分布式多传感器多目标跟踪方法综述

曾雅俊; 王俊; 魏少明; 孙进平; 雷鹏

doi:10.12000/JR22111

分布式多传感器多目标跟踪方法综述

DOI: 10.12000/JR22111

北京航空航天大学电子信息工程学院北京 100191

基金项目: 国家自然科学基金(62171029, 61671035)，预研基金(61404130122)，重点实验室基金(6142502180103)，教育部产学合作协同育人项目(202101105001)

详细信息

作者简介:
曾雅俊，博士生，主要研究方向为多目标跟踪、多源信息融合

王　俊，博士，教授，主要研究方向为雷达信号处理、FPGA/DSP嵌入式系统、目标识别与跟踪、多传感器数据融合

魏少明，博士，实验师，主要研究方向为雷达信号处理、多目标跟踪、数据融合、三维成像

孙进平，教授，博士生导师，主要研究方向为目标跟踪、信号分析检测与估计、稀疏微波成像、图像理解、雷达信号与数据处理的算法及软硬件实现

雷　鹏，博士，副教授，硕士生导师，主要研究方向为数字信号处理、贝叶斯估计、模式识别

通讯作者:
魏少明 shaoming.wei@buaa.edu.cn

责任主编：关键 Corresponding Editor: GUAN Jian
中图分类号: TN951; TN957.51; TN971.⁺1
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出版历程
- 收稿日期: 2022-06-08
- 修回日期: 2022-08-02
- 网络出版日期: 2022-08-15
- 刊出日期: 2023-02-28

Review of the Method for Distributed Multi-sensor Multi-target Tracking（in English）

School of Electronic and Information Engineering, Beihang University, Beijing 100191, China

Funds: The National Natural Science Foundation of China (62171029, 61671035), The Pre-research Foundation (61404130122), The Key Laboratory Foundation (6142502180103), The Ministry of Education’s Industry-University Cooperation and Collaborative Education Project (202101105001)

More Information

Corresponding author: WEI Shaoming, shaoming.wei@buaa.edu.cn

摘要

摘要: 多传感器多目标跟踪是信息融合领域的热点问题，其通过融合多个局部传感器数据，提高目标跟踪精度和稳定性。多传感器多目标跟踪按融合体系可分为分布式、集中式、混合式3类，其中分布式融合结构对网络通信带宽要求低、可靠性和稳定性强，广泛应用于军事、民用领域。该文聚焦分布式多传感器多目标跟踪涉及的目标跟踪、传感器配准、航迹关联、数据融合4项关键技术，主要分析了各关键技术的理论原理与适用条件，重点介绍了不完整测量条件下的空间配准与航迹关联，并给出仿真结果。最后，该文总结了现有分布式多传感器多目标跟踪关键技术存在的问题，并指出了其未来发展趋势。
- 分布式多传感器多目标跟踪 /
- 目标跟踪 /
- 传感器配准 /
- 航迹关联 /
- 数据融合
Abstract: Multi-sensor multi-target tracking is a popular topic in the field of information fusion. It improves the accuracy and stability of target tracking by fusing multiple local sensor information. By the fusion system, the multi-sensor multi-target tracking is grouped into distributed fusion, centralized fusion, and hybrid fusion. Distributed fusion is widely applied in the military and civilian fields with the advantages of strong reliability, high stability, and low requirements on network communication bandwidth. Key techniques of distributed multi-sensor multi-target tracking include multi-target tracking, sensor registration, track-to-track association, and data fusion. This paper reviews the theoretical basis and applicable conditions of these key techniques, highlights the incomplete measurement spatial registration algorithm and track association algorithm, and provides the simulation results. Finally, the weaknesses of the key techniques of distributed multi-sensor multi-target tracking are summarized, and the future development trends of these key techniques are surveyed.
- Distributed Multi-sensor Multi-target Tracking (DMMT) /
- Multi-target tracking /
- Sensor registration /
- Track-to-track association /
- Data fusion

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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

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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

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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

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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

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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

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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

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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

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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

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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。

