A New Approach to High-order Range Cell Migration Correction for SAR Ground Moving Targets Based on Phase Tracking

DU Huagui; SONG Yongping; SUN Xiaoying; JIANG Nan; FAN Chongyi; CHEN Leping; HUANG Xiaotao

doi:10.12000/JR24122

Volume 13 Issue 5

Sep. 2024

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References

Article Navigation > Journal of Radars > 2024 > 13(5): 955-973

Zhou Yejian, Zhang Lei, Wang Hongxian, Xing Mengdao. Performance Analysis on ISAR Imaging of Space Targets[J]. Journal of Radars, 2017, 6(1): 17-24. doi: 10.12000/JR16136

Citation:

DU Huagui, SONG Yongping, SUN Xiaoying, et al. A new approach to high-order range cell migration correction for SAR ground moving targets based on phase tracking[J]. Journal of Radars, 2024, 13(5): 955–973. doi: 10.12000/JR24122

Zhou Yejian, Zhang Lei, Wang Hongxian, Xing Mengdao. Performance Analysis on ISAR Imaging of Space Targets[J]. Journal of Radars, 2017, 6(1): 17-24. doi: 10.12000/JR16136

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A New Approach to High-order Range Cell Migration Correction for SAR Ground Moving Targets Based on Phase Tracking

DOI: 10.12000/JR24122 CSTR: 32380.14.JR24122

1.
College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China
2.
School of Automation, Central South University, Changsha 410073, China

Funds: The National Natural Science Foundation of China (62101566)

More Information

Corresponding author: SONG Yongping, sypopqjkl@163.com
Received Date: 2024-06-13
Rev Recd Date: 2024-07-25

Available Online: 2024-08-05

Publish Date: 2024-08-23

Abstract

Abstract

Range Cell Migration Correction (RCMC) represents an important advancement in the estimation of moving target parameters and imaging of targets in high-resolution Synthetic Aperture Radar (SAR) systems. When the motion of a target or platform becomes complex, the traditional low-order RCMC method may no longer be suitable. Meanwhile, the existing high-order RCMC method based on parameterization is susceptible to issues such as model mismatch and high computational complexity. Additionally, its performance may decrease significantly under a low Signal-to-Noise Ratio (SNR). This research utilizes Extended Kalman Filter (EKF) to track the phase responsible for RCM and develop a phase compensation function to achieve RCMC. The proposed approach is model-independent and can track high-order components in the phase, thereby enabling high-order RCMC of moving targets in SAR. In addition, EKF can filter signals during phase tracking to effectively lower the SNR threshold of the proposed method. Thus, this method offers broad applicability, moderate computational complexity, and the ability to correct non-negligible high-order residual range cell migrations, thereby distinguishing it from traditional methods. This study thoroughly explains the principles and mathematical model behind the proposed method, demonstrating its effectiveness and superiority through multiple sets of simulations and measured data processing.
- Synthetic Aperture Radar (SAR),
- Moving target imaging,
- Range Cell Migration Correction (RCMC),
- Extend Kalman Filter (EKF),
- Phase tracking

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1. 引言

随着雷达空间探测技术的发展，空间目标的高精度成像处理已成为空间探测任务的重要组成部分。对空间目标的雷达观测成像主要采用地基逆合成孔径雷达(Inverse Synthetic Aperture Radar, ISAR)体制实现，目前，针对低轨目标的成像技术比较完善^[1–4]，但从空间目标运动特性上进行ISAR成像体制和信号处理方法设计来提升雷达工作性能的研究偏少，需要直接面对若干问题：(1)根据传统雷达方程可知，由于回波信噪比与雷达目标距离4次方成反比关系，目标轨道高度升高将导致单次回波信噪比急剧下降；(2)传统ISAR成像处理通常将目标认为是“完全”非合作目标，ISAR成像体制与信号处理设计均未能紧密结合目标轨道参数。与空中气动目标和海面舰船目标相比，空间轨道目标的运动相对平稳、可预测性强，而且目标姿态通常严格受控，目标相对雷达视线角变化通常可以根据轨道信息精确解算。此外，与合成孔径雷达(SAR)成像类似，ISAR成像过程也是积累多帧脉冲串相干聚焦实现方位成像，方位相干积累增益可有效地提高成像信噪比质量^[5]。针对SAR系统中相干积累对成像质量的分析已较为完善^[6–8]，考虑方位相干积累增益后，条带SAR雷达方程中成像信噪比将与作用距离的3次方成反比，因此SAR体制参数设计与传统雷达方程是有明显差异的。从成像原理上来看，ISAR成像相干积累角也能带来明显增益，但其成像几何较SAR不同，不能直接应用SAR雷达方程的若干结论^[9–12]。尤其是在空间目标ISAR成像中，轨道参数对成像质量的影响未有深入分析，大角度成像的方位相干积累增益能否弥补轨道升高带来的回波信噪比降低尚无明确结论。

