低轨空间监视的天地协同轨道确定与误差分析
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摘要
为突破地域限制,提高系统效能,我国的低轨空间监视应当在发展地基监视系统的同时,探索论证天基监视系统。论文以天基雷达网协同地基雷达执行低轨空间监视任务为背景,针对地基雷达测站布局、定轨误差传播及基于天基雷达观测数据的轨道改进等问题进行了系统而深入的研究。
讨论了地基雷达的站址选择条件,分析了单基地与多基地雷达系统对空间目标的定位误差,仿真结果表明,三基地以上的雷达系统,主站与辅站的布局为几何对称时,定位误差最小。在最优构型的基础上分析了地基雷达的定轨性能,仿真结果表明,增加辅站可以降低定轨误差,辅站数目达到3时,在测角精度较差的情况下,只需测距信息参与定轨即可获得较高的精度。
引入协方差描述函数法,假设状态变量服从高斯分布,推导了高精度轨道预报中均值和协方差的传播公式。与线性系统的Ricatti方程相比,拟线性函数考虑了微分方程Taylor展开二阶偏导的影响,统计学描述更准确。误差传播分析表明,位置误差的迹向分量与速度误差的径向分量决定了误差量级,轨道预报的精度取决于初始状态和动力学模型的准确性。
针对天地协同空间监视任务,提出了高精度轨道预报推衍与轨道改进相结合的定轨算法流程,即从上一次轨道改进时刻出发,采用精确动力学模型推衍状态和协方差,计算单点观测数据引入时刻的状态和协方差,以此作为初值与观测数据进行轨道改进,推衍与改进循环交替。
为了保证天基雷达稀疏单点观测数据参与轨道改进的精度,给出了基于3σ法则的异常数据剔除条件。仿真表明,高精度轨道推衍与EKF相结合时,天基雷达的稀疏单点数据参与轨道改进,在控制轨道面内误差发散方面,效果显著。对于法向误差,尽管位置误差在改进时刻可以得到修正,但由于测速精度不高,单点观测的信息量少,法向速度误差修正效果不明显,综合影响导致法向误差不再是小幅度范围内振荡,振幅增大,误差波峰处仍维持在初始精度附近,因此误差不能得到整体抑制,只能部分改善。引入Hill方程,给出了法向误差传播方式的数学描述,从数学上解释了测速精度不高的情况下单点观测不能抑制法向误差的原因。
天基雷达的密集短弧观测数据参与轨道改进时,因观测量增加,在提高定轨精度的同时,法向误差也逐渐得到了整体抑制。引入UKF滤波,仿真表明,不仅在精度上稍优于EKF,收敛速度也比EKF快,因此观测数据量较少时可以获得比EKF更高的精度,同时对法向速度误差的滤波效果优势更为明显。
最后,引入Hill方程给出了初始偏差发散的近似解析表达式,直观地解释了数值法初始状态误差传播的仿真结果:位置迹向误差和速度径向误差迅速发散的原因在于,这两个方向的偏差传播公式中含有初始偏差引起的关于时间的一次项。在此基础上,分析了两行轨道根数(TLE)单点拟合发散的初始偏差影响因素,给出了提高单点推衍精度的初始偏差条件,该条件也对应高精度轨道预报采样拟合中残差平方和最小的最优条件,同时对影响残差发散的主要因子进行了分离,为TLE的选择和使用提供了理论依据。
论文采用理论分析与数值仿真相结合的方法,重点探讨了天地协同低轨空间监视中涉及的误差传播和轨道确定等问题,研究成果对我国空间监视系统的设计和发展具有一定的参考价值。
Within the confines of the territory, the space-based sensors should be explored and demonstrated while the ground-based sensors are developed to improve the space surveillance system for low earth orbit (LEO). Assumed that the space-based radar (SBR) net cooperates with the ground-based radar (GBR) for LEO surveillance, the thesis investigates the site arrangement, error propagation and differential correction with observations from SBRs.
The criterion for choosing the site of the GBR is presented. The analysis of the positioning precision about the GBR with multi-bases shows that the optimal arrangement is symmetrical in geometry if the numbers of the auxiliary sensors is over three. And with the optimal arrangement, the high precision of orbit determination could be achieved only with the range measurements from three or more auxiliary sensors, if the standard deviation of the angle measurements is much worse than that of range measurement.
