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Xing Hui, Zhang Yanxiu, Lei Ping, Ma Na, Wang Juanfeng, Kang Dayong. Research on ground detection model and test of optical reconnaissance satellite[J]. Infrared and Laser Engineering, 2022, 51(9): 20210978. doi: 10.3788/IRLA20210978
Citation: Xing Hui, Zhang Yanxiu, Lei Ping, Ma Na, Wang Juanfeng, Kang Dayong. Research on ground detection model and test of optical reconnaissance satellite[J]. Infrared and Laser Engineering, 2022, 51(9): 20210978. doi: 10.3788/IRLA20210978

Research on ground detection model and test of optical reconnaissance satellite

doi: 10.3788/IRLA20210978
  • Received Date: 2022-02-20
  • Rev Recd Date: 2022-03-15
  • Publish Date: 2022-09-28
  • In the field of space optoelectronic countermeasures, the real-time on-orbit tracking of satellites by ground optoelectronic tracking equipment is a prerequisite for interference countermeasures, and optical reconnaissance satellites mostly operate in sun-synchronous orbits. Firstly, according to the optical reconnaissance satellite earth observation was apparent under vertical or lateral swing down more visual, and ground jamming equipment must be located within the optical reconnaissance satellite view characteristic, through independent mathematical deduction, the mathematical model of satellite and ground equipment location relationship between each other, including the ground photoelectric devices of optical reconnaissance satellite observation distance and the mathematical expression of observation angle; Secondly, according to the radiation scattering characteristics of the satellite and their solar panel, as well as the scattering transmission characteristics of the earth's atmospheric environment and terrain background in the visual band, the mathematical model of the scattering radiation transmission of the star and the observation path was derived, and the mathematical expression of the illuminance on the focal plane of photoelectric equipment which represent the target and the background respectively were obtained; Finally, based on the atmospheric scintillation characteristics of the scattered radiation of reconnaissance satellites, using probability statistical theory and engineering experience analysis, it was pointed out that the decisive factor affecting the detection probability was the change in the target background contrast caused by the atmospheric scintillation, based on this, a new detection probability model of the optical reconnaissance satellite by ground optoelectronic equipment was proposed. The actual test data verifies that the calculated results of the model in this paper are in good agreement with the actual measured data.
  • [1] Gan Chuxiong, Liu Jixiang. The Overall Design of Ballistic Missiles and Launch Vehicles [M]. Beijing: National Defense Industry Press, 1993: 301-316. (in Chinese)
    [2] Li Jingzhen. Optical Manual [M]. Xi'an: Shaanxi Science and Technology Press, 2010: 882-885. (in Chinese)
    [3] Zhang Jianqi, Fang Xiaoping. Infrared Physics [M]. Xi'an: Xidian University Press, 2004: 115-117. (in Chinese)
    [4] China Meteorological Administration. Satellite Calibration Field Ground and Typical Surface Object Spectrum Data Set [M]. Beijing: Meteorological Press, 2008: 47-309. (in Chinese)
    [5] Dai Congming, Wei Liliu, Chen Xiuhong. General Atmospheric Radiation Transmission Software (CART) molecular absorption and thermal radiation calculation accuracy verification [J]. Infrared and Laser Engineering, 2013, 42(1): 174-180. (in Chinese)
    [6] Frederick G. Smith, Atmospheric Propagation of Radiation [M]. Bellingham: SPIE Optical Engineering, 1993: 159-201.
    [7] Tatarskii V I. Wave Propagation in a Turbulent Medium [M]. New York: Dover Publications, 1961.
    [8] Luo Zhimin, Wu Zhensen, Guo Lixin, et al. Research on light wave scintillation in turbulent atmosphere [J]. Journal of Xidian University, 2001, 28: 273-277. (in Chinese)
    [9] Zhang Yixin, Chi Zeying. Transmission and Imaging of Light Waves in the Atmosphere [M]. Beijing: National Defense Industry Press, 1997. (in Chinese)
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Research on ground detection model and test of optical reconnaissance satellite

doi: 10.3788/IRLA20210978
  • The 63891 Units of People’s Liberation Army, Luoyang 471003, China