类比SAR雷达方程，本文结合目标轨道参数推导针对空间目标ISAR成像雷达方程的一般形式，进而分析轨道高度、目标雷达姿态角变化引起的方位相干积累增益变化及其对目标成像质量的影响，得到较为直观的理论来指导ISAR成像体制中发射功率、波形等参数的优化设计。仿真实验就不同轨道高度成像质量进行比较，探究方位向增益与轨道参数间的变化关系及其对成像质量的改善情况，实验结果验证了推导结论的准确性。

本文结构如下：第2节结合天线理论推导ISAR系统成像雷达方程；第3.1节从地基雷达观测几何出发对空间目标角速度这一关键因素进行推导，并利用其计算结果得到空间轨道目标ISAR系统成像雷达方程；第3.2节分析第3.1节中观测模型引起计算误差；第3.3节对得到的空间轨道目标ISAR系统成像雷达方程作出一些定性结论；第4节结合目标轨道信息，利用空间轨道目标ISAR系统成像雷达方程指导定分辨率成像仿真，并对轨道参数引起的成像质量变化分析，验证了推导公式和结论的正确性。

2. 空间目标逆合成孔径雷达成像雷达方程

结合天线理论，对收发共天线的雷达系统，单次回波信号功率与雷达参数和作用距离的关系可由传统雷达方程表示：

$S = \frac{{P{G\, ^2}{\lambda ^2}\sigma {T\,_{\rm{i}}}}}{{{{\left( {4{{π}} } \right)}^3}{r^4}\eta }}$

(1)

其中，P为雷达发射机功率，G为天线增益， $\lambda$ 为信号波长， $\sigma$ 为目标的雷达截面积，T_i为相干积累时间，r为雷达作用距离， $\eta$ 为系统损耗。

区别于一般雷达系统，ISAR成像体制具有2维高分辨率，而空间目标尺寸较大。因此，本文针对成像分辨单元信噪比进行成像质量分析，定义目标分辨单元的等效雷达截面积 $\sigma$ ^[13]：

$\sigma = {\sigma _0}{\rho _{\rm{r}}}{\rho _{\rm{a}}}$

(2)

其中， ${\sigma _0}$ 为目标归一化后向散射系数， ${\rho _{\rm{r}}}$ 和 ${\rho _{\rm{a}}}$ 分别为目标ISAR成像纵向和横向分辨率且两者大小相当。一般来说，ISAR成像系统的纵向距离分辨率与斜距r无关而仅和发射信号频率带宽相关^[9]：

${\rho _{\rm{r}}} = \frac{\rm c}{{2B}}$

(3)

其中，c为光速，B为信号带宽。

横向高分辨是通过在相干测量时间内对多帧回波进行多普勒分析获得，与目标雷达视线的相干积累转角直接相关。空间目标在观测过程中姿态平稳，可采用2维转台模型描述其与雷达间的相对运动。假定雷达视线转速为w，相干测量时间为T_i，则相干积累转角 $\Delta \theta = w{T\, _{\rm{i}}}$ ，横距分辨率 ${\rho _{\rm{a}}}$ 可计算为：

${\rho _{\rm{a}}} = \frac{\lambda }{{2\Delta \theta }}$

(4)

将式(3)、式(4)带入重写式(1)，考虑方位相干积累的ISAR成像目标某分辨单元对应的接收功率可表达为：

$S = \frac{{P{G \, ^2}{\lambda ^2}{\sigma _0}{\rho _{\rm r}}}}{{{{\left( {4{{π}} } \right)}^3}{r^4}\eta }} \cdot \frac{\lambda }{{2w}}$

(5)

由式(5)可见，与SAR成像雷达方程类似，雷达视角(Light Of Sight, LOS)变化速度w，即下文所述的目标相对转台中心转角速度，将直接影响分辨单元的回波功率，决定分辨单元信噪比质量。下面将结合空间轨道目标轨道参数对以上公式进行扩展分析。

3. 空间目标轨道参数对成像雷达方程影响分析

3.1 空间目标转角速度分析

本节将从轨道高度变化引起的空间目标转角速度变化出发对上节得到的空间目标ISAR成像方程进行完善。在分析转角速度变化过程中，还将对关键性的雷达斜距变化进行建模分析，得到定分辨率观测下的雷达方程。

假定空间目标处于近圆轨道，考虑地球自转后，目标的相对平近角点可表示为^[14,15]：

$n = \frac{{\sqrt \mu }}{{{{({{\mathop{R}\nolimits} _{\rm{e}}} + h)}^{3/2}}}}$

(6)

其中，引力常数 $\mu = 3.986 \times {10^{14}}({{\rm m}^3}/{{\rm s}^2})$ ，R_e为地球半径，h为目标轨道高度。

