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摘要: 高分辨率SAR图像中蕴含目标与环境丰富的信息，但复杂的电磁散射机制使其难以直观解译，这一直是SAR图像解译的重要研究课题。该文简单梳理了典型几何基元的高频散射建模方法，以面散射、线散射和点散射为线索简要回顾了若干高频散射机制的研究发展过程，并给出几种典型几何基元的散射机制表达式及部分仿真结果，分析了典型散射机制表征面临的难点及应用于SAR图像解译的关键科学问题，提出从几何基元出发，发展对应的散射基元，通过散射基元进行组合和相互作用以树状方式实现更完备和广泛的散射特征表征体系，最后讨论了面向SAR图像散射信息解译来构建散射机制字典的可行性。Abstract: High-resolution SAR images contain rich information about targets and their surroundings, but the complex electromagnetic scattering mechanism makes intuitive interpretation difficult, leading to an important research topic in SAR image interpretation. This paper summarizes the typical geometric primitives modeling method of high-frequency scattering, which is reviewed in detail with respect to surface, wedge, and vertex scatterings. Besides the classical expressions of these typical scattering mechanisms, some simulation results are presented. The difficulties in characterizing typical scattering mechanisms and key scientific problems applied to SAR image interpretation are analyzed. Furthermore, this paper proposes a complete and extensive scattering characteristic characterization system by combining and interacting with the scattering primitives based on the corresponding geometric primitives. Finally, the feasibility of developing a scattering mechanism dictionary for use in interpreting SAR image scattering information is discussed.
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1. 引言
基于导航卫星的双基地SAR(Bistatic Synthetic Aperture Radar based on Global Navigation Satellite System, GNSS-BSAR)是空-地双基地SAR中一种典型的应用[1]，使用在轨的导航卫星作为发射源，地面部署接收机(地基、车载、机载)构成双基地SAR系统[2]。由于导航星座的日趋完善，其全球覆盖性以及重轨特性所带来的优势是其他照射源暂时所不能替代的，其中以地基接收机为主的导航卫星干涉合成孔径雷达(Interference Synthetic Aperture Radar based on the Global Navigation Satellite System, GNSS-InSAR)在场景形变监测领域有着广阔的应用前景[3]，成为了近年来研究热点。
在GNSS-BSAR系统成像方面，已有研究者分别使用不同的导航卫星星座进行了成像验证，包括了北斗[4,5]、GPS[6]、格洛纳斯[7]、伽利略[8]。除此以外文献[9]还提出了多角度融合方法以增强图像信噪比。在形变监测方面，来自伯明翰大学的学者们[10]使用直达波天线，配合长约50 m的线缆构建了理想点目标，并使用格洛纳斯作为发射源，首次实现了精度约为1 cm的1维形变反演结果。该实验初步验证了GNSS-InSAR应用于形变监测的可行性。为了进一步验证场景形变监测的可能，2017年文献[11]通过对接收机进行高精度移位来模拟场景建筑形变，成功反演出了形变，精度约为1 cm。在3维形变方面，2018年北京理工大学的技术团队[12]通过人为构建转发器，进行了精度可控的强点目标形变模拟，使用我国的北斗IGSO卫星，成功实现了精度优于5 mm的3维形变反演，这些验证性实验充分表明了GNSS-InSAR应用于场景形变检测的可能。