图 1 分布式多传感器多目标跟踪流程图

Figure 1. Flowchart of distributed multi-sensor multi-target tracking

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图 2 时间配准方法

Figure 2. Time registration methods

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图 3 空间配准几何示意图

Figure 3. Illustration of spatial registration

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图 4 空间配准场景

Figure 4. Scene of spatial registration

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图 5 WGS84坐标系下配准前后显著性目标位置^[82]

Figure 5. Registration results before and after registration in the WGS84 coordinate system^[82]

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图 6 典型的航迹关联方法及分类

Figure 6. Classification of track-to-track association methods

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图 7 航迹关联场景

Figure 7. Scene of track-to-track association

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图 8 航迹关联正确率^[82]

Figure 8. Accuracy of track association^[82]

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图 9 航迹关联与空间配准关系^[82]

Figure 9. Relationship of track-track association and spatial registration^[82]

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图 10 分布式多传感器估计融合

Figure 10. Distributed multi-sensor estimation fusion

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图 1 Flowchart of distributed multi-sensor multi-target tracking

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图 2 Time registration methods

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图 3 Illustration of spatial registration

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图 4 Scene of spatial registration

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图 5 Registration results before and after registration in the WGS84 coordinate system ^{[
82]}

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图 6 Classification of track-to-track association methods

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图 7 Scene of track-to-track association

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图 8 Accuracy of track association ^{[
82]}

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图 9 Relationship of track-track association and spatial registration ^{[
82]}

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图 10 Distributed multi-sensor estimation fusion

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表 1 典型的多目标跟踪方法性能对比

Table 1. Performance comparison of different multi-target tracking methods

多目标跟踪类型	跟踪方法	跟踪精度	运算量
数据关联类	GNN	低	低
	JPDA	中等	中等
	JIPDA	中等	中等
	MHT	高	高
随机有限集类	PHD	低	低
	CPHD	中等	中等
	TPHD	中等	低
	TCPHD	中等	中等
	MeMBer	中等	中等
	PMBM	高	中等
	GLMB	高	高
	LMB	高	中等

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表 2 多传感器时间配准方法性能对比

Table 2. Comparison of multi-sensor time registration methods

配准类型	配准方法	配准精度	计算量	目标运动状态
插值类	内插外推	较低	低	匀速
	曲线插值	中等	较高	匀速\非匀速
	曲线拟合	中等	较高	匀速\非匀速
参数估计类	最小二乘	中等	中等	匀速
参数估计类	卡尔曼滤波	较高	较高	匀速\非匀速

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表 3 多传感器非合作目标空间配准方法分类

Table 3. Classification of multi-sensor spatial registration methods based on non-cooperative targets

配准方法	实时性	是否能估计目标位置	参与传感器个数	传感器类型
RTQC	离线	否	两个	同类
LS	离线	否	两个	同类
GLS	离线	否	两个	同类
EML	离线	是	两个	同类
KF	在线	是	多个	同类
RFS	在线	是	多个	同类
MLR	离线	是	多个	同类\异类
RBER	离线	是	多个	同类\异类

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表 4 航迹关联性能对比

Table 4. Comparison of multi-sensor track-to-track association methods

航迹关联方法	航迹关联正确率(%)	时间开销(s)
SMBTANTD^[82]	99.6	3.4
Generalized Likelihood^[15]	97.4	2.8
Fuzzy function^[89]	96.7	8.1

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表 5 多传感器估计融合方法对比

Table 5. Comparison of multi-sensor estimation fusion methods

估计融合方法	是否考虑航迹相关	计算量	融合精度	传感器类型
简单凸组合融合	否	低	低	同类
Bar-Shalom-Campo融合	是	较高	较高	同类
基于MAP	是	较高	较高	同类
CI融合	是	较高	较高	同类
GCI融合	是	较高	较高	同类/异类
AA融合	是	较高	较高	同类/异类
基于EKF融合	否	较高	较高	同类/异类
基于UKF融合	否	较高	较高	同类/异类
基于PF融合	否	高	高	同类/异类