如图1(a)观测几何所示，单次脉冲周期Δt_m后，目标从p点运动至p′点，其运行绝对距离可由几何计算得：

$\mathop {pp'}\limits^{\frown} = ({{\mathop{ R}\nolimits} _{\rm{e}}} + h)n\Delta {t_{\rm{m}}} = \frac{{\sqrt \mu \Delta {t_{\rm{m}}}}}{{{{({{\mathop{R}\nolimits} _{\rm{e}}} + h)}^{1/2}}}}$

(7)

图 1 空间观测几何模型及成像模型

Figure 1. Observation and imaging model of satellite targets

下载: 全尺寸图片幻灯片

在目标轨道平面内，目标对于观测站点的相对运动如图1(b)所示，雷达站点处于转台原点，运动起点p的雷达斜距为r，运动终点p′的雷达斜距为r′，原点与终点连线上有一斜距为r处p₀，由几何关系可知：

$\!\!\! r' = r + \Delta r$

(8)

$\mathop {p{p_0}}\limits^{\frown} = \omega \Delta {t_{\rm{m}}}r$

(9)

考虑空间目标平近点角远小于地球自转、单帧成像时间在秒级的情况下，短弧段 $\mathop {pp'}\limits^{\frown}$ 可近似为线段pp′，短弧段 $\mathop {p{p_0}}\limits^{\frown}$ 亦可近似为线段pp₀, Δpp₀p′可近似为直角三角形满足勾股定理：

${\left( {p{p_0}} \right)^2} + {\left( {{p_0}p'} \right)^2} = {\left( {pp'} \right)^2}$

(10)

带入式(7)、式(8)、式(9)，可得：

$w =\frac{{\sqrt { \displaystyle\frac{{\mu \Delta {t_{\rm{m}}}^2}}{{{{\mathop{R}\nolimits} _{\rm{e}}} + h}} - \Delta {r^2}} }}{{r\Delta {t_{\rm{m}}}}}$

(11)

在r²=0处泰勒展开，可以得到近似解：

$w \approx \frac{1}{{r\Delta {t_{\rm{m}}}\sqrt { \displaystyle\frac{{\mu \Delta {t_{\rm{m}}}^2}}{{{{\mathop{R}\nolimits} _{\rm{e}}} + h}}} }}\left( {\frac{{\mu \Delta {t_{\rm{m}}}^2}}{{{{\mathop{R}\nolimits} _{\rm{e}}} + h}} - \frac{{\Delta {r^2}}}{2}} \right)$

(12)

其中，关于雷达斜距变化Δr的求解问题可以简化为研究位于目标轨道平面外一点与轨道上的目标间距离变化关系，如图2所示。

图 2 雷达斜距变化Δr求解模型

Figure 2. Calculation model of change of radar range

下载: 全尺寸图片幻灯片

以地心为坐标轴原点，目标所在轨道平面为xOy平面建立直角坐标系xyz，观测站点S在xOy平面内投影为 $S'\left( {{x_0},{y_0},0} \right)$ ，目标运动至 $p\left( {\left( {{{{R}}_{\rm{e}}} + h} \right)} \right.$ $\left. \cdot {\cos \theta \left( t \right),\left( {{{{R}}_{\rm{e}}} + h} \right)\sin \theta \left( t \right),0} \right)$ ，其中，q(t) = q₀+ $n\left( {t - {t_0}} \right)$ 用以表示目标在轨道上的瞬时位置， ${\theta _0}$ 为单帧成像中心时刻t₀对应的位置参数。对于直角三角形DSS′p，由勾股定理知：

${r^2} = {d^2} + {l^2}$

(13)

其中，垂直距离d在目标运动过程中视为定值，而水平距离l可由下式计算：

$\begin{aligned}{l^2} = & {\left( {\left( {{{{R}}_{\rm{e}}} + h} \right) \cos\theta \left( t \right) - {x_0}} \right)^2}\\ & + {\left( {\left( {{{{R}}_{\rm{e}}} + h} \right)\sin \theta \left( t \right) - {y_0}} \right)^2}\end{aligned}$

(14)

将式(14)带入式(13)并对等式两边关于时间求导：

$\begin{array}{*{20}{c}}\begin{aligned}rr' = & \left[ { - \left( {\left( {{{{R}}_{\rm{e}}} + h} \right) \cos\theta \left( t \right) - {x_0}} \right)\left( {{{{R}}_{\rm{e}}} + h} \right)\sin \theta \left( t \right)} \right.\\& +\left. {\left( {\left( {{{{R}}_{\rm{e}}} + h} \right)\sin \theta \left( t \right) - {y_0}} \right)\left( {{{{R}}_{\rm{e}}} + h} \right)\cos \theta \left( t \right)} \right]n\end{aligned}\\\quad\quad\! { = \left[ {\left( {{{{R}}_{\rm{e}}} + h} \right){x_0}\sin \theta \left( t \right) - \left( {{{{R}}_{\rm{e}}} + h} \right){y_0}\cos \theta \left( t \right)} \right]n}\\\!\!\!\!\!\!\!\! { = \left( {{{{R}}_{\rm{e}}} + h} \right)\sqrt {{x_0}^2 + {y_0}^2} \sin \left( {\theta \left( t \right) - \varphi } \right)n}\end{array}$