Abstract: In the field of space optoelectronic countermeasures, the real-time on-orbit tracking of satellites by ground optoelectronic tracking equipment is a prerequisite for interference countermeasures, and optical reconnaissance satellites mostly operate in sun-synchronous orbits. Firstly, according to the optical reconnaissance satellite earth observation was apparent under vertical or lateral swing down more visual, and ground jamming equipment must be located within the optical reconnaissance satellite view characteristic, through independent mathematical deduction, the mathematical model of satellite and ground equipment location relationship between each other, including the ground photoelectric devices of optical reconnaissance satellite observation distance and the mathematical expression of observation angle; Secondly, according to the radiation scattering characteristics of the satellite and their solar panel, as well as the scattering transmission characteristics of the earth's atmospheric environment and terrain background in the visual band, the mathematical model of the scattering radiation transmission of the star and the observation path was derived, and the mathematical expression of the illuminance on the focal plane of photoelectric equipment which represent the target and the background respectively were obtained; Finally, based on the atmospheric scintillation characteristics of the scattered radiation of reconnaissance satellites, using probability statistical theory and engineering experience analysis, it was pointed out that the decisive factor affecting the detection probability was the change in the target background contrast caused by the atmospheric scintillation, based on this, a new detection probability model of the optical reconnaissance satellite by ground optoelectronic equipment was proposed. The actual test data verifies that the calculated results of the model in this paper are in good agreement with the actual measured data.

    • 大量高分辨率光学侦察卫星频繁过境对国土安全构成了严重威胁,对其进行密切的跟踪监视是十分必要的。在空间光电对抗领域,地面电视跟踪设备主要用于卫星的实时在轨跟踪,在稳定跟踪卫星的前提下,地面光电干扰装备才能对卫星实施窄波束强光干扰,对卫星的跟踪性能决定了这类光电干扰装备的干扰效果。地面电视跟踪设备能否成功捕获并跟踪卫星,与卫星轨道参数、星体的目标光学特性、电视跟踪设备探测能力、可见光大气传输特性等因素有关。

      在可见光波段,卫星星体的目标光学特性与其几何形状、姿态、材料反射率等因素有关。对侦察卫星的可见光散射特性的测量与研究,目前主要通过两种方法:(1) 已知卫星几何结构、表面材料时,可通过构建实物缩比模型,并通过模拟光源对该模型照射,模拟在轨卫星的光照条件与仪器观测角度,测量并建立卫星的目标光散射特性模型;(2) 对于无法获知几何结构、表面材料特性的卫星,则需要对卫星进行大量的在轨观测,并结合光照条件、卫星姿态、大气传输等观测条件,对预先建立的仿真模型进行不断的数据修正和校准,逐步逼近真实模型。

      当前,世界航天大国都建立了较为完善的在轨卫星监控网络,这类监控网络主要跟踪监控在轨卫星的轨道参数,光学侦察卫星是其主要监控对象;对于军事应用背景的侦察卫星,除了对其进行轨道监控外,还需针对不同军事应用,对其进行精准定位、连续跟踪、目标特性测量等,建立主要在轨卫星的目标特性模型与数据。根据卫星光学特性模型与轨道特性,可进行目标探测与识别、捕获与跟踪性能预测,并可据此开展相关地面装备的态势规划与布局设计等。

    • 光学侦察卫星一般运行在太阳同步轨道,为了获得较高的地面光学分辨率,其飞行轨道高度一般不超过1000 km。太阳同步轨道的特点是卫星飞行的轨道平面始终与太阳照射方向成固定夹角,太阳同步轨道卫星必须保持轨道面进动角速度与地球公转同步,因此太阳同步轨道的进动角速度为$2\pi /365.25/24/ 3\;600 = {\text{0}}.1991\;\text{μ} {\rm{rad}}{\text{/s}}$。卫星轨道倾角是指卫星运行轨道法线矢量(由右手定则确定)与地球北极极轴指向的夹角,因此卫星公转面与地球自转的赤道平面重合且转动方向相同时为0°轨道倾角,反之则为180°倾角,太阳同步轨道的进动角速度$ \dot \Omega $与轨道倾角$ i $的关系为[1]