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表 6 典型的多传感器多目标跟踪方法性能对比

Table 6. Performance comparison of multi-sensor multi-target tracking methods

多目标跟踪类型	融合准则	跟踪方法	运算量	跟踪精度
数据关联类	CI融合	JPDA	中等	中等
数据关联类	简单凸组合融合	MHT	高	中等
随机有限集类	GCI/GA融合	PHD	低	低
		CPHD	中等	中等
		MeMBer	中等	中等
		GLMB	高	高
		LMB	中等	高
	AA融合	PHD	低	低
		CPHD	中等	中等
		MeMBer	中等	中等
		GLMB	高	高
		LMB	中等	高

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表 1 Performance comparison of different multi-target tracking methods

Types of multiple target tracking	Tracking methods	Tracking accuracy	Computational complexity
Data association	GNN	Low	Low
	JPDA	Medium	Medium
	JIPDA	Medium	Medium
	MHT	High	High
Random finite set	PHD	Low	Low
	CPHD	Medium	Medium
	TPHD	Medium	Low
	TCPHD	Medium	Medium
	MeMBer	Medium	Medium
	PMBM	High	Medium
	GLMB	High	High
	LMB	High	Medium

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表 2 Comparison of multi-sensor time registration methods

Registration types	Registration methods	Registration accuracy	Computational complexity	Target motion state
Interpolation class	Interpolation and extrapolation	Lower	Lower	Uniform
	Curve interpolation	Medium	Higher	Uniform \ Non-uniform
	Curve fitting	Medium	Higher	Uniform \ Non-uniform
Parameter estimation	Least squares	Medium	Medium	Uniform
Parameter estimation	Kalman filter	Higher	Higher	Uniform \ Non-uniform

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表 3 Classification of multi-sensor spatial registration methods based on non-cooperative targets

Registration methods	Real-time	Can the target position be estimated?	Number of sensors	Sensor type
RTQC	Offline	No	Two	Homogeneous
LS	Offline	No	Two	Homogeneous
GLS	Offline	No	Two	Homogeneous
EML	Offline	Yes	Two	Homogeneous
KF	Online	Yes	Multiple	Homogeneous
RFS	Online	Yes	Multiple	Homogeneous
MLR	Offline	Yes	Multiple	Homogeneous \ Heterogeneous
RBER	Offline	Yes	Multiple	Homogeneous \ Heterogeneous

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表 4 Comparison of multi-sensor track-to-track association methods

Association algorithm	Association rate (%)	Time consumed (s)
SMBTANTD ^{[ 82]}	99.6	3.4
Generalized likelihood ^{[ 15]}	97.4	2.8
Fuzzy function ^{[ 89]}	96.7	8.1

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表 5 Comparison of multi-sensor estimation fusion methods

Estimation fusion method	Whether to consider track correlation	Computational complexity	Fusion accuracy	Sensor type
Simple convex combination fusion	No	Low	Low	Homogeneous
Bar-Shalom-Campo fusion	Yes	Higher	Higher	Homogeneous
MAP fusion	Yes	Higher	Higher	Homogeneous
CI fusion	Yes	Higher	Higher	Homogeneous
GCI fusion	Yes	Higher	Higher	Homogeneous \ Heterogeneous
AA fusion	Yes	Higher	Higher	Homogeneous \ Heterogeneous
EKF fusion	No	Higher	Higher	Homogeneous \ Heterogeneous
UKF fusion	No	Higher	Higher	Homogeneous \ Heterogeneous
PF fusion	No	High	High	Homogeneous \ Heterogeneous

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表 6 Performance comparison of multi-sensor multi-target tracking methods

Types of multiple target tracking	Fusion criteria	Tracking methods	Computational complexity	Tracking accuracy
Data association	CI Fusion	JPDA	Medium	Medium
Data association	Simple convex combination fusion	MHT	High	Medium
Random finite set	GCI/GA fusion	PHD	Low	Low
		CPHD	Medium	Medium
		MeMBer	Medium	Medium
		GLMB	High	High
		LMB	Medium	High
	AA fusion	PHD	Low	Low
		CPHD	Medium	Medium
		MeMBer	Medium	Medium
		GLMB	High	High
		LMB	Medium	High

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参考文献(133)