(15)

短时Δt_m内， $r \approx r' \Delta {t_{\rm{m}}}$ ，并将式(15)带入可得：

$\Delta r = \frac{{\left( {{{\mathop{R}\nolimits} _{\rm{e}}} + h} \right)\sqrt {{x_0}^2 + {y_0}^2} \sin \left( {\theta \left( t \right) - \varphi } \right)n\Delta {t_{\rm{m}}}}}{r}$

(16)

其中， $\varphi = \arctan \left( {\displaystyle\frac{{{y_0}}}{{{x_0}}}} \right)$ 。

为进一步简化式(16)，当以OS′作为x正半轴，即y₀=0, $\varphi = 0$ 时，在雷达可视范围内 $\left| \theta \right| \le {\theta _0}$ ，式(16)可写为：

$\Delta r = \frac{{\left( {{{\mathop{R}\nolimits} _{\rm{e}}} + h} \right){x_0}\sin \theta \left( t \right)n\Delta {t_{\rm{m}}}}}{r}$

(17)

重写式(11)、式(12)：

$\!\!\!\!\!\!\! w = \sqrt {\frac{\mu }{{r\left( {{{\mathop{R}\nolimits} _{\rm{e}}} + h} \right)}} - {{\left( {\frac{{\left( {{{\mathop{R}\nolimits} _{\rm{e}}} + h} \right){x_0}\sin \theta \left( t \right)n}}{{{r^3}}}} \right)}^2}}$

(18)

$w \! \approx \! \sqrt {\frac{\mu }{{r\left( {{{\mathop{R}\nolimits} _{\rm{e}}} + h} \right)}}} \!-\! \frac{1}{{2{r^3}\sqrt \mu }}{\left( {{{\mathop{R}\nolimits} _{\rm{e}}} + h} \right)^{5/2}{\left( {{x_0}\sin \theta \left( t \right)n} \right)^2}}$

(19)

为保证方位向分辨率一定，总转角 $\Delta \theta$ 需固定，那么相干时间T_i将随目标高度变化：

${T\,_{\rm{i}}} = \frac{{\Delta \theta }}{w}$

(20)

结合式(6)、式(18)，重写空间目标ISAR成像雷达方程：

$S = \frac{{P{G \, ^2}{\lambda ^3}{\sigma _0}{\rho _{\rm{r}}}}}{{2{{\left( {4{{π}} } \right)}^3}{r^3}\eta }} \cdot \sqrt {\frac{{{r^2}\left( {{{\mathop{R}\nolimits} _{\rm{e}}} + h} \right)}}{{\mu {r^2} - {{\left( {{{\mathop{R}\nolimits} _{\rm{e}}} + h} \right)}^3}{{\left( {{x_0}\sin \theta \left( t \right)n} \right)}^2}}}}$

(21)

3.2 关于Δr求解的模型误差

由于地球自转的影响，空间目标相对于雷达站点的运动轨迹并不是一个闭合的圆，如图3(b)所示。本文采用的近似模型将其轨道近似为圆如图3(a)所示，对于短时间观测任务来说，两者误差可控制在一定程度内。这里分别使用不同高度的轨道参数对LOS转角速度w进行求解并与实际值对比，选择库尔勒作为观测站点，结果如图4所示。其中，真实值为通过STK验证后的实际LOS转角速度，理论值为按式(18)计算得到的结果，近似值为按式(19)计算得到的结果。计算结果与实际值间的误差主要由模型简化引起，可由与轨道高度相关的函数补偿。补偿后的雷达作用距离方程可写成：

$\begin{aligned}S & = \frac{{P{G \, ^2}{\lambda ^3}{\sigma _0}{\rho _{\rm{r}}}}}{{2{{\left( {4{π} } \right)}^3}{r^3}\eta }}\\& \cdot \!\! {\left(\! {\sqrt {\frac{\mu }{{{{{R}}_{\rm{e}}} \!+\! h}} \!-\! \frac{{{{\left( {\left( {{{{R}}_{\rm{e}}} + h} \right){x_0}\sin \theta \left( t \right)n} \right)}^2}}}{{{r^2}}}} \!-\! C\left( h \right)r} \right)^{ - 1}}\end{aligned}$

(22)

