Jitter Detection of ZY3-02 Satellite Platform Using Phase-Correlation Registration Based on Symmetrical Energy Distribution
1 引言
卫星平台颤振是指卫星在轨运行期间,平台的姿态控制、太阳帆板调整、星上运动部件周期性运动或因变轨冷热交变等因素引发的一种幅值较小的振动[1-2],它不仅会影响星体内部之间的安装关系,还会造成数据获取异常,导致后续数据处理难度较大或产品质量较差。因此,平台颤振探测是高分辨率对地观测卫星数据处理过程中的必要环节[3-5],也是高分辨率对地观测卫星研究的重点和难点。
卫星平台颤振探测方法近年来取得了一定发展,根据探测所依赖的参考基准,可将其归纳为4类:基于角位移传感器高频数据的探测[6-7]、基于密集地面控制的探测[8-9]、基于光学影像及其产品的探测[10-12]和基于卫星辅助数据的探测[13]。
2016年5月30日,资源三号02星在太原卫星发射中心成功进入预定轨道[14]。资源三号02星是继资源三号01星之后的又一颗高分辨率立体测图业务卫星。双星组网运行,大幅提高了我国1∶50000立体测图信息源的获取能力。目前,针对资源三号01星平台颤振探测的研究较多,结合多光谱相机各谱段电荷耦合器件(CCD)之间的安装关系,利用高精度亚像素相位相关配准算法获取多光谱各谱段影像的视差曲线,最终得到平台的颤振情况。亚像素相位相关配准算法根据计算原理包括三类:拟合插值[15-16]、奇异值分解[17-18]和局部上采样[19-20]。局部上采样亚像素相位相关配准采用零填充的方式将频域灰度矩阵放大后再进行互相关,具有理论简单的特点,但配准精度难以达到设计值,且计算量较大。奇异值分解亚像素相位相关配准的核心是奇异值分解和相位解缠,具有较高的抗干扰性,但理论复杂,且解缠过程易引入不确定解。拟合插值亚像素相位相关配准是对互相关信息逆变换后的最优值计算,配准精度取决于最优值的提取精度,受影像质量的影响较大。研究结果表明:资源三号01星平台颤振的频率为0.65 Hz左右,在轨初期的振幅较大,可达到3″,在轨稳定后,振幅小于1″。资源三号02星与01星采用相同的平台,部分载荷进行了升级,且新增了一套实验性激光测高载荷。为了探测资源三号02星的平台颤振情况,考虑到资源三号02星多光谱影像数据质量较优,本文在拟合插值亚像素相位相关配准方法范畴内提出了一种基于能量对称的相位相关配准算法,采用模拟数据和真实数据验证所提配准算法的精确性和可靠性,通过高精度亚像素的密集配准获取逐像素的视差图,根据平台的线性平滑运动特性拟合平台的颤振曲线,利用扩展卡尔曼滤波(EKF)处理原始星敏感器数据和陀螺数据,得到卫星平台的真实姿态数据,最后基于真实的平台姿态数据对颤振探测结果进行复合验证。
2 卫星平台颤振探测
平台颤振探测对遥感卫星而言具有重要价值,学者们针对多颗遥感卫星平台开展了研究工作,颤振探测结果如表1所示[21]。可以看出,不同的卫星因搭载载荷、内部安装关系、轨道高度等不同,颤振的频率和振幅也不尽相同。
2.1 资源三号02星多光谱相机结构
资源三号02星搭载的多光谱相机采用多色TDI CCD推扫式成像系统。为了更好地获取地面的多光谱信息,各波段CCD需紧密安装在同一扫描列上,TDI CCD的物理特性使得每个波段之间均存在固定的物理间隔,导致各波段在成像上具有时间差。各波段CCD成像示意图如图1所示。
图 1. 资源三号02星多光谱相机成像示意图
Fig. 1. Schematic of multi-spectral camera imaging on ZY3-02 satellite
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资源三号02星多光谱相机包含蓝、绿、红和近红外4个波段,依次记为B1、B2、B3和B4,地面分辨率均为5.8 m。多光谱各波段共视场成像,即同一时刻各波段CCD拍摄区域对应地面相隔一定距离的地面区域,同一区域被各波段CCD在不同的连续时刻拍摄到。每个波段由3片CCD组成,每片CCD包含3072个探测元器件。为了方便后期进行影像拼接,波段内相邻CCD之间具有195 pixel的重叠,每个像素大小为0.02 mm。在相机焦平面上,4个波段线阵CCD器件在沿轨方向上依次平行摆放,其不同谱段各片CCD的安装物理关系如图2所示。