[1]	韩崇昭, 朱洪艳, 段战胜, 等. 多源信息融合[M]. 北京: 清华大学出版社, 2006: 1–13. HAN Chongzhao, ZHU Hongyan, DUAN Zhansheng, et al. Multi-Source Information Fusion[M]. Beijing: Tsinghua University Press, 2006: 1–13.
[2]	陈科文, 张祖平, 龙军. 多源信息融合关键问题、研究进展与新动向[J]. 计算机科学, 2013, 40(8): 6–13. doi: 10.3969/j.issn.1002-137X.2013.08.002. CHEN Kewen, ZHANG Zuping, and LONG Jun. Multisource information fusion: Key issues, research progress and new trends[J]. Computer Science, 2013, 40(8): 6–13. doi: 10.3969/j.issn.1002-137X.2013.08.002.
[3]	李龙飘. 多传感器系统中信息融合技术的研究[D]. [硕士论文], 中北大学, 2009. LI Longpiao. Research on data fusion technique of multi-sensor system[D]. [Master dissertation], North University of China, 2009.
[4]	苏军平. 多传感器信息融合关键技术研究[D]. [硕士论文], 西安电子科技大学, 2018. SU Junping. Research on the key technology of the multi-sensor information fusion[D]. [Master dissertation], Xidian University, 2018.
[5]	王晓丽. 基于雷达组网提高空中目标航迹测量精度的数据融合方法研究[D]. [硕士论文], 电子科技大学, 2012. WANG Xiaoli. Research on data fusion based on netted radar to improve measurement precision of aerial targets’flight track[D]. [Master dissertation], University of Electronic Science and Technology of China, 2012.
[6]	ZHU Shanshan. Multi-source information fusion technology and its engineering application[J]. Research in Health Science, 2020, 4(4): 408–422. doi: 10.22158/rhs.v4n4p408.
[7]	ANITHA R, RENUKA S, and ABUDHAHIR A. Multi sensor data fusion algorithms for target tracking using multiple measurements[C]. 2013 IEEE International Conference on Computational Intelligence and Computing Research, Enathi, India, 2013: 1–4.
[8]	AEBERHARD M, SCHLICHTHARLE S, KAEMPCHEN N, et al. Track-to-track fusion with asynchronous sensors using information matrix fusion for surround environment perception[J]. IEEE Transactions on Intelligent Transportation Systems, 2012, 13(4): 1717–1726. doi: 10.1109/TITS.2012.2202229.
[9]	SHEN Qiang, LIU Jieyu, ZHOU Xiaogang, et al. Centralized fusion methods for multi-sensor system with bounded disturbances[J]. IEEE Access, 2019, 7: 141612–141626. doi: 10.1109/ACCESS.2019.2943163.
[10]	赵蕊, 贺建军. 多传感器信息融合技术[J]. 计算机测量与控制, 2007, 15(9): 1124–1126, 1134. doi: 10.3969/j.issn.1671-4598.2007.09.001. ZHAO Rui and HE Jianjun. Technology of multi-sensor information fusion[J]. Computer Measurement &Control, 2007, 15(9): 1124–1126, 1134. doi: 10.3969/j.issn.1671-4598.2007.09.001.
[11]	吕漫丽, 孙灵芳. 多传感器信息融合技术[J]. 自动化技术与应用, 2008, 27(2): 79–82. doi: 10.3969/j.issn.1003-7241.2008.02.025. LV Manli and SUN Lingfang. Multi-sensor information fusion technology[J]. Techniques of Automation and Applications, 2008, 27(2): 79–82. doi: 10.3969/j.issn.1003-7241.2008.02.025.
[12]	何友, 彭应宁, 陆大絟. 多传感器数据融合模型综述[J]. 清华大学学报: 自然科学版, 1996, 36(9): 14–20. HE You, PENG Yingning, and LU Dajin. Survey of multisensor data fusion models[J]. Journal of Tsinghua University:Science and Technology, 1996, 36(9): 14–20.
[13]	WANG Zhangjing, WU Yu, and NIU Qingqing. Multi-sensor fusion in automated driving: A survey[J]. IEEE Access, 2020, 8: 2847–2868. doi: 10.1109/ACCESS.2019.2962554.
[14]	LIN Xiangdong, BAR-SHALOM Y, and KIRUBARAJAN T. Multisensor multitarget bias estimation for general asynchronous sensors[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(3): 899–921. doi: 10.1109/TAES.2005.1541438.