其中，C(h)为补偿函数。需要说明的是，补偿函数与目标轨道参数和观测点坐标均有关，且对于本文关于空间目标ISAR成像雷达方程的影响有限，故未进一步讨论。

图 3 Δr求解近似模型与实际模型

Figure 3. Approximate and actual model of Δr

下载: 全尺寸图片幻灯片

图 4 不同轨道高度下目标转角速度计算结果

Figure 4. Calculation of target′s rotate speed at different heights

下载: 全尺寸图片幻灯片

3.3 空间目标ISAR成像雷达方程分析

与条带SAR雷达方程类似，式(20)中ISAR系统回波信号的接收功率与横向分辨率 ${\rho _{\rm{a}}}$ 无关，与LOS转角速度w成反比，而w随轨道目标轨道高度升高而降低。轨道高度升高引起转角速度减小进而导致成像所需相干时间增加。这一变化可部分抵消因目标斜距增大引起的回波能量分散效果，也就是说回波信号接收功率因相干增益不再随作用距离增大呈4次方下降，其下降速度应小于作用距离的4次方，具体数值还与目标与雷达间相对位置有关，一般应介于3次方与4次方之间。采用大角度的ISAR成像处理可弥补轨道升高带来的回波接收功率降低，较普通雷达体制有明显的距离优势。

4. 仿真实验分析

为验证空间目标ISAR成像雷达方程中，回波信号接收功率下降速度的结论。仿真实验将在成像分辨率固定的情况下，仅改变目标轨道高度引起作用距离变化，对相近姿态下的空间目标进行成像观测，研究得到的RD图像中信号功率的变化以及图像质量的变化。实验中ISAR系统主要参数如表1，目标轨道主要参数倾角为42.8°，升交点赤经(Right Ascension of Ascending Node, RAAN)为34.7°E，观测点分别选取库尔勒、北京、西安，其经纬度信息如表2。

表 1 实验ISAR系统主要参数

Table 1. Main parameters of ISAR system

参数	数值
载频	16.7 GHz
带宽	1 GHz
方位向分辨率	0.18 m
距离向分辨率	0.15 m
脉冲重复频率	200 Hz

下载: 导出CSV

| 显示表格

表 2 实验地基ISAR观测站位置

Table 2. Position parameters of radar sites

地点	经纬度
库尔勒	41.5°N, 86.8°E
北京	39.9°N, 116.4°E
西安	31.1°N, 108.4°E

下载: 导出CSV

| 显示表格

4.1 目标轨道高度变化对回波信号接收功率的影响

对于式(21)，为简化计算，本实验中选取 ${\theta _0} = 0$ ，也就是目标均处于轨道上与观测点最近位置附近，其转角速度w达到该轨道上的最大值，其回波接收功率为同一轨道最小值。

目标轨道高度变化将引起目标轨道半径的变化，图5为归一化的回波信号接收功率随目标轨道半径的变化曲线，可以看出对于轨道半径在7400 km以上(作用距离在1400 km以上)的目标，其回波信号接收功率随斜距下降速度介于斜距变化的3次方与4次方之间，具体影响因子与目标与观测点相对位置、观测弧段均有关。在雷达位于西安的观测过程中，低轨道观测甚至出现相干增益超过斜距下降3次方影响的现象，这是由于低轨目标其相干增益与其轨道高度直接相关，而斜距变化与轨道高度变化并不是严格的线性相关，也就说低轨观测中，目标与观测点相对位置以及观测弧段的变化也将较大程度影响回波信号的接收功率。

图 5 归一化回波信号接收功率随目标轨道半径变化曲线

Figure 5. Normalization curve of received power changing in different orbit radii

下载: 全尺寸图片幻灯片

4.2 目标轨道高度变化对成像质量的影响

结合ISAR体制下目标所具有的孤立散射特点，参考点目标成像质量评价中的积分旁瓣比^[16](Integrated SideLobe Ratio, ISLR)，本文计算各图像中心单元的目标与背景噪声像素能量比(Target Noise Ratio, TNR)来反映成像质量。理论上来说，孤立散射点成像后对应像素单元与背景噪声的能量比应与脉冲回波信噪比、脉压长度、脉冲积累数等因素均相关。但为直观反映不同轨高下脉冲积累数变化带来的图像信噪比增益变化，本文将所有单脉冲回波信噪比统一设置为10 dB，仅改变脉冲积累数进行实验。

${\rm{TNR = }}\frac{{{{{E}}_{\rm{t}}}}}{{{{{E}}_{\rm{b}}}}}$

(23)

其中，E_t为目标像素能量积分，E_b为背景像素能量积分。

实验选取西安站观测结果进行成像质量分析，其中方位维、距离维无单位，代表像素点位置，图6为某空间目标在791 km轨道某处成像结果，目标中心单元的距离维、方位维剖面如图6所示。选取相近姿态下，目标在3个不同轨道高度的成像结果作为对比，如图7所示，其量化质量评价结果如表3所示。

从表3可以看出，随轨道高度升高脉冲积累数增加，相干处理后图像TNR也相应增大，这与3.3节中轨道高度对大角度ISAR成像体制影响的结论一致；其脉冲积累数与TNR之比直观反映相干积累对图像质量提升的作用，在脉冲回波信噪比、脉压长度、等因素相同的情况下，可近似为一定值，但可以预见的是在实际中将随着高度升高而增大。

图 6 目标图像距离、方位剖面图

Figure 6. Range and azimuth profiles of target image

下载: 全尺寸图片幻灯片

图 7 相近观测视角下，不同轨道高度成像结果对比图

Figure 7. Comparison result of target imaging at different heights with similar LOS parameters