若要实现GNSS-InSAR场景的3维形变反演，需要同时至少3颗卫星从不同角度照射场景。由于GNSS-InSAR系统的拓扑高度非对称性以及导航信号的窄带特性[13]，加上导航卫星的重轨并非是严格意义上的重轨，除了不可避免的空间基线外，重轨时间也并非严格一致，因此在实际数据采集中，需要对系统构型以及数据采集时间进行严格的优化设计。文献[14]提出了一种联合优化方法，解决了面向大场景下的多星多角度构型优化问题，配合多个接收机实现综合分辨性能优异的大场景成像。文献[15]提出了空间去相干的理论描述框架，表明了空间去相干在GNSS-InSAR中的必要性，但未对数据采集时间进行说明。从当前实际情况出发，不精确的数据采集时间可能会造成存储资源浪费，空间去相干导致的数据截取进一步降低了数据有效性。具体如图1所示：
针对上述问题，本文提出了一种GNSS-InSAR场景连续数据采集优化方法，通过结合当前数据的卫星轨迹和两行星历数据文件(STK Two-Line Element sets, TLE)预测轨迹，基于相干系数轨迹对齐，获取卫星重轨时间间隔，得到最优的数据采集策略，从源头上降低数据的空间去相干性，提升所采集数据有效性，节约存储资源。在第2部分对GNSS-InSAR场景数据采集优化方法进行了详细介绍。第3部分针对提出的方法进行了实验设计，开展了实测数据采集，并针对采集的数据进行了初步分析。第4部分对全文进行总结。
2. GNSS-InSAR场景数据采集优化模型
2.1 GNSS-InSAR相干系数理论模型
对于GNSS-InSAR图像而言，经过保相成像处理后，场景中任意一点
(x0,y0) 的像素信息分别对应分辨单元内所有散射体回波的相参叠加，可建模为s(x0,y0)=∬f(x,y;t)exp[−j2πλr(x,y;P)]⋅W(x−x0,y−y0;P)dxdy+n(x0,y0;t) (1) 其中，
f(x,y;t) 为时间t 下的地表散射系数，P 为对应的合成孔径中心位置矢量，W(x,y;P) 表示系统的点扩散函数(PSF),n(x,y;t) 为图像的加性噪声。对于SAR图像的同名点像素，其相干系数可表示为[16]ρ=∬sm(x0,y0)s∗s(x0,y0)dxdy√∬sm(x0,y0)s∗m(x0,y0)dxdy∬ss(x0,y0)s∗s(x0,y0)dxdy (2) 其中，下标m表示主图像，
s 表示辅图像。根据柯西不等式可以判断：0≤ρ≤1 ，当ρ=0 时表示同名点完全不相干，当ρ=1 时，同名点完全相干。将点目标像素模型式(1)带入到式(2)并化简得到
ρ=∬sav(x,y)exp[−j2πλ(r(x,y;Pm)−r(x,y;Ps))]|W(x−x0,y−y0;Pm)|2dxdy√(∬sm(x,y)exp[−j2πλr(x,y;Pm)]|W(x−x0,y−y0;Pm)|2dxdy+nm)×(∬ss(x,y)exp[+j2πλr(x,y;Ps)]|W(x−x0,y−y0;Pm)|2dxdy+ns) (3) 式(3)的推导使用了如下近似：
(1) 由于导航卫星的高轨道特性，使得
W(x−x0, y−y0;Pm)≈W(x−x0,y−y0;Ps) 成立；(2) 相邻两天的噪声相干系数为0，即
n(x0,y0;tm)×n(x0,y0;ts)=0 (4) (3) 相邻两天的目标散射系数为
sav(x,y) ，即sav(x,y)≈f(x,y;tm)f∗(x,y;ts) (5) 对式(3)中的相干系数
ρ 进一步分解得到ρ=ρth×ρti×ρsp (6) 其中，热噪声相干系数
ρth 与时间相干系数ρti 分别由系统与实际目标决定。对于PS点[17]而言，地表散射系数相对稳定，不随时间变化，同时为了便于后续分析，假定散射系数为1得到空间相干系数
ρsp 的简化式为ρsp=∬exp[−j2πλ(r(x,y;Pm)−r(x,y;Ps))]|W(x−x0,y−y0;Pm)|2dxdy√(∬|W(x−x0,y−y0;Pm)|2dxdy)(∬|W(x−x0,y−y0;Pm)|2dxdy) (7) 从式(7)推导结果可以知道，空间基线主要是影响
r(x,y;P) 从而导致空间去相干。2.2 数据采集优化模型
导航卫星的重轨时间并非稳定不变，因此需要对数据采集时间进行有效预测，从源头上降低空间去相干，提高数据有效性。
假定主图像数据采集时间为
