Comparison of Initial Orbit Determination Methods with Very-Short-Arc Angle Observations from LEO Space Debris
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摘要: 光学观测是空间目标观测中最常见的一种观测方式。采用扫描模式工作时光学观测得到的观测弧段弧长通常很短,有时甚至不到被观测空间目标运行周期的1%,这样的角度数据被称为甚短弧角度数据。基于近圆LEO空间碎片地基实测场景,研究比较仅利用角度数据进行初始轨道确定常用方法的性能差异,分析观测弧长对不同初轨确定算法的定轨成功率和误差的影响,为初轨确定工作提供参考。对比分析了常用的几种方法,包括Laplace方法、Gauss方法、Gooding方法和近几年提出的距离搜索算法等。大规模实测数据处理结果显示,距离搜索算法的成功率高于90%,初轨半长轴统计误差仅为25 km。初轨结果表明,距离搜索算法定轨成功率高于其他算法。研究成果可为解决空间碎片初轨确定问题提供参考。Abstract: Optical observation is the most common observation method for space objects. When optical telescopes work in scanning mode, the obtained observation arc length is usually very short, even less than 1% of the orbital period of the observed space object. And such angle observation arc is called Very-Short-Arc (VSA) angle observation. Based on the VSA of the near-circular LEO space debris, this paper studies the performance differences of commonly used methods for initial orbit determination. The influence of observation arc length on the success rate and error of different initial orbit determination algorithms is analyzed. The results can provide reference for initial orbit determination. Several commonly used methods, such as Laplace method, Gauss method, Gooding method and Range-Search (RS) algorithm, proposed in recent years, are compared and analyzed. The results of large-scale VSA show that the success rate of the RS algorithm is higher than 90%, and the statistical error of the semi-major axis of the initial orbit elements is only 25 km. Results show that the succeed rate of RS method is better than other algorithms. The research results can provide reference for subsequent observation data processing.
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表 1 仿真地基监测LEO目标10~30 s弧长数据初轨结果
Table 1. IOD results of the arcs with length ranging from 10~30 s of LEO objects with ground-based observations
方法 观测误差
RMS/( " )成功率/(%) 半长轴误差
/kmGauss 0 96.0 50 0.5 92.5 80 5 40.0 4000 10 32.5 5000 Laplace 0 92.5 170 0.5 41.7 220 5 2.5 250 10 0.81 270 Gooding 0 97.5 55 0.5 64.2 345 5 8.3 800 10 4.2 830 表 2 仿真地基监测LEO目标30~60 s弧长数据初轨结果
Table 2. IOD results of the arcs with length ranging from 30~60 s of LEO objects with ground-based observations
方法 观测误差
RMS/( " )成功率/(%) 半长轴误差
/kmGauss 0 100.0 50 0.5 92.5 60 5 85.0 1500 10 80.0 4500 Laplace 0 29.2 300 0.5 35.0 320 5 21.7 290 10 10.8 260 Gooding 0 96.6 50 0.5 95.8 280 5 56.7 300 10 30.8 300 表 3 识别出的空间目标和观测弧段数量
Table 3. Number of the identified space objects and the arcs
日期 观测弧段
数量识别出所属目
标的弧段数量识别出的空
间目标数量2017–08–24 4100 3458 1299 2017–08–25 1626 1396 594 2017–08–26 4894 4163 1587 表 4 地基光电阵监测LEO目标观测数据初轨结果
Table 4. IOD results of space objects observed by the ground-based EO array
方法 弧长/s 成功率/(%) 半长轴误差/km Gauss 10~30 52.5 1800 30~60 94.4 600 Laplace 10~30 8.6 250 30~60 27.6 260 Gooding 10~30 33.1 265 30~60 81.2 285 RS method 10~30 72.10 50 30~60 87.86 25 表 5 仿真天基监测LEO目标10~30 s弧长数据初轨确定结果
Table 5. IOD results of the arcs with length ranging in 10~30 s of LEO objects with space-based observations
方法 观测误差
RMS/(")成功率/(%) 半长轴误差/km Gauss 0 72.1 430 0.5 57.6 500 5 34.7 2000 10 29.5 4000 Gooding 0 80.1 190 0.5 67.2 290 5 54.6 570 10 47.8 780 表 6 仿真天基监测LEO目标30~60 s弧长数据初轨确定结果
Table 6. IOD results of the arcs with length ranging in 30~60 s of LEO objects with space-based observations
方法 观测误差
RMS/(")成功率/(%) 半长轴误差/km Gauss 0 69.1 130 0.5 68.2 150 5 61.0 500 10 59.0 800 Gooding 0 98.0 130 0.5 90.0 230 5 58.8 380 10 32.4 522 -
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