下载: 全尺寸图片幻灯片

表 3 不同轨道高度图像质量评价

Table 3. Comparison result of imaging quality at different heights

轨道高度(km)	成像时间(s)	脉冲积累数	TNR	脉冲积累数/TNR
791	9.94	1988	6.82	291.58
1200	12.40	2484	8.61	288.58
1800	16.82	3364	11.45	293.80

下载: 导出CSV

| 显示表格

4.3 实验总结

本节实验应用推导的雷达成像方程从回波功率、成像质量两方面进行定分辨成像分析，可总结以下结论。(1)通过有效结合轨道信息，空间目标ISAR成像处理应采用更接近于合作(或半合作)目标的成像处理方式，进一步根据本文方法估计方位分辨性能可在保证横向分辨率的基础上有效指导成像角域优化选择。(2)总体而言，空间目标ISAR观测的回波信噪比受轨道高度升高而下降，另一方面较大的相干积累角ISAR成像，方位相干积累增益可部分补偿目标轨道高度增加引起的信噪比损失，也就是文中所述的回波接收功率下降量级小于斜距4次方，但大于SAR系统中斜距3次方的关系。(3)目标轨道参数、观测几何模型可有效指导空间轨道目标的成像工作功率、波形参数设计，实现ISAR成像信噪比预估计，同时可利用相干积累角的计算进行成像时间段的优化选择，满足高分辨成像任务。

5. 结束语

本文从基本雷达方程出发，推导空间轨道目标ISAR成像雷达方程的一般形式，分析空间目标轨道参数对目标转角速度以及成像相干积累增益的影响，定性分析了采用相干体制下的大转角ISAR雷达系统进行空间观测的优势，提出较为简便的成像信噪比估计方法。仿真实验验证ISAR成像的方位相干增益可部分弥补目标轨道高度增加引起的ISAR成像质量下降，为空间目标ISAR成像体制和信号处理设计、成像信噪比估计、成像时间段优化选择提供了理论基础。

References(41)