      式中:a为卫星轨道半长轴;e为轨道偏心率;$\;{\mu} = 398\;600.5 \;{{\rm{km}}^3}/{{\rm{s}}^2}$为地球引力常数;$ {J_2} = 1.082\;63 \times {10^{ - 3}} $为地球非球形摄动一阶常数;$ {a_e} = 6\;378 \;{\rm{km}} $为地球赤道半径。例如,对于“锁眼”KH-12光学侦察卫星,其轨道近地点300 km、远地点1000 km,则其轨道长轴a=7028 km,偏心率e=0.0498,则其轨道倾角i=97.95º,其轨道运行周期为${T_s} = 2\pi \sqrt {({a^3}/\mu )} = 5\;863.5$ s。因此KH-12卫星为逆行(由南向北)轨道,轨道面与极轴的夹角为7.95°。轨道高度、偏心率、轨道倾角相同的太阳同步轨道,其轨道平面可根据需要选择很多种,典型的如晨昏轨道(卫星始终运行在地球昼夜交界线上空)、昼夜轨道(卫星始终运行在地球当地时正午-午夜线上空)等。

      从地面观测太阳同步轨道卫星时,由于地球曲率的影响,其过境时间与卫星周期、轨道高度、椭圆偏心率等因素有关,光学侦察卫星的轨道高度很低,可近似为圆形轨道。光学侦察卫星对地观测时,一般垂直下视侦察或有一定的侧摆角度,地面设备对其实施跟踪干扰时,必须位于卫星的侦察画幅带范围内,地面设备与卫星轨迹地面投影线的距离一般不超过数百千米,如图1所示。

      Figure 1.  Relationship between satellite transit trajectory and geographic location

      图1(a)中,卫星S沿圆弧线BB′从地平线升起和降落,观测点A与卫星轨迹地面投影线相交于O图1(b)是其地面投影图,GN为地理北极指向。若以卫星升起最高点时刻为0时,观测点与卫星地面投影距离为Rd,则T时刻卫星距离为:

      卫星轨道倾角确定时,不同纬度的卫星轨道地面投影线与北极指向变化很大。将地球按照理想球体处理,如图2所示,箭头指向左上方的圆弧为卫星轨迹地面投影线,其轨道倾角为i,地球表面北纬N°线与卫星轨道投影线相交于O点,穿过O点指向北极的经线为地理北极指向GN。

      Figure 2.  Included angel between satellite transit trajectory and geographic north

      O点处对应的卫星轨迹投影线与地理北极指向的夹角$ \alpha $为:

      如北纬40°线上,KH-12卫星地面投影线指向角约为北偏西10.2°。以地理北极为初始指向,顺时针旋转角度为方位角,则观测方向方位、俯仰角度为:

      获知地面观测点与卫星的相对地理位置关系后,再根据地球与太阳相对运行关系可以得到对应年历、纬度、时间对应的太阳高角和太阳方位角,若卫星过境时刻的太阳方位角$ {\theta _{SA}} $、俯仰角$ {\theta _{SE}} $,则太阳照射方向与观测方向相对卫星的方位、俯仰夹角为:

    • 卫星亮度与太阳照射条件有关,在光度学领域[2],大气层外太阳光照度为1.39×105 lx;在辐射度学领域[3],太阳在大气层外的可见光辐射照度约为632 W/m2。在天文观测领域,常用视星等的概念描述天体的亮度及其在地面形成的照度,定义标准烛光1 m处的照度为1 lx的视星等为0,视星等为M的天体的照度为:

      式中:0E为0等星的照度,视星等0的绝对星等为−13.98,其照度为0E=10−13.98×0.4=2.56×10−6 lx,人眼可视的最暗星体为6等星,则6E=1×10−8 lx。

      对于光学侦察卫星,一般采用大口径对地观测镜头,其外形大致呈圆柱形。由于对地观测的需要,其观测镜头方向一般朝向地面方向,即垂直指向地面的圆柱体。如KH-12直径约4 m,长度约13 m。假定卫星星体为直径d、长度l的均匀朗伯体,大气层外太阳光照度为E0,星体反射率为${I_1} = \dfrac{{{E_0}}}{\pi }lr{\;\rho _1}(1 + \cos {\gamma _A})\cdot \cos [{\theta _{SE}} - {R_d}/{a_e}]\cos [{\theta _E} + {R_d}/{a_e}]$,则地面观测设备观测到的星体太阳光反射辐射强度为:

      公式(9)为简单圆柱体的光散射模型,若卫星星体形状复杂时,普遍采用的方法是:将星体视为很多个小面元平面朗伯体,根据其空间位置进行逐面元求和或积分,小面元${\rm{d}}S$反射率$ \;{\;\rho _s} $、太阳光入射角$ {\gamma _s} $、观测角$ {\theta _s} $的反射辐射强度$ d{I_1} $为:

