the models. With the NRLMSISE-00 empirical model as the density reference standard, an equation for temperature corrections and density is established by correcting the temperature parameters of Jacchia-Roberts empirical density model to calibrate density. The improved Gauss-Newton correction algorithm is chosen to avoid divergent solution of the equation in specific regions. The spatial-temporal characteristics of temperature corrections are captured by Empirical Orthogonal Function (EOF), and are then compared with the characteristics of temperature corrections captured by the traditional Spherical Harmonics (SH). Results show that more than 85% and 80% variations of temperature corrections are involved in the first 4 EOFs and the first 9 SH expansion functions. The first EOF reflects the overall bias of temperature corrections. The coefficients corresponding to the second to fourth EOF show that the temperature corrections have diurnal periodicity, and the coefficients obtained with the SH also have diurnal periodicity. Jacchia-Roberts model is calibrated by the reconstructed temperature corrections using the first 4 EOFs and the first 9 SH expansion functions, and the calibrated density deviations of Jacchia-Roberts reduce by 9.06% and 5.37%, respectively. It is confirmed that the EOF method has better efficiency than the SH method in temperature parameter correction and density model calibration.