The Covariance Analysis DEscribing function Technique (CADET) is implemented in high-precision orbit prediction to obtain the propagation of the mean vector and covariance supposed that the state is a gaussian variable. Compared with the linear variance equation i.e. matrix Ricatti equation, the quasi-linear approximation technique considers the second order of the partial derivatives of the differential equation with respect to the state vector which is more precise in statistics. According to the simulation, the along-track error in position and the radial error in velocity are dominative during propagation. And the propagating precision is determined by the priori standard deviation and the state noise.
The orbit determination algorithm combined with the high-precision orbit propagation and differential correction is presented for the space surveillance with the cooperation of the GBR and the SBRs. In other words the latest estimated mean and covariance are propagated until the time that observations are available. And the predicted mean and covariance at that time as the priori are updated with the observations, then the propagation continues.
For the precision of the sparse observational data from SBRs the pre-process based on 3σrule is derived. The simulation shows that the high-precision orbit propagation and update by the extended Kalman filter (EKF) can control the along-track error in position and the radial error in velocity very well. While the cross-track error could not be controlled in whole with the low precision measurement of range rate almost helpless against cross-track error in velocity if the observation is single set. And this could be explained by the Hill equation clearly.
When the short-arc dense observational data is used in differential correction, the precision is improved and the cross-error is controlled well in comparison with the sparse data. And when the unscented Kalman filter (UKF) is applied to update, the filter converges quicker and the precision is higher than that of EKF, especially the cross-track error in velocity could be controlled much better.
The error propagation resulted from initial deviation could be described by Hill equation to explain the numerical simulation above: the along-track error in position has the linear factor about time so does the radial error in velocity, while the equation of the cross-error is a simple harmonic oscillator. And the initial deviation condition is given by Hill equation to control the error propagation of the TLE generated from the single point. And the condition is consistent with the minimal sum of squares of residuals of the TLE generated from sampling. Also the main divergent factor in initial deviation is separated, which may be operational in selecting TLE.
The thesis mainly discusses the error propagation and the orbit determination in space surveillance with the cooperation of the SBRs and the GBR, and the achievement could be some help for the design and the development of the national space surveillance system.
讨论了地基雷达的站址选择条件,分析了单基地与多基地雷达系统对空间目标的定位误差,仿真结果表明,三基地以上的雷达系统,主站与辅站的布局为几何对称时,定位误差最小。在最优构型的基础上分析了地基雷达的定轨性能,仿真结果表明,增加辅站可以降低定轨误差,辅站数目达到3时,在测角精度较差的情况下,只需测距信息参与定轨即可获得较高的精度。
引入协方差描述函数法,假设状态变量服从高斯分布,推导了高精度轨道预报中均值和协方差的传播公式。与线性系统的Ricatti方程相比,拟线性函数考虑了微分方程Taylor展开二阶偏导的影响,统计学描述更准确。误差传播分析表明,位置误差的迹向分量与速度误差的径向分量决定了误差量级,轨道预报的精度取决于初始状态和动力学模型的准确性。
针对天地协同空间监视任务,提出了高精度轨道预报推衍与轨道改进相结合的定轨算法流程,即从上一次轨道改进时刻出发,采用精确动力学模型推衍状态和协方差,计算单点观测数据引入时刻的状态和协方差,以此作为初值与观测数据进行轨道改进,推衍与改进循环交替。
为了保证天基雷达稀疏单点观测数据参与轨道改进的精度,给出了基于3σ法则的异常数据剔除条件。仿真表明,高精度轨道推衍与EKF相结合时,天基雷达的稀疏单点数据参与轨道改进,在控制轨道面内误差发散方面,效果显著。对于法向误差,尽管位置误差在改进时刻可以得到修正,但由于测速精度不高,单点观测的信息量少,法向速度误差修正效果不明显,综合影响导致法向误差不再是小幅度范围内振荡,振幅增大,误差波峰处仍维持在初始精度附近,因此误差不能得到整体抑制,只能部分改善。引入Hill方程,给出了法向误差传播方式的数学描述,从数学上解释了测速精度不高的情况下单点观测不能抑制法向误差的原因。
天基雷达的密集短弧观测数据参与轨道改进时,因观测量增加,在提高定轨精度的同时,法向误差也逐渐得到了整体抑制。引入UKF滤波,仿真表明,不仅在精度上稍优于EKF,收敛速度也比EKF快,因此观测数据量较少时可以获得比EKF更高的精度,同时对法向速度误差的滤波效果优势更为明显。
最后,引入Hill方程给出了初始偏差发散的近似解析表达式,直观地解释了数值法初始状态误差传播的仿真结果:位置迹向误差和速度径向误差迅速发散的原因在于,这两个方向的偏差传播公式中含有初始偏差引起的关于时间的一次项。在此基础上,分析了两行轨道根数(TLE)单点拟合发散的初始偏差影响因素,给出了提高单点推衍精度的初始偏差条件,该条件也对应高精度轨道预报采样拟合中残差平方和最小的最优条件,同时对影响残差发散的主要因子进行了分离,为TLE的选择和使用提供了理论依据。