      若星体可近似简化为规则几何体,且反射率与入射角、观测角为该几何体的空间位置函数,则可对上式进行几何体表面积分,从而获得星体反射辐射强度:

      若星体不能简化为规则几何体,则需要进行小面元辐射求和,获得整个星体的反射辐射强度,即:

      对于太阳同步轨道卫星,其太阳能电池板一般朝向太阳照射方向,可视为平面朗伯体,其可见光波段反射率一般在5%左右,但由于其面积很大,作为星体辐射的一部分不可忽视。根据前文分析,假定太阳能电池板平面法线太阳照射方向相同,太阳能电池板面积A,反射率$ {\;\rho _2} $,则地面观测设备接收的太阳能电池板反射辐射强度为:

      若大气传输透过率为$ {\tau _a} $、观测点距离卫星R时,观测设备入瞳处的星体辐射照度为:

      卫星星体成像到探测器靶面上时,若卫星星体所张立体角小于探测器像元,给定光学系统入瞳D、透过率$ {\tau _0} $、单元探测器面积Ad,则目标在探测器靶面上的辐射照度为:

      若卫星星体在探测器靶面上的成像大于单元探测器,假定卫星星体辐照能量均匀,目标在探测器上的成像面积Sd(大于Ad),则目标在探测器靶面上的辐射照度为:

    • 从地面观测卫星时,还要考虑背景辐射强度,若给定单位立体角的路径亮度LV,光学系统F数(f/D),则单元探测器接收背景辐射照度为:

      不同气象条件、不同光照条件、不同地表反射特性[4]时,观测路径的背景亮度不同,背景亮度可通过辐射传输软件计算,CART是中科院安徽光机所开发的一款辐射传输软件,可获得较高的计算精度[5]图3所示为垂直上行观测路径上、不同太阳天顶角β(º)时,路径亮度Lv(W·m2·sr−1)的计算结果。CART软件计算选取的气象参数为:大陆地区6月大气模式、大陆型气溶胶、能见度23 km、相对湿度50%,地表为草地。

      Figure 3.  Path brightness at different sun zenith angles

    • 大气湍流可导致光强起伏,地面电视跟踪设备探测卫星时,如同人眼观察恒星,存在目标强度的闪烁,强度闪烁与折射率结构常数Cn2有关[6],测量表明,在大气对流层内(高度约10~20 km),白天Cn2随海拔高度h呈-4/3指数下降,地面附近高度1 m的折射率结构常数记为Cn2,则垂直上行观测路径至高度h的平均折射率结构常数为:

      地面附近的大气湍流最强,高度上升20 km,折射率结构常数下降约6个数量级,因此对流层以上高度,大气湍流对光强闪烁的贡献可忽略不计。

      大气湍流引起的光强起伏服从对数正态分布,对于球面波,根据Tatarskii的大气湍流理论[7]和相关研究参考文献[8-9],折射率结构常数Cn2不变时,对数强度起伏方差$ {\sigma _I} $为:

      在可见光波段(0.4~0.76 μm),$ {\sigma _0} $为:

      当观测路径穿越整层大气时,传输路径长度R可用对流层观测路径长度等效,等效路径长度与对流层高度h和观测仰角θ有关,即$ R = h/\sin \theta $。白天,地面附近折射率结构常数Cn2约为10−14 m−2/3量级,按照公式(18),垂直上行传输20 km的平均Cn2(A)=1.5×10−18 m−2/3,根据公式(19)、(20),观测仰角20°时,可得到σI=0.165。观测卫星时,由于观测路径穿越了整层大气,其强度起伏的对数方差可按照上述方法计算。

      假定观测设备探测到的卫星与背景辐射强度均服从对数正态分布,不考虑探测器其它噪声信号时,探测系统从背景信号中检出目标信号的概率Pd为:

      若给定探测概率Pd,可得到对应标准正态分布函数变量值k,从而得到目标与背景辐射强度差值,若给定概率值对应随机变量值为$ \sqrt 2 {\sigma _I}k $,根据探测器成像面上目标背景对比度定义,有:

