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以Celestrak网站公开的Fengyun 1 C、Iidium-33编目轨道数据库为参考碎片编目信息进行了碎片识别方法的仿真验证,仿真流程如图8所示。
随机生成初始时刻,筛选该时刻光轴指向的天区中可见恒星与碎片并生成仿真星图。星图中碎片的位置由TLE与SGP4模型预报得到。
分别采用DTW与轨迹形貌差异量化检验融合的碎片识别方法、轨迹直线拟合参数误差检验碎片识别方法进行仿真星图中空间碎片的识别。分别仿真验证碎片可见性间断问题与目标角速度对两种方法识别稳定性的影响。验证碎片可见性间断对识别稳定性的影响时,生成轨道高度相似的碎片TLE,随即从姿态连续变化的20帧星图中剔除一定帧数模拟碎片可见性间断;验证碎片角速度对识别稳定性的影响时,保持剔除星图帧数不变,生成轨道高度不同的碎片TLE,模拟碎片角速度差异。
考虑姿态指向误差三轴各
$\pm 3''(3\sigma )$ 、质心提取误差UV方向各$ \pm 0.5 \;{\rm{pixel}}(3\sigma )$ ,真实轨迹与预报轨迹间随机误差服从高斯分布$S \sim N\left( {0,0.258\;1} \right)$ 。取随机误差分布的置信区间为$1.5\sigma $ 、轨迹长度误差阈值为${{{T}}_l}{\text{ = 0}}{{.35 \;{\rm{pixel}}}}$ 、轨迹斜率误差为${T_\theta } = {0.808^{ - 2.805{\omega _{\rm{pixel}}}}} + 0.02$ ,其中${\omega _{\rm{pixel}}}$ 为曝光时间内碎片在像面上移动的像素数。表1、表2分别为两种方法的碎片识别结果。其中,方法1为轨迹直线拟合参数误差检验识别法;方法2为DTW与轨迹形貌差异量化检验融合识别法。由统计结果可以看出,当碎片可见性连续且角速度较大时,两种方法均能实现碎片稳定识别。随着数据连续率下降或碎片角速度减小,轨迹直线拟合参数误差检验识别法成功识别碎片数目占可见碎片总数的比例逐渐下降,而DTW与轨迹形貌差异量化检验融合识别法则能保证全部碎片稳定识别。
Simulated frame num Data continuity rate Angular rate of debris/(″)·s−1 Simulated total debris Proportion of identified number to the total Method1 Method2 20 100% 2 700 100 97.1% 98.3% 20 90% 2 700 100 90.1% 97.6% 20 80% 2 700 100 83.6% 100.0% 20 70% 2 700 100 77.2% 96.7% 20 60% 2 700 100 72.0% 99.1% 20 50% 2 700 100 67.8% 98.5% Table 1. Influence of data continuity rate on the identification stability between two methods
Simulated frame num Data continuity rate Angular rate of debris/(″)·s−1 Simulated total debris Proportion of identified number to the total Method1 Method2 20 60% 3 600 100 98.3% 100% 20 60% 2 700 100 72.0% 96.2% 20 60% 1 500 100 45.3% 97.5% 20 60% 720 100 26.1% 99.7% 20 60% 360 100 10.6% 98.3% 20 60% 200 100 0 97.1% Table 2. Influence of angular rate of debris on the identification stability between two methods
分析发现,轨迹直线拟合参数误差检验法识别失败多由于轨迹直线拟合后斜率误差超过阈值引起。下面分析数据连续率和碎片角速度对轨迹拟合斜率误差的影响。以仿真中两个可见碎片为例,分别绘制两碎片仿真观测数据在数据连续率为100%、数据连续率为50%时的碎片轨迹以及轨迹直线拟合的结果如图9、图10所示。碎片轨迹的拟合斜率及拟合斜率误差见表3。
Figure 9. Debris 1 trajectory fitting results. (a) Data continuity rate 100%; (b) Data continuity rate 50%
Figure 10. Debris 2 trajectory fitting results. (a) Data continuity rate 100%; (b) Data continuity rate 50%
Name Do not extract simulated observations Extract 10 frames from the simulated images Fitting slope Error Fitting slope Error Real Predicted Real Predicted Debris 1 17.587 17.885 0.298 17.743 17.471 0.272 Debris 2 0.710 4.236 3.526 −0.066 2 4.411 4.477 Table 3. Fitting slope and error of simulation samples
由碎片1、2的轨迹拟合结果对比可以看出,碎片1角速度较大,轨迹较长,真实轨迹与预报轨迹间的误差对拟合斜率影响不大,碎片可见性间断对碎片1的斜率拟合结果没有明显影响;但碎片2速度较小,轨迹较短,拟合斜率受真实轨迹与预报轨迹间的误差影响较大,此时碎片可见性间断加剧了误差对斜率拟合的影响,进而导致斜率误差不满足阈值限制。仿真结果表明,当碎片相对任务航天器运动角速度在一个积分时间内小于0.01°时轨迹直线拟合参数误差检验识别法失效。
综上,轨迹直线拟合参数误差检验识别法的识别稳定性易受碎片角速度、碎片可见性间断问题的影响,而DTW与轨迹形貌差异量化检验融合的碎片识别方法则是一种能实现碎片稳定识别的方法。
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采用某型号光学相机进行了四次观星实验。实验所用光学相机视场20°×20°、灵敏度7 mV、像面大小1024×1024、曝光时间为0.1 s。由于观测距离限制,敏感器无法实现对空间碎片的地面观测,因此实验以轨道高度低于碎片的低轨卫星为观测对象。实验前根据网站Heavens Above提供观测时段卫星过境信息,筛选出敏感器可见卫星并记录其TLE作为编目信息数据库。