[15]	何友, 王国宏, 陆大絟, 等. 多传感器信息融合及应用[M]. 北京: 电子工业出版社, 2000: 2–11. HE You, WANG Guohong, LU Dajin, et al. Multisensor Information Fusion with Applications[M]. Beijing: Publishing House of Electronics Industry, 2000: 2–11.
[16]	高青. 多传感器数据融合算法研究[D]. [硕士论文], 西安电子科技大学, 2008. GAO Qing. Algorithms research on multisensor data fusion[D]. [Master dissertation], Xidian University, 2008.
[17]	肖斌. 多传感器信息融合及其在工业中的应用[D]. [硕士论文], 太原理工大学, 2008. XIAO Bin. Multi-sensor information fusion and its application in industry[D]. [Master dissertation], Taiyuan University of Technology, 2008.
[18]	陈文辉, 马铁华. 多传感器信息融合技术的研究与进展[J]. 科技情报开发与经济, 2006, 16(19): 212–213. doi: 10.3969/j.issn.1005-6033.2006.19.124. CHEN Wenhui and MA Tiehua. The research and progress of multi-sensor information fusion techniques[J]. Sci-Tech Information Development &Economy, 2006, 16(19): 212–213. doi: 10.3969/j.issn.1005-6033.2006.19.124.
[19]	NAZARI M, PASHAZADEH S, and MOHAMMAD-KHANLI L. An adaptive density-based fuzzy clustering track association for distributed tracking system[J]. IEEE Access, 2019, 7: 135972–135981. doi: 10.1109/ACCESS.2019.2941184.
[20]	DASH D and JAYARAMAN V. A probabilistic model for sensor fusion using range-only measurements in multistatic radar[J]. IEEE Sensors Letters, 2020, 4(6): 1–4. doi: 10.1109/LSENS.2020.2993589.
[21]	SHARMA A and CHAUHAN S. Sensor fusion for distributed detection of mobile intruders in surveillance wireless sensor networks[J]. IEEE Sensors Journal, 2020, 20(24): 15224–15231. doi: 10.1109/JSEN.2020.3009828.
[22]	KUMAR M, GARG D P, and ZACHERY R A. A method for judicious fusion of inconsistent multiple sensor data[J]. IEEE Sensors Journal, 2007, 7(5): 723–733. doi: 10.1109/JSEN.2007.894905.
[23]	LLINAS J and HALL D L. An introduction to multi-sensor data fusion[C]. The 1998 IEEE International Symposium on Circuits & Systems, Monterey, USA, 1998: 537–540.
[24]	HU Jinwen, ZHENG Boyin, WANG Ce, et al. A survey on multi-sensor fusion based obstacle detection for intelligent ground vehicles in off-road environments[J]. Frontiers of Information Technology &Electronic Engineering, 2020, 21(5): 675–692. doi: 10.1631/FITEE.1900518.
[25]	XIAO Fuyuan. Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy[J]. Information Fusion, 2019, 46: 23–32. doi: 10.1016/j.inffus.2018.04.003.
[26]	KHALEGHI B, KHAMIS A, KARRAY F O, et al. Multisensor data fusion: A review of the state-of-the-art[J]. Information Fusion, 2013, 14(1): 28–44. doi: 10.1016/j.inffus.2011.08.001.
[27]	LIGGINS II M, POULARIKAS A D, HALL D, et al. Handbook of Multisensor Data Fusion: Theory and Practice[M]. 2nd ed. Boca Raton: CRC Press, 2009: 3–16.
[28]	GAO Shesheng, ZHONG Yongmin, and LI Wei. Random weighting method for multisensor data fusion[J]. IEEE Sensors Journal, 2011, 11(9): 1955–1961. doi: 10.1109/JSEN.2011.2107896.
[29]	CARON F, DAVY M, DUFLOS E, et al. Particle filtering for multisensor data fusion with switching observation models: Application to land vehicle positioning[J]. IEEE Transactions on Signal Processing, 2007, 55(6): 2703–2719. doi: 10.1109/TSP.2007.893914.
[30]	MITCHELL H B. Multi-Sensor Data Fusion: An Introduction[M]. Berlin: Springer, 2007: 1–22.
[31]	MAHLER R P S. Statistical Multisource-Multitarget Information Fusion[M]. Boston: Artech House, Inc., 2007: 305–682.