tm ，该采集时间可以通过文献[14]中的广义优化模型进行求解，辅图像数据采集时间为ts=tm+Δt ,Δt 为时间间隔，那么最优化数据采集模型可通过式(7)推导而来Δt=argmax{∬|˜W(x,y;Pm)|2exp[−j2πλ(r(x,y;Pm)−r(x,y;P(tm+Δt)))]dxdy} (8) 其中，
˜W(x,y;Pm) 为tm 下等效归一化PSF,P(tm+ Δt) 为Δt 时间偏置下得合成孔径中心位置矢量。第1天数据采集需要进行实验设计以确定最优数据采集时刻，往后的重轨天数据采集可以根据数据采集优化模型，同时结合星历文件进行预测。整体的预测流程如图2所示，
n 为任意一天采集的数据，k 为重轨天数间隔。
图 2 GNSS-InSAR数据采集时间优化流程Figure 2. Time optimization process of GNSS-InSAR data acquisition实际卫星位置对应的实际时间设为
tn ，经过模型优化得到的时间偏差为Δt ，那么第n+k 天对应的实际数据采集时间可表示为tn+k=tn+Δt (9) 3. 实验验证
3.1 GNSS-InSAR场景3维形变反演实验设计
对于固定场景的形变监测，首次数据采集的时候需要严格设计系统构型，使分辨率达到最优化。本次实验接收机部署在北京理工大学信息科学试验楼楼顶西北角，实施监测场景位于西偏北30°。使用理论分辨率计算公式[18]对该场景进行分辨率设计。仿真参数具体参见表1。
表 1 数据采集试验仿真参数Table 1. Data acquisition test simulation parameters参数 值 照射源 北斗 IGSO1～5 PRF 1000 Hz 带宽 10.23 MHz 合成孔径时间 600 s TLE文件更新日期 2019年4月29日 预定数据采集日期 2019年4月30日 以分辨单元面积作为判定依据，得到预定采集日期当天全时段下各个卫星在预定场景下所能得到的分辨单元面积如图3所示。
为了实现3维形变反演，需要同一时间下有3颗卫星对场景进行照射。图3中10点前后与17点前后满足当前场景上空有3颗IGSO卫星可见的条件。更进一步，为了使分辨单元面积达到最优，可以得到具体的数据采集时间。具体如图4红框标注，分别是9点30分前后与17点30分前后。
为了配合实验，在场景布置转发器，整体的系统构型如图5所示。
图 5 GNSS-InSAR场景3维形变反演实验拓扑构型设计结果Figure 5. GNSS-InSAR topological configuration design results of 3D deformation retrieval experiment3.2 重轨数据采集时间优化
以2019年4月30日采集的实测数据作为第
n 天数据，对于北斗的IGSO而言，重轨时间约为1天，即m =1，同时下载当天最新的TLE文件。以IGSO1为例，结合图2进行详细说明：(1) 使用实测数据的直达波进行卫星位置解算，同时根据TLE文件推算当天和相邻天的卫星轨迹。经过相干系数轨迹匹配之后，得到的轨迹如图6所示。
图 6 对齐后的TLE卫星轨迹与实测数据卫星轨迹Figure 6. Aligned TLE satellite trajectory and measured data satellite trajectory(2) 以匹配得到的TLE卫星轨迹作为参考，对重轨天的TLE卫星轨迹进行数据采集优化模型求解，系统的PSF与优化模型仿真结果分别如图7与图8所示。
图 7 场景[–147, 20, 0]处理论PSFFigure 7. Theoretical PSF in scene at position of [–147, 20, 0]对图8的结果分析可知，第1个峰值点为其本身，由于空间基线为0，相干系数为1。第2个峰值点相干系数为0.999644，满足除了第1个峰值点外相邻天相干系数最大值条件，因此第2个峰值点就是最佳重轨时的空间相干系数。此时经过模型优化得到的时间间隔为：
Δt=86163s=23h56min3s ，结合第1天的实测数据轨迹对应的时间t1=9h26min0s ，第2天准确的数据采集时间为：t2=9h22min3s 。3.3 结果分析
为了说明优化结果的正确性，在实验场景中放置转发器模拟理想点目标(图5)，同时按照优化后的时间进行5月1日数据采集。实际采集时间为
9h21min53s ，总采集时间约650 s。相邻两天的空间相干系数轨迹匹配结果如图9所示。从图9中峰值点位置来看，重轨数据采集优化模型得到的结果和实际结果相吻合。为了进一步说明，图10给出了IGSO1卫星实测数据成像结果。
对相邻两天的图像相干系数进行求解，得到图11所示结果。在同一坐标系下，仿真目标位于[–147, 20, 0]，空间相干系数为0.999644；转发器位于[–147, 20, 0]，相干系数为0.9996；两者的相干系数基本保持一致。