      以探测概率为97.7%时,对应k=2,按照σI=0.165计算,得到$ C = 0.6 $

    • 以光学侦察卫星典型轨道高度500 km为例,按照圆轨道近似,其角速度约1.107 mrad/s,观测点位于轨道地面投影线垂直中线上,距离为500 km,卫星轨道露出地平线的飞行时间约为0.12 TS=680 s,地面观测站位于北纬40°线上。如图4所示,图(a)绘出了观测距离R随观测时间T的变化情况,图(b)为观测角度$ \theta $随观测距离R变化情况,两条曲线从上到下分别为俯仰和方位角度。假定观测点位于东经110°、北纬40°交点,卫星于10月10日上午10时过境,利用太阳角度计算工具得到太阳方位角136.2°,俯仰角31.6°,根据图4可得到太阳、观测点相对卫星的夹角$ \gamma $随距离R时间的变化情况。

      Figure 4.  Changes in the observation angle and distance during the satellite transit period

      若星体尺寸Φ4 m×13 m、太阳能电池板4 m×6 m,星体反射率0.2、太阳能电池板反射率0.05,根据公式(8)、(14),可计算卫星星等M与观测仰角$ {\theta _E} $的变化关系,如图5所示。如观测仰角10°时,目标卫星亮度约为6等星,此时观测距离2340 km,此时卫星对观测仪器照度约为4.53×10−11 W/m2

      Figure 5.  Brightness of the satellite's magnitude varies with the observation elevation angle

      若假定目标卫星在探测器靶面成像小于一个像元,光学系统口径400 mm、焦距1000 mm、探测器象元10 μm×10 μm、光学系统透过率0.6。根据上节理论模型和条件,距离1350 km时,目标卫星的星等亮度约为3.1等,观测仰角37°,其在探测器靶面的辐射照度为0.54 W/m2,根据上述假设条件,标准气象能见度条件下,利用CART计算的背景亮度为22 (W·m−2·sr−1),由公式(17)可得背景光在探测器靶面的辐射照度为1.66 W/m2。此时目标背景对比度为0.32,刚好满足2.3节提出的探测概率模型约束条件,即前文假设的地面探测设备和探测条件下的探测距离为1350 km。

      图6为地面设备对某过境卫星的试验测量结果。图6的数据表明,跟踪探测过程中卫星亮度闪烁十分明显,跟踪仰角越低,星等亮度起伏越严重,符合前文给出的大气闪烁模型变化规律;跟踪仰角越高,星等亮度越大,变化趋势符合前文给出的星等亮度模型规律。图7为观测仰角20°左右的卫星星等亮度变化数据,其亮度数据主要集中在6.2±0.2星等范围内,强度闪烁方差约占0.2个星等亮度,根据星等亮度定义,则其强度起伏方差的对数值为$ {\sigma _I} = \ln ({10^{0.4 \times 0.2}}) = $ 0.184 ,根据前文计算结果($ {\sigma _I} = 0.165 $)并结合测量条件比对,理论计算值与测量数据吻合度较好。

      Figure 6.  Measured results of transit satellite magnitude brightness

      Figure 7.  Measured results of the transit satellite brightness at 20º elevation

      因此,文中提出的星体探测模型与测量结果的趋势规律一致。在光学侦察卫星轨道数据支持下,可依据该模型推算地面装备的探测距离及仰角,据此开展装备态势预先设计,在目标特性测量数据支持下,可依据卫星亮度变化规律进行目标探测与识别等方面的应用。

    • 侦察卫星星体形状、尺寸、表面反射率等条件,决定了卫星反射太阳光的辐射强度,观测仪器入瞳面积与卫星在探测器靶面的辐射照度呈正比关系,探测器靶面上的背景辐射照度与观测仪器F数呈反比关系;另外,随着距离增大、目标仰角降低,观测路径透过率降低,目标在探测器靶面上的辐射照度也会降低。

      理论模型与试验研究表明,白天探测光学侦察卫星时,太阳光是自然界最大的干扰源,而大气闪烁是影响观测设备探测目标的重要因素,观测仰角越低,观测路径穿越的大气层厚度越大,目标卫星与背景的强度闪烁越大,目标探测越困难。因此,目标星等亮度不是决定地面设备探测能力的唯一因素,在低星等亮度条件下,只要观测路径背景亮度足够低,大气闪烁又满足探测概率条件时,观测设备依然可以稳定探测跟踪目标。

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