[32]	DALEY R. Estimating the wind field from chemical constituent observations: Experiments with a one-dimensional extended Kalman filter[J]. Monthly Weather Review, 1995, 123(1): 181–198. doi: 10.1175/1520-0493(1995)123<0181:ETWFFC>2.0.CO;2.
[33]	WAN E A and VAN DER MERWE R. The Unscented Kalman Filter[M]. HAYKIN S. Kalman Filtering and Neural Networks. New York: John Wiley & Sons, Inc., 2001: 221–280.
[34]	ARASARATNAM I and HAYKIN S. Cubature Kalman filters[J]. IEEE Transactions on Automatic Control, 2009, 54(6): 1254–1269. doi: 10.1109/TAC.2009.2019800.
[35]	GUSTAFSSON F. Particle filter theory and practice with positioning applications[J]. IEEE Aerospace and Electronic Systems Magazine, 2010, 25(7): 53–82. doi: 10.1109/MAES.2010.5546308.
[36]	VO B N, MALLICK M, BAR-SHALOM Y, et al. Multitarget Tracking[M]. WEBSTER J G. Wiley Encyclopedia of Electrical and Electronics Engineering. New York: John Wiley & Sons, 2015: 1–11.
[37]	BAR-SHALOM Y. Multitarget-Multisensor Tracking: Applications and Advances[M]. Boston: Artech House, 1990: 2–9.
[38]	FORTMANN T, BAR-SHALOM Y, and SCHEFFE M. Sonar tracking of multiple targets using joint probabilistic data association[J]. IEEE journal of Oceanic Engineering, 1983, 8(3): 173–184. doi: 10.1109/JOE.1983.1145560.
[39]	COLGROVE S B, DAVIS A W, and AYLIFFE J K. Track initiation and nearest neighbours incorporated into probabilistic data association[J]. Journal of Electrical and Electronics Engineers,Australia, 1986, 6(3): 191–198.
[40]	CHANG K C and BAR-SHALOM Y. Joint probabilistic data association for multitarget tracking with possibly unresolved measurements and maneuvers[J]. IEEE Transactions on Automatic Control, 1984, 29(7): 585–594. doi: 10.1109/TAC.1984.1103597.
[41]	MUSICKI D and EVANS R. Joint integrated probabilistic data association-JIPDA[C]. The 5th International Conference on Information Fusion, Annapolis, USA, 2002: 1120–1125.
[42]	SINGER R A and SEA R G. New results in optimizing surveillance system tracking and data correlation performance in dense multitarget environments[J]. IEEE Transactions on Automatic Control, 1973, 18(6): 571–582. doi: 10.1109/TAC.1973.1100421.
[43]	SONG T L, LEE D G, and RYU J. A probabilistic nearest neighbor filter algorithm for tracking in a clutter environment[J]. Signal Processing, 2005, 85(10): 2044–2053. doi: 10.1016/j.sigpro.2005.01.016.
[44]	REID D B. An algorithm for tracking multiple targets[J]. IEEE transactions on Automatic Control, 1979, 24(6): 843–854. doi: 10.1109/TAC.1979.1102177.
[45]	BLACKMAN S S. Multiple hypothesis tracking for multiple target tracking[J]. IEEE Aerospace and Electronic Systems Magazine, 2004, 19(1): 5–18. doi: 10.1109/MAES.2004.1263228.
[46]	MAHLER R P S. Multitarget Bayes filtering via first-order multitarget moments[J]. IEEE Transactions on Aerospace and Electronic systems, 2003, 39(4): 1152–1178. doi: 10.1109/TAES.2003.1261119.
[47]	MAHLER R. PHD filters of higher order in target number[J]. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(4): 1523–1543. doi: 10.1109/TAES.2007.4441756.
[48]	GARCÍA-FERNÁNDEZ Á F and SVENSSON L. Trajectory PHD and CPHD filters[J]. IEEE Transactions on Signal Processing, 2019, 67(22): 5702–5714. doi: 10.1109/TSP.2019.2943234.