Cosmos-2344卫星于2021年6月3日21:15:49.468 - 21:15:52.383经过敏感器视场时的真实轨迹与预报轨迹如图11所示。可以看出,低轨卫星观测结果与碎片特征建模结果类似,但卫星相对碎片姿态稳定能力较好,因此连续可见性相对较好。
四次观星实验共计观测到低轨卫星20个,分别采用DTW与轨迹形貌差异量化检验融合的碎片识别方法、轨迹直线拟合参数误差检验碎片识别方法进行实拍星图中空间目标的识别。其中,DTW与轨迹形貌差异量化检验融合识别法在目标通过光学相机视场的全过程中均能稳定识别,而轨迹直线拟合参数误差检验识别法在目标可见性较差的时段会出现关联失败的情况。
实验中每2 s进行一次目标识别,以其中3个目标为例,分别统计目标通过光学相机视场的全过程中两种方法成功识别次数占卫星在视场中停留时间内识别总次数的比例。统计结果见表4。其中,方法1为轨迹直线拟合参数误差检验识别法;方法2为DTW与轨迹形貌差异量化检验融合识别法。
Name Zenith angle/(°) Magnitudes mV Total identification times Proportion of identification times to the total Method1 Method2 Object 1 87 3.5 13 100% 100% Object 2 84 4.0 10 90% 100% Object 3 81 4.6 11 72.7% 100% Table 4. Identification results of low-orbit satellites in stargazing experiments
目标1高度角高且亮度较大,目标轨迹靠近像面中心且可见性较好,此时两种方法均能稳定识别。随着目标轨迹偏向视场边缘且亮度下降,目标可见性及质心提取精度变差,轨迹直线拟合参数误差检验识别法稳定性下降,而DTW与轨迹形貌差异量化检验融合识别法则仍能保持稳定识别。
综上,DTW与轨迹形貌差异量化检验融合识别法是一种有效的空间碎片天基识别方法,在碎片真实轨迹可见性间断、质心提取精度较差时能保持稳定的识别能力。
Space-based identification method for space debris based on trajectory consistency detection
doi: 10.3788/IRLA20220076
- Received Date: 2022-05-10
- Rev Recd Date: 2022-06-25
- Publish Date: 2022-11-30
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Key words:
- space debris /
- space-based observation /
- trajectories consistency detection /
- statistical testing
Abstract: Aiming at on-orbit correlation between space-based observations and cataloging of space debris, observation model of space-based optical cameras for debris was established, the impact of on-orbit environment on observations was analyzed, furthermore, a space debris identification method based on trajectory consistency detection was designed. In order to satisfy the applications on-orbit, a debris identification method, fusion of DTW and trajectory topography difference quantification, was proposed. Firstly, using DTW to screen out one predicted trajectory which is closest to the real trajectory; Further, quantifying the morphology difference between the closest trajectories found in the first step as the standard deviation of the total error between them; Finally, using statistical testing to confirm the consistency between the two trajectories. The two trajectories were consistent means that the debris was identified successfully. The comparison of the stability between the method proposed in this paper and the method based on trajectory line fitting and parameter error testing was carried out, and the results demonstrate that, method based on fusion of DTW and trajectory topography difference quantification is the more stable method, and the stability is improved by 56.5% compared with another method. The method proposed in this paper is not being affected by the factors such as debris motion characteristics and observation environment, and can be widely used in satellite perception and protection.