多光谱相机相邻谱段同列CCD之间的安装间隔固定,卫星在飞行过程中相邻谱段CCD对同一地物不同时刻成像,获取的影像为含有微小时间差异的影像集。影像对中的各影像是在不同时刻获取的,通过高精度的影像配准能够获得微小时间内卫星平台相对姿态变化的信息。
表 1. 不同卫星平台颤振的频率和振幅
Table 1. Jitter frequency and amplitude of different satellite platforms
Satellite or sensor | Launch year | Frequencya /Hz | Amplitudeb /m |
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ISS[22-23] | 1993 | 0.01-300.00 | - | ETS-VI[13] | 1994 | 0.39-250.00 | - | MOC-NA[3] | 1996 | 1-4 | ≈15 | ASTER[4,24-25] | 1999 | 1.5-1.6 | 6-7 | QuickBird [4] | 2001 | 1.0, 4.3 | 2.5, 0.1 | SPOT 5[4] | 2002 | ≈0.003 | ≈20 | ALSat-1[26] | 2002 | 0.5 | - | Nigeria Sat[26] | 2003 | 0.5 | - | UK-DMC[26] | 2003 | 0.6 | - | MEX-HRSC[27-28] | 2003 | 0.1-0.2, 1.7 | 8 | HiRISE[4,29] | 2005 | ≈1.6 | ≈1 | Beijing-1[30] | 2005 | 200 | 3 | ALOS[31-32] | 2006 | 6-7, 60-70 | 1000, 100 | Kompsat-2[33] | 2006 | 210 | 0.14 | LROC[29,34] | 2009 | 6 | 0.1-1.0 | Mapping Satellite-1[35] | 2010 | 0.105, 0.635, 4.000 | 0.2, 0.1, 0.1 | Pleiades-HR[22] | 2011 | 70.9-78.4 | 0.14 | ZY3-01[5,10,12,36-37] | 2012 | 0.6-0.7 | 2.5-7.5 | Yaogan-26[6] | 2014 | 100, 200, 300 | 0.1, 0.1, 0.1 | aSatellite attitude jitter frequency may be detected in roll, pitch, or both; the information listed here are from either or both. bThe amplitude has been transformed from on-orbit arcsec or pixel to ground meter (from satellite to ground), which can show the influence of jitter intuitively. Amplitudes not listed in existing records and research are indicated by “-”. |
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图 2. 多光谱相机不同波段各片间的安装关系
Fig. 2. Installation relation among CCDs at different spectral bands in multi-spectral camera
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2.2 基于能量对称的相位相关配准
相位相关影像配准法利用傅里叶变换将待配准的影像块转换到频域进行互相关,只采用影像块频域互功率谱中的相位信息,降低了图像灰度值的影响,减小了对影像内容的依赖,具有较高的抗干扰性[38]。
相位相关影像配准法的原理是基于傅里叶变换的平移特性,即当两影像块只存在平移时,在频率域上体现出一个线性的相位角差。若待配准的两个影像块函数g和f之间的偏移量分别为Δx和Δy,则[22]
对(1)式两边分别进行傅里叶变换,并结合傅里叶变换的平移性质可得
式中:G和F分别为影像g和f的傅里叶变换矩阵。对(2)式变形可得到两影像块的互功率谱函数Q(u,v)为
式中:
为G的共轭。对(3)式所示的互功率谱函数进行傅里叶逆变换,可得到(Δx,Δy)处的单位脉冲函数δ(Δx,Δy)为
式中:fIFT为快速傅里叶逆变换函数。当两影像块为同一区域的影像时,在脉冲函数的(Δx,Δy)处会取得峰值,其他位置处的值则远小于峰值,且接近0。
在基于能量对称的相位相关配准算法中,峰值前后值的大小次序决定着形式略有不同的计算公式,因此峰值计算分3种情况来讨论,当峰值前面的值大于后面的值时,峰值计算示意图如图3所示。
图 3. 能量峰值计算示意图
Fig. 3. Schematic of energy peak calculation
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峰值点B(x2,y2)周围的点A(x1,y1)和C(x3,y3)存在y1>y3的关系。过C点和B点做直线l1,其与过B点垂线的夹角为α,根据能量对称分布可知,存在另外一条直线l2与l1关于峰值点P的垂线对称。因此,从A点以倾角为90°-α做直线l2交l1于P点,其中P点的横坐标x与B点横坐标x2之差x-x2即为亚像素偏移量。
根据图3可知,存在两个几何关系,用公式表示如下:
通过对(5)式进行推导化简,可得一元二次方程:
(6)式可以简化为
式中:a=2(y3-y2);b=10y2-y1-9y3;c=3y1-12y2+9y3。则(7)式根据一元二次方程解可得
其中,满足x1<x<x2的解即为所求。
同理,当峰值点B(x2,y2)周围的点A(x1,y1)和C(x3,y3)存在y1<y3的关系时,可得
利用(7)~(8)式可求得(9)式的x值,其中满足x2<x<x3的解即为所求。
当峰值前面的值小于后面的值时,仅将x1和x3的值调换,推导过程同上。特殊情况下,当峰值点B(x2,y2)周围的点A(x1,y1)和C(x3,y3)存在y1=y3的关系时,则认为影像块无偏移,即x=0。
2.3 卫星姿态复合验证平台颤振
2.3.1 基于波形叠加理论的卫星颤振复原
利用多光谱不同波段间的影像配准获得像方视差,能够探测到平台中存在的颤振,该颤振属于相对姿态变化。为了得到卫星平台绝对姿态的变化,需要采用基于波形叠加理论将相对姿态转化为绝对姿态。
如图4所示,t1时刻,卫星b波段拍摄地面点O,经过L/v时间后,卫星a波段拍摄地面点O,此时的时间为t2(可知t2-t1=L/v),抖动探测的值实际为在t2-t1时间段内卫星平台发生的姿态相对抖动。探测结果可以表示[39]为
式中: f(t1)和f(t2)分别为t1和t2时刻的绝对抖动量;g(t1)为t1时刻的相对抖动量。
根据波形的基本合成与分解理论,在相对抖动的振幅、频率、初相位、常值以及绝对抖动的频率已知的基础上,可以求解绝对抖动模型中的各个参数,(10)式中的各参数可以表示为
式中:af和ag为绝对抖动和相对抖动的振幅;bf和bg为t1时刻绝对抖动和相对抖动的初相位;Δbf为t2时刻相对于t1时刻初相位的变化量。
将(11)式代入(10)式,可以求得af和bf,即:
图 4. 卫星平台抖动探测示意图。(a) t1时刻卫星b波段拍摄地面点O;(b) t2时刻卫星a波段拍摄地面点O
Fig. 4. Schematic of jitter detection of satellite platform. (a) b-band camera scanned ground point O at moment t1; (b) a-band camera scanned ground point O at moment t2
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将(12)式代入(13)式,可进一步简化求解得到
2.3.2 基于联合滤波的姿态确定
星敏陀螺组合的定姿策略是姿态确定系统的一种可靠的方案,可以得到较高的精度[40]。在星敏陀螺联合定姿系统中,陀螺为系统提供相对姿态值,是主要的姿态敏感器,星敏为姿态确定提供绝对姿态值,一般作为陀螺的辅助姿态敏感器,通常利用星敏感器的测量值来修正陀螺的漂移误差等。
星敏的测量方程为
式中:t为时刻;Z(t)为实际观测向量;H(t)为观测矩阵;X(t)为观测变量;V(t)为观测噪声方差阵。
陀螺的测量方程为
式中:ωg为卫星相对惯性空间的转速在本体系中的实际值;ω为卫星相对惯性空间的转速在本体系中的理想值;b为常值漂移;ηg为均值为零的白噪声。
线性连续滤波状态方程为
式中:F(t)=
,[
×]为
的对角阵,
=ωg-
,
为b的估计值;W(t)=