[49]	VO B T, VO B N, and CANTONI A. On multi-Bernoulli approximations to the Bayes multi-target filter[C]. International Conference on Information Fusion, Xi’an, China, 2007: 1–8.
[50]	VO B T, VO B N, and CANTONI A. The cardinality balanced multi-target multi-Bernoulli filter and its implementations[J]. IEEE Transactions on Signal Processing, 2009, 57(2): 409–423. doi: 10.1109/TSP.2008.2007924.
[51]	VO B T and VO B N. Labeled random finite sets and multi-object conjugate priors[J]. IEEE Transactions on Signal Processing, 2013, 61(13): 3460–3475. doi: 10.1109/TSP.2013.2259822.
[52]	PAPI F, VO B N, VO B T, et al. Generalized labeled multi-Bernoulli approximation of multi-object densities[J]. IEEE Transactions on Signal Processing, 2015, 63(20): 5487–5497. doi: 10.1109/TSP.2015.2454478.
[53]	REUTER S, VO B T, VO B N, et al. The Labeled multi-Bernoulli filter[J]. IEEE Transactions on Signal Processing, 2014, 62(12): 3246–3260. doi: 10.1109/TSP.2014.2323064.
[54]	GARCÍA-FERNÁNDEZ Á F, WILLIAMS J L, GRANSTRÖM K, et al. Poisson multi-Bernoulli mixture filter: Direct derivation and implementation[J]. IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(4): 1883–1901. doi: 10.1109/TAES.2018.2805153.
[55]	LIN Xiangdong, BAR-SHALOM Y, and KIRUBARAJAN T. Exact multisensor dynamic bias estimation with local tracks[J]. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(2): 576–590. doi: 10.1109/TAES.2004.1310006.
[56]	BLAIR W D, RICE T R, ALOUANI A T, et al. Asynchronous data fusion for target tracking with a multitasking radar and optical sensor[C]. The SPIE of 1482, Acquisition, Tracking, and Pointing V, Orlando, USA, 1991: 234–245.
[57]	李莉. 最小二乘法时间配准在测量数据融合中的应用[J]. 仪表技术, 2017(12): 35–36, 49. doi: 10.19432/j.cnki.issn1006-2394.2017.12.010. LI Li. Application of time registration of the least square method in measurement data fusion[J]. Instrumentation Technology, 2017(12): 35–36, 49. doi: 10.19432/j.cnki.issn1006-2394.2017.12.010.
[58]	吴聪, 王红, 李志淮, 等. 基于最小二乘曲线拟合的时间配准方法研究[J]. 舰船电子对抗, 2013, 36(4): 44–47, 51. doi: 10.16426/j.cnki.jcdzdk.2013.04.018. WU Cong, WANG Hong, LI Zhihuai, et al. Research into time registration method based on least-square curve fitting[J]. Shipboard Electronic Countermeasure, 2013, 36(4): 44–47, 51. doi: 10.16426/j.cnki.jcdzdk.2013.04.018.
[59]	张圣华, 王书基, 孙潮义. 多雷达数据融合中时间对准问题的研究[J]. 舰船电子工程, 2001, 21(2): 23–25. doi: 10.3969/j.issn.1627-9730.2001.02.005. ZHANG Shenghua, WANG Shuji, and SUN Chaoyi. Research on time registration in multi-radar data fusion[J]. Ship Electronic Engineering, 2001, 21(2): 23–25. doi: 10.3969/j.issn.1627-9730.2001.02.005.
[60]	梁凯, 潘泉, 宋国明, 等. 基于曲线拟合的多传感器时间对准方法研究[J]. 火力与指挥控制, 2006, 31(12): 51–53. doi: 10.3969/j.issn.1002-0640.2006.12.015. LIANG Kai, PAN Quan, SONG Guoming, et al. The study of multi-sensor time registration method based on curve fitting[J]. Fire Control and Command Control, 2006, 31(12): 51–53. doi: 10.3969/j.issn.1002-0640.2006.12.015.
[61]	YU Hongbo, WANG Guohong, and CAO Qian. A novel approach for time registration of multi-radar data[J]. Applied Mechanics and Materials, 2013, 385/386: 1377–1380. doi: 10.4028/www.scientific.net/AMM.385-386.1377.
