Move-stop-move Target Tracking with Low-altitude Surveillance Radars

XU Kaiming; WANG Bailu; LI Suqi; DENG Yunkai; WANG Jinghe

doi:10.12000/JR21211

Volume 11 Issue 3

Jun. 2022

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Abstract

References

Article Navigation > Journal of Radars > 2022 > 11(3): 443-458

LI Qiang and FAN Huaitao. Channel phase mismatch calibration for multichannel in azimuth SAR imaging aided by digital elevation model[J]. Journal of Radars, 2019, 8(5): 616–623. doi: 10.12000/JR19009

Citation:

XU Kaiming, WANG Bailu, LI Suqi, et al. Move-stop-move target tracking with low-altitude surveillance radars[J]. Journal of Radars, 2022, 11(3): 443–458. doi: 10.12000/JR21211

Citation:

XU Kaiming, WANG Bailu, LI Suqi, et al. Move-stop-move target tracking with low-altitude surveillance radars[J]. Journal of Radars, 2022, 11(3): 443–458. doi: 10.12000/JR21211

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Move-stop-move Target Tracking with Low-altitude Surveillance Radars

DOI: 10.12000/JR21211

XU Kaiming^{1, 2},
WANG Bailu^{3
,
,},
LI Suqi³,
DENG Yunkai^{1, 2},
WANG Jinghe¹

1.
The Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
2.
The School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
3.
School of Micro-electronics and Communication Engineering, Chongqing University, Chongqing 400044, China

Funds: The National Natural Science Foundation of China (61901094), The Fundamental Research Funds for the Central Universities (2021CDJJMRH-009), The Starting Research Fund from Chongqing University (02140011044134)

More Information

Corresponding author: WANG Bailu, wangbailu@cqu.edu.cn
Received Date: 2021-12-30
Rev Recd Date: 2022-03-29

Available Online: 2022-04-06

Publish Date: 2022-04-25

Abstract

Abstract

Low-altitude small targets, represented by rotor unmanned aerial vehicles, always adopt slow move-and-stop strategy or employ an obstacle blocking strategy to avoid radar detection and conduct point-and-point strikes or interference on important information equipment and strategic bases. This type of target can appear and disappear from the radar Field of View (FoV) multiple times, thus, it is referred to as move-stop-move targets. Dealing with this type of target using traditional tracking models and algorithms can lead to discontinuities in target identity and track fragmentation. To this end, this study investigates the tracking problem of move-stop-move targets with the Labeled Multi-Bernoulli (LMB) filter based on random finite set statistics. To describe the evolution characteristics of multiple entries to the radar FoV, first, we introduce the third type of birth procedure, that is, the Re-Birth (RB) procedure. Specifically, based on the spatial and kinematic relationships between target states before and after returning to the radar FoV, a Spatial Correlation-based RB (SC-RB) procedure is proposed. Then, in the framework of Bayesian filtering, we derive the SC-RB-LMB filter with the proposed SC-RB model, which is capable of tracking move-stop-move targets continuously with its identity unchanged. In typical low-altitude surveillance scenarios, the effectiveness of the proposed model and algorithm is highlighted.
- Low-altitude surveillance radar,
- Move-stop-move target tracking,
- Random finite set statistics,
- Rebirth procedure model,
- LMB filter

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1. 引言

合成孔径雷达（Synthetic Aperture Radar, SAR）具备全天候、全天时、远距离、高分辨率对地成像能力，已经成为现代微波遥感领域的重要技术手段之一^[1]。获取陆海环境更高的分辨能力和更大的测绘范围一直是各种遥感手段不断突破的方向。方位向多通道体制以空间维度采样的增加消除分辨率和幅宽对时间维度采样率的矛盾制约^[2]，目前已经成为高分辨率宽幅SAR成像的主流技术手段之一，并成功应用于国内外多颗在轨SAR卫星，包括高分三号^[3]、TerraSAR-X^[4], RADARSAT-2^[5]和ALOS-2^[6]。

