空间碎片激光测距中轨道偏差的非线性传播  

Orbital Uncertainty Nonlinear Propagation for Space Debris Laser Ranging

作　　者：张利军 舒鹏 李荣旺[1,3] 李语强 ZHANG Lijun;SHU Peng;LI Rongwang;LI Yuqiang(Yunnan Observatories,Chinese Academy of Sciences,Kunming 650216,China;University of Chinese Academy of Sciences,Beijing 100049,China;Key Laboratory of Space Object and Debris Observation,Chinese Academy of Sciences,Nanjing 210023,China)

机构地区：[1]中国科学院云南天文台,昆明650216 [2]中国科学院大学,北京100049 [3]中国科学院空间目标与碎片观测重点实验室,南京210034

出　　处：《天文学进展》2024年第4期656-668,共13页Progress In Astronomy

基　　金：国家重点研发计划(2022YFC2203800);国家自然科学基金(12303082,12293034);云南省“兴滇英才支持计划”青年人才专项;国家资助博士后研究人员计划(GZC20232975)。

摘　　要：在对空间碎片进行激光测距时,往往会因为轨道预报偏差较大而导致测距成功率低,为此,结合无迹变换方法与高斯混合模型,对空间碎片轨道偏差进行传播,得到空间碎片在终端的分布情况(即概率密度函数),从而为激光测距提供可靠的依据。首先选取了空间碎片激光测距中的典型轨道,并设定初始轨道偏差,通过无迹变换方法非线性地预报偏差的均值和协方差矩阵,高斯混合模型逼近偏差的概率密度函数,并将结果转换到以测站为中心的站心球坐标系中,所得结果与蒙特卡洛方法得到的结果一致:预报距离的绝对误差在20 m以内,方位角、俯仰角的误差不超过2″,预报的概率密度函数曲线能较好地符合蒙特卡洛仿真结果,且计算效率提升百倍以上。这表明该方法可以快速地提供高精度的偏差预报,为后续激光测距提供可靠的依据。In laser ranging of space debris,the success rate is often low due to significant orbit prediction errors.To address this,a method that combines the unscented transformation technique with the Gaussian Mixture Model to propagate the orbital uncertainty of space debris is proposed.This approach yields the debris’s state moments(generally mean and covariance matrix)or probability density function(PDF)at their terminal time,thereby providing a robust foundation for laser ranging.First,typical orbits in current laser ranging of space debris are selected to establish initial orbit uncertainty.Then,the unscented transformation method is utilized to nonlinearly predict the mean and covariance matrix of this uncertainty.Subsequently,the Gaussian Mixture Model is employed to approximate the probability density function of the uncertainty,and the results are converted into the station coordinate system centered on the station.The outcomes align with those derived from the Monte Carlo method:the absolute error of predicted range remains within 20 m,while the errors in azimuth and elevation angles do not surpass 2 arc seconds.Furthermore,the predicted probability density function curve closely mirrors the Monte Carlo simulation results,and the computational time efficiency is enhanced by over one hundred times.This demonstrates that the method not only offers high-precision uncertainty prediction but also furnishes a reliable foundation for subsequent laser ranging.Additionally,it effectively mitigates the substantial computational demands associated with Monte Carlo simulations.

关 键 词：激光测距 偏差演化 轨道预报 无迹变换 高斯混合模型 

分 类 号：P123.3[天文地球—天体测量]