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以灵敏度(14 Mv)、视场(15°)为例,像平面的平均星数接近58 000颗,如表1所示。像平面将充斥大量恒星,背景不仅包括暗黑的天空背景,还包括由恒星散射光造成的整个像面的不均匀分布,这对恒星目标的提取、剔除,进而捕获目标提出重大挑战。
表 1 星数与不同星等、视场之间的关系
Table 1. Stellar population for different magnitude and field of view
Item Magnitude ≤7.0 ≤8.0 ≤10 ≤11 ≤12 ≤13 ≤14 Star number in 4π space 12 890 38 082 297 267 776 664 1 933 747 4 614 474 10 586 016 Average star number in ${15^ \circ }$ 70.3 207.7 1 621.3 4 236 10 547 25 168 57 738 即使采用硬件流水技术加速星点提取,目标提取同样存在问题。如图1所示,对于灵敏度更高的天基设施,虽然运行过程中只对某参数进行了微弱调整,却导致背景提取目标数出现大范围波动,与常规星敏感器星点提取特征相差较大。
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空间目标形貌复杂,材料特性未知,为计算其光学特性,一般会采用简化模型,将其等效为规则形貌的漫反射体。如图2所示,在O-XYZ本体坐标系中,目标的单位矢量与Z轴夹角为
$\varphi $ ,与X轴夹角为$\theta $ ,太阳矢量方向沿着Y轴方向,目标单位矢量与太阳矢量的夹角为$\vartheta $ ,太阳矢量与观测矢量夹角为$\gamma $ ,与观测矢量的夹角为$\beta $ ,与观测平台的距离为$L$ ,目标的漫反射率为${\sigma _{{s}}}$ ,不考虑地球散射光的影响,则空间目标在观测平台处产生的可见光照度为:图 2 空间目标在观测相机处幅照度示意图
Figure 2. Diagram of the luminance of a space target at the observation camera site
$${E_{ob}} = {\left( {\pi {L^2}} \right)^{ - 1}}{E_{sun}}\int\limits_0^{2\pi } {\int\limits_0^\pi {{\sigma _s}{r^2}\sin \varphi \cos \vartheta \cos \beta d\varphi d\theta } } ,\vartheta ,\beta \leqslant 90°,$$ 在同样敏感器配置下,E0为零等星的能量,则空间目标的等价星等可通过下式得到:
$$m = - 2.512 \times \log \left( {\frac{{{E_{{\rm{ob}}}}}}{{{E_0}}}} \right)$$ (1) 探测距离与星等的关系
设目标漫反射率
${\sigma _{{s}}}{\rm{ = }}0.2$ ,太阳与观测平台夹角$\gamma {\rm{ = }}{0^ \circ }$ ,空间目标大小10 cm球体,可获得不同观测距离与星等的关系如表2所示。表 2 空间目标不同观测距离与星等之间的关系
Table 2. Visual magnitude of space targets at different observation distances
Item Value Range L/km 800 900 1 000 1 100 1 200 1 300 1 400 Magnitude 10.48 10.74 10.97 11.18 11.37 11.54 11.70 (2) 目标相位角与星等的关系
亮度特征与距离有关,假设卫星轨道高度600 km,空间目标为10 cm球体,目标漫反射率
${\sigma _{{s}}} = 0.2$ ,固定距离L = 1 400 km,目标相位角(太阳视线与观测视线的夹角)与星等之间的关系如表3所示。表 3 空间目标不同的相位角与星等之间的关系
Table 3. Visual magnitude of space target for different solar exclusive angle
$\gamma $ 0 10 20 30 40 50 60 70 80 90 Magnitude 11.99 12.14 12.20 12.24 12.28 12.32 12.40 12.52 12.70 12.95 实际上,空间目标包括平面、球面、圆锥面、不规则几何等多种复杂形貌。除上述因素外,空间目标的姿态、表面材料性质等是另一大因素,不同材质的散射特性非常不同,可以预知,相同的太阳入射场景,其不同方向的目标辐射亮度也将不同。可见,复杂的光变曲线、目标凌星、探测器固有缺陷导致的高亮瞬态噪点等这些探测的固有因素,给目标身份的确定、目标长时关联带来巨大困难。
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FPGA完成整幅星图的预处理,点源提取等任务,提取结果见图3。如图3所示,当FPGA资源量从5 000增长到40 000时,实际处理的星图面积也从1/8提升到1,说明背景恒星较多时,较少的FPGA资源难以满足星图处理需求。
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拍摄真实的夜空图,提取像元数与提取星数之间的关系参见表4,不同的背景参数
$\kappa $ (参见2.1节)实施效果参见图4。表 4 不同背景参数所达到的提取指标
Table 4. Outcomes for different sets of background parameter κ
$\kappa $ Extracted pixels Extracted stars Average pixels per star Star number Extraction probability 4 4 453 251 17.74 507 49.50% 3.5 5 237 283 21.14 507 55.80% 3 6 361 327 19.45 507 64.49% 2.5 8 602 407 18.51 507 80.27% 2 13 883 500 17.74 507 98.6% 由图4可知,当