通道失配校正和多通道信号重建是方位多通道SAR信号处理的两个关键技术环节。多通道信号重建旨在对空间上非均匀分布的多个通道采样信号进行联合处理，得到等效于单通道SAR系统的空间维均匀采样信号^[7]。在进行非均匀采样数据重建处理之前，多个通道接收回波的幅度、相位、延时等特性需要校正一致，以避免重建图像中出现干扰图像判读的“鬼影”虚假目标^[8]。针对方位多通道SAR系统失配校正问题，德国宇航中心、西安电子科技大学、上海交通大学、中国科学院电子学研究所等国内外研究机构相继进行了大量研究，提出了多种处理方案^[9–11]。

通道相位失配校正主要分为基于内定标系统的标定方法和基于回波数据的估计方法^[12]。由于实际SAR系统中通道失配来源复杂，完全依靠内定标系统不仅代价高昂而且系统十分庞大^[13]。基于回波数据的通道失配估计方法受到国内外学者的广泛研究^[14]。通常来讲，通道间特性失配源于系统特性不理想，与成像场景无关，目前已经发展的通道失配校正方法也是基于此假设。但是，虽然失配特性不一致源于SAR系统特性，其造成的影响与场景特性却是紧密相关的，特别是起伏地形高程。目前发展的通道失配校正方法均未考虑地形起伏的影响，基于平地假设的校正方法在地形起伏明显的场景中，失配校正性能将受到很大影响。当前，高精度数字高程模型(Digital Elevation Model, DEM)重建技术经过国内外学者多年研究，已经逐渐成熟并得到广泛应用^[15]。本文详细分析了方位向多通道SAR系统存在偏航、俯仰和地形起伏条件下的通道失配特点，给出运用辅助DEM信息进行补偿的解析表达式，针对仿真实验数据和机载4通道SAR实验数据开展处理工作，验证所提方法的有效性。

2. 基于辅助DEM的方位多通道SAR相位失配补偿方法

方位多通道SAR信号无模糊重建的基础是各天线子孔径沿航迹方向均匀排布。但是，在实际工作过程中，受高空气流和侧风的影响，天线基线常常偏离平台的飞行轨迹，平台姿态往往存在偏航、俯仰和横滚^[16]，如图1所示。在星载SAR系统中，地球自转等效于系统中存在一个固定偏航角。

图 1 机载SAR系统飞行姿态示意图

Figure 1. The attitude of airborne SAR system

下载: 全尺寸图片幻灯片

其中，平台横滚角带来的影响主要是回波的接收增益发生变化，场景目标到多个通道天线相位中心的斜距变化是相同的，因此不会导致通道间的相位误差。天线偏航和俯仰不仅会导致波束在方位向指向发生改变，成像区域改变，而且会导致子孔径天线相位中心位置发生偏移^[16]。天线相位中心偏移导致的相位差异在不同通道中是不同的，由此导致通道间的相位误差。

图2中，Y 轴指向平台前进方向，Z轴垂直地面向上，X轴形成右手直角坐标系，平台飞行高度H, ${L_n}$ 表示天线子孔径n到参考通道的顺轨间隔，场景目标T坐标为(x, y, h)。以方位向两通道SAR系统为例进行分析，方位向前端通道称为主通道，后端通道称为辅通道，偏移前相位中心表示为 $P\,$ ，偏移后相位中心表示为 $\bar {P\;}$ 。这里以主通道为参考通道，分析平台偏航和俯仰给辅通道带来的影响，结论同样适用于任意通道数目的多通道SAR系统。窄波束条件下SAR系统符合波束中心近似假设，图3给出平台姿态变化在斜距方向导致相位中心变化示意图。

图 2 天线相位中心偏移示意图

Figure 2. Movement of SAR antenna phase center

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图 3 2维横截面图

Figure 3. 2-D cross-sectional view

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假设 ${\theta _{\rm{yaw}}}$ 表示偏航角， ${\theta _{\rm{pitch}}}$ 表示俯仰角，如图3所示，则偏航和俯仰导致的相位中心在3维空间的变化量可以表示为