论文采用理论分析与数值仿真相结合的方法,重点探讨了天地协同低轨空间监视中涉及的误差传播和轨道确定等问题,研究成果对我国空间监视系统的设计和发展具有一定的参考价值。
Within the confines of the territory, the space-based sensors should be explored and demonstrated while the ground-based sensors are developed to improve the space surveillance system for low earth orbit (LEO). Assumed that the space-based radar (SBR) net cooperates with the ground-based radar (GBR) for LEO surveillance, the thesis investigates the site arrangement, error propagation and differential correction with observations from SBRs.
The criterion for choosing the site of the GBR is presented. The analysis of the positioning precision about the GBR with multi-bases shows that the optimal arrangement is symmetrical in geometry if the numbers of the auxiliary sensors is over three. And with the optimal arrangement, the high precision of orbit determination could be achieved only with the range measurements from three or more auxiliary sensors, if the standard deviation of the angle measurements is much worse than that of range measurement.
The Covariance Analysis DEscribing function Technique (CADET) is implemented in high-precision orbit prediction to obtain the propagation of the mean vector and covariance supposed that the state is a gaussian variable. Compared with the linear variance equation i.e. matrix Ricatti equation, the quasi-linear approximation technique considers the second order of the partial derivatives of the differential equation with respect to the state vector which is more precise in statistics. According to the simulation, the along-track error in position and the radial error in velocity are dominative during propagation. And the propagating precision is determined by the priori standard deviation and the state noise.
The orbit determination algorithm combined with the high-precision orbit propagation and differential correction is presented for the space surveillance with the cooperation of the GBR and the SBRs. In other words the latest estimated mean and covariance are propagated until the time that observations are available. And the predicted mean and covariance at that time as the priori are updated with the observations, then the propagation continues.
For the precision of the sparse observational data from SBRs the pre-process based on 3σrule is derived. The simulation shows that the high-precision orbit propagation and update by the extended Kalman filter (EKF) can control the along-track error in position and the radial error in velocity very well. While the cross-track error could not be controlled in whole with the low precision measurement of range rate almost helpless against cross-track error in velocity if the observation is single set. And this could be explained by the Hill equation clearly.
When the short-arc dense observational data is used in differential correction, the precision is improved and the cross-error is controlled well in comparison with the sparse data. And when the unscented Kalman filter (UKF) is applied to update, the filter converges quicker and the precision is higher than that of EKF, especially the cross-track error in velocity could be controlled much better.
The error propagation resulted from initial deviation could be described by Hill equation to explain the numerical simulation above: the along-track error in position has the linear factor about time so does the radial error in velocity, while the equation of the cross-error is a simple harmonic oscillator. And the initial deviation condition is given by Hill equation to control the error propagation of the TLE generated from the single point. And the condition is consistent with the minimal sum of squares of residuals of the TLE generated from sampling. Also the main divergent factor in initial deviation is separated, which may be operational in selecting TLE.
The thesis mainly discusses the error propagation and the orbit determination in space surveillance with the cooperation of the SBRs and the GBR, and the achievement could be some help for the design and the development of the national space surveillance system.
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