References

[1]	YANG Jian, LIU Chang, and WANG Yanfei. Detection and imaging of ground moving targets with real SAR data[J]. IEEE Transactions on Geoscience and Remote Sensing, 2015, 53(2): 920–932. doi: 10.1109/TGRS.2014.2330456.
[2]	DU Huagui, SONG Yongping, JIANG Nan, et al. A novel SAR ground maneuvering target imaging method based on adaptive phase tracking[J]. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61: 5211916. doi: 10.1109/TGRS.2023.3294252.
[3]	PERRY R P, DIPIETRO R C, and FANTE R L. SAR imaging of moving targets[J]. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1): 188–200. doi: 10.1109/7.745691.
[4]	ZHOU Feng, WU Renbiao, XING Mengdao, et al. Approach for single channel SAR ground moving target imaging and motion parameter estimation[J]. IET Radar, Sonar & Navigation, 2007, 1(1): 59–66. doi: 10.1049/iet-rsn:20060040.
[5]	TIAN Jing, CUI Wei, and WU Shuang. A novel method for parameter estimation of space moving targets[J]. IEEE Geoscience and Remote Sensing Letters, 2014, 11(2): 389–393. doi: 10.1109/LGRS.2013.2263332.
[6]	SUN Yan and WILLETT P. Hough transform for long chirp detection[J]. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(2): 553–569. doi: 10.1109/TAES.2002.1008986.
[7]	CARRETERO-MOYA J, GISMERO-MEN J, ASENSIO-LÓPEZ A, et al. Application of the radon transform to detect small-targets in sea clutter[J]. IET Radar, Sonar & Navigation, 2009, 3(2): 155–166. doi: 10.1049/iet-rsn:20080123.
[8]	XU Jia, YU Ji, PENG Yingning, et al. Radon-Fourier transform for radar target detection, (I:) Generalized Doppler filter bank[J]. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(2): 1186–1202. doi: 10.1109/TAES.2011.5751251.
[9]	XU Jia, YU Ji, PENG Yingning, et al. Radon-Fourier transform for radar target detection (II): Blind speed sidelobe suppression[J]. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(4): 2473–2489. doi: 10.1109/TAES.2011.6034645.
[10]	QIAN Lichang, XU Jia, SUN Wenfeng, et al. CLEAN based blind speed side lobe (BSSL) suppression in the Radon Fourier Transform (RFT) for multi-target detection[C]. IEEE 12th International Conference on Computer and Information Technology, Chengdu, China, 2012: 490–495. doi: 10.1109/CIT.2012.108.
[11]	CHEN Xiaolong, GUAN Jian, LIU Ningbo, et al. Maneuvering target detection via Radon-fractional Fourier transform-based long-time coherent integration[J]. IEEE Transactions on Signal Processing, 2014, 62(4): 939–953. doi: 10.1109/TSP.2013.2297682.
[12]	RAO Xuan, TAO Haihong, SU Jia, et al. Axis rotation MTD algorithm for weak target detection[J]. Digital Signal Processing, 2014, 26: 81–86. doi: 10.1016/j.dsp.2013.12.003.
[13]	SUN Zhi, LI Xiaolong, YI Wei, et al. A coherent detection and velocity estimation algorithm for the high-speed target based on the modified location rotation transform[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2018, 11(7): 2346–2361. doi: 10.1109/JSTARS.2018.2834535.
[14]	王超, 王岩飞, 刘畅, 等. 基于参数估计的高分辨率SAR运动目标距离徙动校正方法[J]. 雷达学报, 2019, 8(1): 64–72. doi: 10.12000/JR18054. WANG Chao, WANG Yanfei, LIU Chang, et al. A new approach to range cell migration correction for ground moving targets in high-resolution SAR system based on parameter estimation[J]. Journal of Radars, 2019, 8(1): 64–72. doi: 10.12000/JR18054.
[15]	XU Jia, XIA Xianggen, PENG Shibao, et al. Radar maneuvering target motion estimation based on generalized Radon-Fourier transform[J]. IEEE Transactions on Signal Processing, 2012, 60(12): 6190–6201. doi: 10.1109/TSP.2012.2217137.
[16]	KONG Lingjiang, LI Xiaolong, CUI Guolong, et al. Coherent integration algorithm for a maneuvering target with high-order range migration[J]. IEEE Transactions on Signal Processing, 2015, 63(17): 4474–4486. doi: 10.1109/TSP.2015.2437844.
[17]	XIONG Wei, ZHANG Ying, DONG Xichao, et al. A novel ship imaging method with multiple sinusoidal functions to match rotation effects in geosynchronous SAR[J]. Remote Sensing, 2022, 12(14): 2249. doi: 10.3390/rs12142249.
[18]	LI Xiaolong, CUI Guolong, YI Wei, et al. A fast maneuvering target motion parameters estimation algorithm based on ACCF[J]. IEEE Signal Processing Letters, 2015, 22(3): 270–274. doi: 10.1109/LSP.2014.2358230.
[19]	LI Xiaolong, CUI Guolong, KONG Lingjiang, et al. Fast non-searching method for maneuvering target detection and motion parameters estimation[J]. IEEE Transactions on Signal Processing, 2016, 64(9): 2232–2244. doi: 10.1109/TSP.2016.2515066.
[20]	贺雄鹏, 廖桂生, 许京伟, 等. 机动目标距离徙动校正与检测算法[J]. 系统工程与电子技术, 2018, 40(1): 1–8. doi: 10.3969/j.issn.1001-506X.2018.01.01. HE Xiongpeng, LIAO Guisheng, XU Jingwei, et al. Maneuvering target range migration correction and detection algorithm[J]. Systems Engineering and Electronics, 2018, 40(1): 1–8. doi: 10.3969/j.issn.1001-506X.2018.01.01.
[21]	贺雄鹏, 廖桂生, 许京伟, 等. 基于频率轴反转的机动目标距离徙动补偿方法[J]. 电子学报, 2018, 46(6): 1496–1502. doi: 10.3969/j.issn.0372-2112.2018.06.032. HE Xiongpeng, LIAO Guisheng, XU Jingwei, et al. Range migration compensation method for maneuvering target based on frequency axis reversal[J]. Acta Electronica Sinica, 2018, 46(6): 1496–1502. doi: 10.3969/j.issn.0372-2112.2018.06.032.