$\left. {\begin{array}{*{20}{c}} {\Delta x = {L_n}\sin {\theta _{\rm{yaw}}}} \\ {\Delta z = {L_n}\sin {\theta _{\rm{pitch}}}} \end{array}} \right\}$

(1)

目标T和校正前后辅通道的天线相位中心位置

$\left. \begin{array}{l} {\rm T}:\left( {x,h} \right)\\ P:\left( {0,H} \right)\\ \bar {P\,}:\left( {\Delta x,H + \Delta z} \right) \end{array} \right\}$

(2)

其中， $x$ 和 $h$ 分别表示目标 $\rm T\,$ 的地距向和高度向的位置坐标， $H$ 表示平台飞行高度。由成像几何关系，天线相位中心偏移导致的相位失配可以表示为

$\begin{align} \varphi =& \frac{{2{\text{π}} }}{\lambda }\left( \sqrt {{{(x{\rm{ - }}\Delta x)}^2} + {{(H + \Delta z - h)}^2}}\right. \\ {\rm{}}& \left.- \sqrt {{x^2} + {{(H - h)}^2}} \right) \end{align}$

(3)

其中， $\lambda$ 表示载波波长。在星载SAR和机载SAR系统中，条件 $\Delta x \ll x$ 和 $\Delta z \ll H - h$ 均有效成立，可以得到近似不等式如式(4)

$\begin{align} {x^2} + {(H - h)^2} &\gg 2x\Delta x{\rm{ + }}2(H - h)\Delta z \\ {\rm{}}&\gg \Delta {x^2}{\rm{ + }}\Delta {z^2} \end{align}$

(4)

在上述假设条件下，将式(3)中的双曲形式泰勒级数展开至2次项可以得到

$\varphi \approx \frac{{2{\text{π}} }}{\lambda }\left( {\frac{{{\rm{ - }}x\Delta x{\rm{ + }}(H - h)\Delta z}}{{\sqrt {{x^2} + {{(H - h)}^2}} }}} \right)$

(5)

基于成像几何关系，可以得到下视角 ${\theta _{{\rm{look}}}}$ 的三角函数关系如式(6)

$\left. {\begin{array}{*{20}{c}} {\cos {\theta _{{\rm{look}}}} = \frac{{\left( {H - h} \right)}}{{\sqrt {{x^2} + {{\left( {H - h} \right)}^2}} }}} \\ {\sin {\theta _{{\rm{look}}}} = \frac{x}{{\sqrt {{x^2} + {{\left( {H - h} \right)}^2}} }}} \end{array}} \right\}$

(6)

综上，将式(6)代入式(5)可以得到偏航角和俯仰角导致的通道间相位偏差

$\begin{align} \varphi =& \frac{{2{\text{π}} {L_n}}}{\lambda }\left( {\rm{ - }}\sin {\theta _{{\rm{look}}}}\sin {\theta _{\rm{yaw}}}\right.\\ {\rm{}}& \left.+{\rm{cos}}{\theta _{{\rm{look}}}}\sin {\theta _{\rm{pitch}}} \right) \end{align}$

(7)

在机载SAR系统工作过程中，偏航和俯仰不断发生变化，通道间相位失配具有方位时变特性。同时，从式(7)可以看出，相位失配随场景地物对应的下视角变化，呈现距离向空变特点，因此式(7)可以重写为

$\begin{align} \varphi \left( {t,h} \right) =& \frac{{2{\text{π}} {L_n}}}{\lambda }\Bigr( {\rm{ - }}\sin \left( {{\theta _{{\rm{look}}}}\left( h \right)} \right)\sin \left( {{\theta _{\rm{yaw}}}\left( t \right)} \right) \\ {\rm{}}& +{\rm{ cos}}\left( {{\theta _{{\rm{look}}}}\left( h \right)} \right)\sin \left( {{\theta _{\rm{pitch}}}\left( t \right)} \right)\Bigr) \end{align}$

(8)