,ηb为均值为零的白噪声。
2.3.3 姿态与颤振相关性验证
通过高精度配准得到的平台颤振数据与利用EKF得到的姿态数据均可以反映平台的姿态变化,将两者之间的系统差值消除后,理论上两者具有较强的一致性。采用皮尔逊相关系数[41]验证颤振探测结果与姿态数据的相关性:
式中:C为列向量i和j的协方差矩阵。相关系数在R矩阵的副对角线上。
3 实验验证与分析
3.1 配准算法精度验证
采用模拟数据和在轨数据,通过逐像素的密集配准获取亚像素配准结果,与其他相位相关配准算法相比,验证所提配准算法(PC)的配准精度。这里的对比算法包括:基于抛物线拟合的相位相关配准(PF)、基于sinc函数拟合的相位相关配准(SC)、基于曲面拟合的相位相关配准(SF)、基于奇异值分解的相位相关配准(SVD)和基于上采样的相位相关配准(UP)。
模拟数据由更高分辨率的影像降采样获取,即在高分辨率影像上截取范围为第1行至第3nline行且第1列至第3nsample列的(1—3nline,1—3nsample)影像块,3倍降采样至(1—nline,1—nsample),作为左影像;在同一张高分辨率影像上截取范围为第2行至第3nline+1行且第2列至第3nsample+1列的(2—3nline+1,2—3nsample+1)影像块,3倍降采样至(1—nline,1—nsample),作为右影像。理论上,左右影像对的逐像素行列方向视差真值为1/3 pixel,能够较好地评价亚像素配准精度。模拟影像对的尺寸为600 pixel×200 pixel(nline=600,nsample=200),理论影像偏移为1/3 pixel。采用6种配准算法获得视差图,为了直观显示,消除视差中的理论偏移,得到如图5所示的配准误差图。
图 5. 模拟数据配准误差图。(a) PC;(b) PF;(c) SC;(d) SF;(e) SVD;(f) UP
Fig. 5. Images of registration error acquired form simulation data. (a) PC; (b) PF; (c) SC; (d) SF; (e) SVD; (f) UP
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由图5可以看出,PC得到的视差整体分布均匀。为了定量获取配准误差,计算配准误差的均值和均方根误差,结果如表2所示,可见,与其他几种算法相比,所提算法的均值和均方根误差(RMSE)最小,具有较大的精度优势。
表 2. 模拟数据配准误差统计值
Table 2. Statistics of registration error acquired form simulation data
Algorithm | Error /pixel |
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Mean | RMSE |
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PC | -0.007 | 0.046 | PF | 0.068 | 0.088 | SC | 0.032 | 0.060 | SF | 0.069 | 0.089 | SVD | 0.143 | 0.156 | UP | -0.078 | 0.085 |
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将6种配准算法应用到在轨数据中,对比各个算法对平台微小颤振引起的像方偏移的探测能力。理论上,卫星在轨飞行期间,平台的颤振平滑性较好,因此探测结果的平滑性可以作为衡量配准精度的一种方法。实验随机选取一景多光谱数据,6种算法的颤振探测结果如图6所示。可见,相较于其他几种算法,PC探测结果具有较好的平滑性,能够反映平台的平滑运动特性。
图 6. 不同算法的在轨数据颤振探测曲线图
Fig. 6. Jitter curves detected from on-orbit data using different algorithms
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所提算法具有较高的配准精度,能够有效获取卫星平台颤振引起的视差,为资源三号02星平台的颤振探测提供了技术参考。
3.2 卫星平台颤振探测实验
3.2.1 实验方案