[22]	CHEN C C and ANDREWS H C. Target-motion-induced RADAR imaging[J]. IEEE Transactions on Aerospace and Electronic Systems, 1980, AES-16(1): 2–14. doi: 10.1109/TAES.1980.308873.
[23]	张泽. 空间目标的SAR/ISAR成像方法研究[D]. [硕士论文], 哈尔滨工业大学, 2019. doi: 10.27061/d.cnki.ghgdu.2019.000599. ZHANG Ze. Research on SAR/ISAR imaging method for space target[D]. [Master dissertation], Harbin Institute of Technology, 2019. doi: 10.27061/d.cnki.ghgdu.2019.000599.
[24]	ZHU Daiyin, WANG Ling, YU Yusheng, et al. Robust ISAR range alignment via minimizing the entropy of the average range profile[J]. IEEE Geoscience and Remote Sensing Letters, 2009, 6(2): 204–208. doi: 10.1109/LGRS.2008.2010562.
[25]	SAUER T and SCHROTH A. Robust range alignment algorithm via Hough transform in an ISAR imaging system[J]. IEEE Transactions on Aerospace and Electronic Systems, 1995, 31(3): 1173–1177. doi: 10.1109/7.395222.
[26]	ZHANG Lei, SHENG Jialian, DUAN Jia, et al. Translational motion compensation for ISAR imaging under low SNR by minimum entropy[J]. EURASIP Journal on Advances in Signal Processing, 2013, 2013(1): 33. doi: 10.1186/1687-6180-2013-33.
[27]	LIU Lei, ZHOU Feng, TAO Mingliang, et al. Adaptive translational motion compensation method for ISAR imaging under low SNR based on particle swarm optimization[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2015, 8(11): 5146–5157. doi: 10.1109/JSTARS.2015.2491307.
[28]	SHAO Shuai, LIU Hongwei, ZHANG Lei, et al. Integration of super-resolution ISAR imaging and fine motion compensation for complex maneuvering ship targets under high sea state[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60: 5222820. doi: 10.1109/TGRS.2022.3147266.
[29]	FU Jixiang, XING Mengdao, AMIN M, et al. ISAR translational motion compensation with simultaneous range alignment and phase adjustment in low SNR environments[C]. 2021 IEEE Radar Conference, Atlanta, USA, 2021: 1–6. doi: 10.1109/RadarConf2147009.2021.9455148.
[30]	LIU Fengkai, HUANG Darong, GUO Xinrong, et al. Joint range alignment and autofocus method based on combined Broyden-fletcher-Goldfarb-Shanno algorithm and whale optimization algorithm[J]. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61: 5214617. doi: 10.1109/TGRS.2023.3306474.
[31]	DJEDDI M and BENIDIR M. A two parallel extended Kalman filtering algorithm for the estimation of chirp signals in non-Gaussian noise[C]. The 13th European Signal Processing Conference, Antalya, Turkey, 2005: 1–4.
[32]	YANG Jungang, HUANG Xiaotao, JIN Tian, et al. New approach for SAR imaging of ground moving targets based on a keystone transform[J]. IEEE Geoscience and Remote Sensing Letters, 2011, 8(4): 829–833. doi: 10.1109/LGRS.2011.2118739.
[33]	LI Gang, XIA Xianggen, and PENG Yingning. Doppler keystone transform: An approach suitable for parallel implementation of SAR moving target imaging[J]. IEEE Geoscience and Remote Sensing Letters, 2008, 5(4): 573–577. doi: 10.1109/LGRS.2008.2000621.
[34]	黄小平, 王岩, 缪鹏程. 目标定位跟踪原理及应用—MATLAB仿真[M]. 北京: 电子工业出版社, 2018. HUANG Xiaoping, WANG Yan, and MIAO Pengcheng. Principles and Applications of Target Localization and Tracking—MATLAB Simulation[M]. Beijing: Publishing House of Electronics Industry, 2018.
[35]	LI Min, SUN Defeng, and TOH K C. A convergent 3-block semi-proximal ADMM for convex minimization problems with one strongly convex block[J]. Asia-Pacific Journal of Operational Research, 2015, 32(4): 1550024. doi: 10.1142/S0217595915500244.
[36]	CHEN Lin, JIANG Bowen, LIU Yuqi, et al. Application of adaptive EKF in real-time orbit determination[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2021, 43(4): 187. doi: 10.1007/s40430-021-02867-z.
[37]	LIU Jianjuan, CHEN Hongmei, and LIU Nanbo. Effective Sage-Husa Kalman filter for sins/Doppler/platform compass integrated navigation system[C]. 2016 IEEE Chinese Guidance, Navigation and Control Conference, Nanjing, China, 2016: 541–546. doi: 10.1109/CGNCC.2016.7828843.
[38]	HUANG Penghui, LIAO Guisheng, YANG Zhiwei, et al. Ground maneuvering target imaging and high-order motion parameter estimation based on second-order Keystone and generalized Hough-HAF transform[J]. IEEE Transactions on Geoscience and Remote Sensing, 2017, 55(1): 320–335. doi: 10.1109/TGRS.2016.2606436.
[39]	孙景波. 旋翼无人机雷达回波微动特征分析与提取[D]. [硕士论文], 中国民航大学, 2021. doi: 10.27627/d.cnki.gzmhy.2021.000057. SUN Jingbo. Micro-motion feature analysis and extraction of rotor UAV radar echoes[D]. [Master dissertation], Civil Aviation University of China, 2021. doi: 10.27627/d.cnki.gzmhy.2021.000057.
[40]	DU Huagui, SONG Yongping, ZHOU Jiwen, et al. A novel parameter estimation method for polynomial phase signals via adaptive EKF[J]. IEEE Internet of Things Journal, 2024, 11(11): 20816–20830. doi: 10.1109/JIOT.2024.3373642.
[41]	王武. 机载圆周SAR-GMTI关键技术研究[D]. [博士论文], 国防科技大学, 2019. doi: 10.27052/d.cnki.gzjgu.2019.000357. WANG Wu. Study on key techniques for circular SAR-GMTI[D]. [Ph.D. dissertation], National University of Defense Technology, 2019. doi: 10.27052/d.cnki.gzjgu.2019.000357.

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A New Approach to High-order Range Cell Migration Correction for SAR Ground Moving Targets Based on Phase Tracking

DOI: 10.12000/JR24122 CSTR: 32380.14.JR24122