在地形起伏明显的区域，场景地物对应的下视角与平地假设下不同。如果采用简单的平地假设，针对存在高程起伏的地物，通道间相位失配补偿将出现错误，导致最终的重建图像中出现虚假目标。如图4所示，假设平台飞行高度为3000 m，场景中高程地物高出参考水平面300 m，建筑物顶端视角 ${\theta _1}$ 为50°。如果不考虑场景地形起伏，建筑物顶端斜距对应的视角 ${\theta _2}$ 约为44.42°。在子孔径间隔0.5 m的C波段机载SAR中，假设机载系统存在5°偏航角和3°俯仰角，采用平地假设进行相位失配校正，造成的偏差约为6.5°，在背景环境较弱的条件下会出现干扰虚假目标。如果在校正相位失配时考虑地形起伏影响，可以准确校正姿态导致的通道间相位失配，有效抑制重建后图像中的虚假目标。

图 4 高程引起的成像叠掩示意图

Figure 4. Imaging overlap caused by topograghic relief

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基于辅助DEM的方位多通道SAR通道失配补偿流程如图5所示，具体处理步骤如下：

图 5 基于DEM辅助的方位多通道SAR通道失配补偿方法流程图

Figure 5. The flowchart of the proposed channel phase mismatch calibration method based on the aided DEM

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(1) 根据惯性测量单元(IMU)记录的3维速度信息，针对多通道回波数据进行1阶运动补偿，补偿之后认为参考通道处于理想直线航迹上；

(2) 在距离频域和方位时域进行2维自适应校正幅度误差，校正表达式如式(9)所示，其中 $n$ 表示对通道2进行校正的次数， ${f_{\rm{r}}}$ 表示距离频率， $t$ 表示方位时间；

$\left. \begin{aligned} {\rm{}}&{S_2^{n + 1}\left( {{f_{\rm{r}}},t} \right) = S_2^n\left( {{f_{\rm{r}}},t} \right)\frac{{\displaystyle\int {\left| {{S_1}\left( {{f_{\rm{r}}},t} \right)} \right|{\rm d}t} }}{{\displaystyle\int {\left| {S_2^n\left( {{f_{\rm{r}}},t} \right)} \right|{\rm d}t} }}}\\ {\rm{}}&{S_2^{n + 2}\left( {{f_{\rm{r}}},t} \right) = S_2^{n + 1}\left( {{f_{\rm{r}}},t} \right)\frac{{\displaystyle\int {\left| {{S_1}\left( {{f_{\rm{r}}},t} \right)} \right|{\rm d}{f_{\rm{r}}}} }}{{\displaystyle\int {\left| {S_2^{n + 1}\left( {{f_{\rm{r}}},t} \right)} \right|{\rm d}{f_{\rm{r}}}} }}} \end{aligned} \right\}$

(9)

(3) 进行距离压缩；

(4) 采用方位互相关方法^[11]进行通道间延时误差校正；

(5) 在机载系统中，飞行姿态具有方位向时变特点，场景高程起伏也具有方位空变特点，采用方位向子孔径处理方式，假设子孔径内方位向高程不变，利用辅助DEM信息计算场景地物对应的下视角，并结合IMU记录的平台姿态数据校正距离空变、方位时变相位误差；

(6) 采用子空间投影方法^[13]校正残余的非空变、非时变相位误差；

(7) 采用滤波器组方法^[7]进行多通道信号重建，得到无模糊的单通道信号；

(8) 最后采用调频变标(CS)算法进行单通道数据成像处理，得到无模糊SAR图像。

3. 仿真与机载SAR数据处理结果

为了验证本文算法有效性，分别开展仿真数据处理和机载多通道SAR试验数据处理。首先，参照实际飞行试验中采用的方位多通道机载SAR系统设置仿真实验，实验参数由表1给出。

表 1 仿真机载实验参数

Table 1. System parameters of the simulated airborne experiment

系统参数	数值
通道数目	4
飞行高度(m)	3000
平台速度(m/s)	120
载频(GHz)	5.4
发射信号带宽(MHz)	210
脉冲重复频率(Hz)	150
多普勒带宽(Hz)	384