基于所提算法探测资源三号02星的平台颤振,设计了如图7所示的实验方案。选取多光谱分片CCD影像对(选定CCD1和CCD2的蓝绿谱段),采用基于能量对称的相位相关配准算法获得影像对的视差图,对同一行视差图求均值,计算所有列,得到配准视差曲线,采用卫星姿态叠加理论将相对姿态转化为绝对姿态。卫星姿态确定方法采用EKF方法对星敏和陀螺数据联合滤波,得到高精度的卫星姿态数据。验证视差图得到的姿态与星敏陀螺定姿结果的一致性,最后利用快速傅里叶变换求解平台的颤振频率与振幅。
3.2.2 实验结果及分析
选取2016年7月16日拍摄的718轨108景、2016年8月28日拍摄的1379轨235景、2018年6月7日拍摄的11229轨268景和2018年6月16日拍摄的11365轨257景进行实验。每景多光谱影像包含3组分片CCD影像,每组分片CCD影像由蓝、绿、红和近红外4个谱段组成。选取第1组分片CCD的蓝谱段和绿谱段作为实验数据,采用相位相关配准算法获取视差图,4景影像视差如图8所示。
图 8. 蓝绿谱段间的影像视差图。(a) 718轨;(b) 1379轨;(c) 11229轨;(d) 11365轨
Fig. 8. Parallax images between blue and green spectra. (a) Track 718; (b) track 1379; (c) track 11229; (d) track 11365
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通过影像配准视差图可以直观地发现,影像由于姿态颤振引起的视差具有较明显的规律性。为了进一步定量探测卫星平台的颤振情况,逐行求影像配准视差图的均值,将视差图转化为便于数据分析的二维相对视差曲线图。由于相对视差曲线图仅记录卫星平台在短时间间隔内的相对姿态,为了能有效反应卫星平台的绝对姿态,需要采用(12)式和(14)式将相对视差曲线转化为绝对姿态变化曲线。
为了验证多光谱影像探测颤振的可靠性,采用EKF联合处理原始星敏陀螺数据,将获得的定姿结果作为复合参考数据,依据颤振探测值和姿态值的时间序列,复合叠加对比两者之间的差异。由于卫星平台在消除航偏角和地球曲率影响等过程中引入了线性变化量,故而这里利用一阶多项式拟合抑制姿态数据中部分线性的变化量。复合验证实验结果如图9所示。
光滑曲线为探测得到的平台颤振曲线,折线中的数据点为星敏陀螺联合滤波得到的姿态数据。结合两列数据的相关系数计算结果(图9)可以看出,卫星姿态数据与平台颤振探测曲线具有很高的一致性,验证了探测结果的可靠性。采用快速傅里叶变换对4景影像探测到的颤振曲线进行分析,可以得到资源三号02星卫星平台的颤振信息,如表3所示。
图 9. 卫星姿态数据复合平台颤振图。(a) 718轨;(b) 1379轨;(c) 11229轨;(d) 11365轨
Fig. 9. Satellite attitude data verify platform jitter. (a) Track 718; (b) track 1379; (c) track 11229; (d) track 11365
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表 3. 实验数据的颤振信息
Table 3. Jitter information for experimental data
Track ID | Frequency /Hz | Amplitude /s |
---|
718 | 0.63 | 0.99 | 1379 | 0.63 | 1.12 | 11229 | 0.65 | 0.41 | 11365 | 0.65 | 0.97 |
|
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根据探测结果可知,资源三号02星卫星平台存在的颤振为0.63~0.65 Hz,振幅为0.41″~1.12″,且具有一定的随机性。
4 结论
本课题组提出了一种基于能量对称分布的相位相关配准算法,该算法的配准精度可达0.05 pixel。通过匹配多光谱影像不同谱段的CCD影像,获得了短时间内像方视差变化信息,用以探测资源三号02星平台的颤振信息,采用星敏陀螺数据联合滤波得到的姿态数据作为参考复合数据,验证了多光谱影像配准得到的平台颤振与姿态数据具有较高的一致性,明确了颤振探测方法的可靠性。首次得出资源三号02星平台存在频率为0.63~0.65Hz、振幅为0.41″~1.12″的颤振。
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