图9与图10的结果表明经过数据采集优化模型后得到的时间间隔与实际卫星轨迹的重轨时间相互吻合，在保证600 s预期合成孔径时间下，可以最大限度减少数据采集时间，节约存储资源。同时避免后期由于数据对齐带来的数据有效性降低问题。
4. 结论
在GNSS-InSAR场景1维/3维形变反演应用中，针对由于导航卫星重轨时间的非严格一致性与有效数据截取带来的数据冗余，数据有效性低等问题，本文提出了一种面向GNSS-InSAR场景数据采集的优化模型，采用实测数据与TLE文件相结合，根据当天数据采集时间，预测相邻天重轨时间，从而实现精确的数据采集。实测数据验证结果表明了数据采集时间优化模型的正确性。该方法的提出有利于GNSS-InSAR场景1维/3维形变反演实验的开展，在降低原始数据冗余度基础上，保证了有效数据时间长度大于预期合成孔径时间。
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图 1 高频散射发展历程示意图
Figure 1. Schematic diagram of the development of high frequency scattering
图 6 正六边形平板散射仿真示意图
Figure 6. Schematic diagram of regular hexagonal plate scattering simulation
图 13 组合曲面模型后向散射仿真示意图
Figure 13. Backscattering simulation schematic diagram of combined curved surface model
图 14 组合曲面模型仿真结果图
Figure 14. Scattering simulation result of combined curve surface model
图 25 典型结构的几何基元表征
Figure 25. Geometric primitive characterization of typical structures
表 1 正六边形平板散射仿真参数表
Table 1. Scattering simulation parameters of regular hexagonal plate
参数 数值 参数 数值 频率(GHz) 1 角度间隔(°) 1 入射角(°) 0 观测距离 远场 出射角(°) –80°～80° 外切圆半径(m) 0.8485 
下载: 导出CSV
表 2 椭球散射仿真参数表
Table 2. Scattering simulation parameters of ellipsoid
参数 数值 参数 数值 频率(GHz) 10 角度间隔(°) 1 入射角(°) 0 观测距离 远场 出射角(°) –100～100 半径(m) 3, 2, 2
下载: 导出CSV
表 3 球散射仿真参数表
Table 3. Scattering simulation parameters of sphere
参数 数值 参数 数值 频率(GHz) 10 角度间隔(°) 1 入射角(°) 0 观测距离 远场 出射角(°) –100～100 半径(m) 3
下载: 导出CSV
表 4 组合曲面模型散射仿真参数表
Table 4. Scattering simulation parameters of combined curve surface model
参数 数值 参数 数值 频率(GHz) 1 角度间隔(°) 2 入射角(°) 0 观测距离 远场 角度范围 0～180
下载: 导出CSV
表 5 平板散射仿真参数表
Table 5. Scattering simulation parameters of flat plane
参数 数值 参数 数值 频率(GHz) 1 角度间隔(°) 1 入射角(°) 0 观测距离 300 出射角(°) –81～79 平板边长(m) 8
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表 6 劈尖边散射仿真参数表
Table 6. Scattering simulation parameters of wedge
参数 数值 参数 数值 r/λ 0～1 n 0.6189 ϕ0 45° r0 212.15 m ϕ 90° r 50 m
下载: 导出CSV
表 7 房屋模型散射仿真参数表
Table 7. Scattering simulation parameters of house
参数 数值 参数 数值 频率(GHz) 1 角度间隔(°) 2 入射角(°) 1 观测距离 远场 角度范围(°) –90～90
下载: 导出CSV
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