$\kappa = 2$ 时,能将图中500颗恒星提出,提取成功率达到98.6%。但同时看到,需要提取上万像素点才能达到上述要求,这对星载资源处理提出了重大挑战。 -
原始图像及处理结果参见图5,图(a)为原始图像,图(b)为目标图像,图(c)为证认后的目标轨迹。有效提取的7个疑似目标中,对应图(b),绿色(1),蓝色(2),红色(3),紫色(4)是真实的运动目标,已经被有效提取,对于其他干扰点,则全部滤除。
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研制了具有高灵敏度目标探测功能的载荷并进行了地面试验,获得了不同天区星图和空间目标数据。地面星图经UCAC星表进行分析,灵敏度接近14 Mv,参见图6。
图7为拍摄的运动目标图像(包括4颗目标),经过处理后的结果参见图7(a),运动目标的识别结果参见图7(b)。由图7可知,图像中的4个目标全部被识别出来,对于中间轨迹中断、速度畸变情况,轨迹关联做了较好处理,能够将多次断连的轨迹关联起来。
High sensitive automatic detection technique for space objects
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摘要: 在线捕获GEO远距离暗弱目标,实时监视轨道目标状态对于空间安全具有越来越重要的意义。在灵敏度接近14 Mv情况下,密集恒星、恒星散射光效应将极大影响目标探测。为解决上述问题,提出一种背景稠密恒星同步剔除和空间目标证认方法,利用目标短时间内规律运行的特征,实现目标的捕获、分类和在线跟踪,地面仿真和试验充分验证了方法的有效性和准确性。文中方法对于太阳系内行星、小行星探测等深空项目亦具有重要的借鉴意义。Abstract: In orbit capturing and real-time monitoring the status of distant dimmer space targets is of vital importance for space safety. However, when the sensitivity approaches 14 magnitude, the intensive stellar population, the stellar scattering light will reduce the detection efficiency greatly, resulting in a limited detection range and ability. To solve this problem, a simple method for space object capturing, classification and online tracking was presented, synchronously eliminating the dense background stars and sequentially extracting the possible space targets, utilizing the regular motion of a moving object in a short timespan. Ground simulations and tests validate the effectiveness and accuracy of the method. It seems that this method can also be used as a basic function for deep space projects, such as asteroid and planet exploration in the solar system.
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表 1 星数与不同星等、视场之间的关系
Table 1. Stellar population for different magnitude and field of view
Item Magnitude ≤7.0 ≤8.0 ≤10 ≤11 ≤12 ≤13 ≤14 Star number in 4π space 12 890 38 082 297 267 776 664 1 933 747 4 614 474 10 586 016 Average star number in ${15^ \circ }$ 70.3 207.7 1 621.3 4 236 10 547 25 168 57 738 表 2 空间目标不同观测距离与星等之间的关系
Table 2. Visual magnitude of space targets at different observation distances
Item Value Range L/km 800 900 1 000 1 100 1 200 1 300 1 400 Magnitude 10.48 10.74 10.97 11.18 11.37 11.54 11.70 表 3 空间目标不同的相位角与星等之间的关系
Table 3. Visual magnitude of space target for different solar exclusive angle
$\gamma $ 0 10 20 30 40 50 60 70 80 90 Magnitude 11.99 12.14 12.20 12.24 12.28 12.32 12.40 12.52 12.70 12.95 表 4 不同背景参数所达到的提取指标
Table 4. Outcomes for different sets of background parameter κ
$\kappa $ Extracted pixels Extracted stars Average pixels per star Star number Extraction probability 4 4 453 251 17.74 507 49.50% 3.5 5 237 283 21.14 507 55.80% 3 6 361 327 19.45 507 64.49% 2.5 8 602 407 18.51 507 80.27% 2 13 883 500 17.74 507 98.6% -
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