下载: 导出CSV

| 显示表格

假设平台存在5°偏航角和3°俯仰角。在场景中设置5个点目标，等间距分布，位于中间位置的点目标高程为0，其他4个点目标分别设置不同的高度，如图6所示。

图 6 场景点目标间距及高程设置

Figure 6. Five points set in the simulated scene

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图7展示了仿真实验数据处理结果。图7(a)给出的是未进行通道失配校正的多通道信号重建结果。由于通道失配的影响，场景中5个点目标均存在明显的虚假目标，分别分布在真实目标方位向前后位置。由于虚假目标的位置与目标的最近斜距有关，对比A, B和C点不难发现位于距离向不同位置点目标的虚假目标与真实目标的间距不同。同时，对比B点和E点可以发现，由于高程的影响，位于相同地距位置的点目标在斜距图像中出现在不同距离门中。

图 7 仿真实验结果

Figure 7. Experimental results of the simulation

下载: 全尺寸图片幻灯片

图7(b)中给出平地假设条件下通道失配校正结果。可以发现，没有高程的B点虚假目标得到有效抑制。由于未考虑地形起伏影响，场景中A, C, D, E 4个点目标仍然存在可见的虚假目标。同时，高程较高的C点和E点，虚假目标强度明显高于高程较低的A点和D点。图7(c)中给出考虑地形起伏条件下通道失配校正结果。可以发现，场景中A, B, C, D, E 5个点目标对应的虚假目标均得到有效抑制。仿真实验中虚假目标抑制的定量评估结果在表2中给出。

表 2 仿真实验定量评估结果(dB)

Table 2. Quantitative assessment result of the simulation (dB)

目标	未校正	未考虑高程起伏	考虑高程起伏
A	–5	–34	–53
B	–7	–50	–50
C	–5	–28	–53
D	–6	–37	–51
E	–5	–27	–52

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| 显示表格

中国科学院电子学研究所自主研制C波段方位4通道机载SAR系统，于2017年7月在舟山开展飞行试验，主要系统参数在表3中给出。系统采用1发4收的工作方式，整个天线阵面发射信号，方位向均匀分成4个通道接收回波。图8给出飞行过程中偏航和俯仰角度。

表 3 C波段方位向4通道机载SAR实验参数

Table 3. Experimental parameters of the C-band azimuth four channel airborne SAR system

系统参数	数值
通道数目	4
平台高度(m)	3000
平台速度(m/s)	129.64
载频(GHz)	5.4
发射信号带宽(MHz)	210
方位向天线尺寸(m)	0.624
脉冲重复频率(Hz)	137.19

下载: 导出CSV

| 显示表格

图 8 试验过程中的平台姿态信息

Figure 8. The attitude information recorded by the IMU

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图9展示了方位4通道机载SAR试验数据处理结果。图9(a)给出的是未进行通道失配校正的多通道信号重建结果。由于通道失配的影响，场景中存在明显的虚假目标，干扰图像的正常判读。特别是左岸煤炭码头停靠的干散货船，散射强度较大，对应的虚假目标非常明显。所选区域在方位向临海，虚假目标在平静的海面上尤其明显。图9(b)中给出平地假设条件下通道失配校正结果。可以发现，虚假目标的影响大大减弱。但是由于存在高程的山地影响，图像中强散射的目标仍然存在可见的虚假目标。图9(c)中给出考虑地形起伏条件下通道失配校正结果。可以发现，场景中虚假目标均得到有效抑制。

图 9 机载SAR数据处理结果

Figure 9. Imaging results of the airborne SAR experimental data

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4. 结论

方位向多通道星载SAR是实现高分辨率宽幅成像的重要技术手段之一，机载方位多通道SAR是验证系统和算法有效性的必要手段。基于外部DEM辅助信息，本文提出一种适用于高程起伏条件下，方位多通道条带SAR系统的通道相位失配校正方法。仿真实验表明算法能够精确补偿平台姿态导致的通道相位失配。将本文算法应用于机载多通道SAR实验数据处理，在高程起伏区域获取了良好的通道一致性校正和重建处理结果，验证了本文算法的有效性。

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