半解析卫星轨道不确定性快速估计方法

Semi-analytical Method for Rapid Estimation of Orbital Uncertainty

基于半解析法和球形单边采样无迹变换提出一种轨道不确定性快速估计方法。首先在考虑J2摄动和大气阻力摄动的基础上,构建轨道要素解析模型用于瞬时轨道要素快速估计。随后基于该轨道要素快速估计方法,结合球形单边采样无迹变换传播初始轨道不确定性,依据高斯摄动方程和球形单边采样点的特性对传播后的采样点进行修正,估计传播后的轨道不确定性。最后将提出的半解析法与高斯和模型相结合,以提高精度。数值仿真分析了所提出的轨道不确定性估计方法相较无迹变换法的计算效率提升程度,并依据似然一致性度量将所提出的方法与蒙特卡洛法、无迹变换法等进行了精度比较。结果表明,所提方法的计算效率相较于传统无迹变换法有较大提升,且具有合适的精度。

A fast orbital uncertainty propagation method is proposed based on semi-analytical method and spherical simplex sigma-point selection unscented transformation.Firstly,on consideration of the J2 perturbation and atmospheric drag,an analytical model with secular term,long periodic term and short periodic term of orbital elements is constructed as the dynamics model for fast orbital elements propagation.Subsequently,the spherical simplex sigma-point selection unscented transformation is chosen to propagate the initial orbital uncertainty.Then,modification is done to adjust the sigma-points according to the Gauss variational equations and the characteristics of the spherical simplex sigma-points to estimate the probability density function of the final orbital uncertainty.Finally,the proposed semi-analytical method is combined with the Gaussian mixture model to improve the accuracy.In the simulation analysis,the computational efficiency of the proposed orbital uncertainty estimation method is analyzed compared with that of the traditional unscented transformation method.Then,the accuracy of these methods is evaluated based on the likelihood agreement measure.The results show that the calculation efficiency of the proposed method is improved compared to the traditional unscented transformation method,and is with appropriate accuracy.