[62]	LI Song, CHENG Yongmei, BROWN D, et al. Comprehensive time-offset estimation for multisensor target tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(3): 2351–2373. doi: 10.1109/TAES.2019.2948517.
[63]	TAGHAVI E, THARMARASA R, KIRUBARAJAN T, et al. A practical bias estimation algorithm for multisensor-multitarget tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 2016, 52(1): 2–19. doi: 10.1109/TAES.2015.140574.
[64]	OKELLO N N and CHALLA S. Joint sensor registration and track-to-track fusion for distributed trackers[J]. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(3): 808–823. doi: 10.1109/TAES.2004.1337456.
[65]	RHODE S, USEVICH K, MARKOVSKY I, et al. A recursive restricted total least-squares algorithm[J]. IEEE Transactions on Signal Processing, 2014, 62(21): 5652–5662. doi: 10.1109/TSP.2014.2350959.
[66]	FORTUNATI S, FARINA A, GINI F, et al. Least squares estimation and Cramér-Rao type lower bounds for relative sensor registration process[J]. IEEE Transactions on Signal Processing, 2011, 59(3): 1075–1087. doi: 10.1109/TSP.2010.2097258.
[67]	PULFORD G W. Analysis of a nonlinear least squares procedure used in global positioning systems[J]. IEEE Transactions on Signal Processing, 2010, 58(9): 4526–4534. doi: 10.1109/TSP.2010.2050061.
[68]	BAI Shulin and ZHANG Yumei. Error registration of netted radar by using GLS algorithm[C]. The 33rd Chinese Control Conference, Nanjing, China, 2014: 7430–7433.
[69]	LU Chenyang, WANG Xiaorui, and KOUTSOUKOS X. Feedback utilization control in distributed real-time systems with end-to-end tasks[J]. IEEE Transactions on Parallel and Distributed Systems, 2005, 16(6): 550–561. doi: 10.1109/TPDS.2005.73.
[70]	ZHOU Yifeng, LEUNG H, and YIP P C. An exact maximum likelihood registration algorithm for data fusion[J]. IEEE Transactions on Signal Processing, 1997, 45(6): 1560–1573. doi: 10.1109/78.599998.
[71]	CHITOUR Y and PASCAL F. Exact maximum likelihood estimates for SIRV covariance matrix: Existence and algorithm analysis[J]. IEEE Transactions on Signal Processing, 2008, 56(10): 4563–4573. doi: 10.1109/TSP.2008.927464.
[72]	OKELLO N N and RISTIC B. Maximum likelihood registration for multiple dissimilar sensors[J]. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(3): 1074–1083. doi: 10.1109/TAES.2003.1238759.
[73]	MCMICHAEL D W and OKELLO N N. Maximum likelihood registration of dissimilar sensors[C]. The 1st Australian Data Fusion Symposium, Adelaide, Australia, 1996: 31–34.
[74]	HELMICK R E and RICE T R. Removal of alignment errors in an integrated system of two 3-D sensors[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(4): 1333–1343. doi: 10.1109/7.259537.
[75]	KOSUGE Y and OKADA T. Bias estimation of two 3-dimensional radars using Kalman filter[C]. The 4th IEEE International Workshop on Advanced Motion Control, Mie, Japan, 1996: 377–382.
[76]	NABAA N and BISHOP R H. Solution to a multisensor tracking problem with sensor registration errors[J]. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1): 354–363. doi: 10.1109/7.745706.
[77]	LI W, LEUNG H, and ZHOU Yifeng. Space-time registration of radar and ESM using unscented Kalman filter[J]. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(3): 824–836. doi: 10.1109/TAES.2004.1337457.
[78]	胡洪涛, 敬忠良, 胡士强. 一种基于Unscented卡尔曼滤波的多平台多传感器配准算法[J]. 上海交通大学学报, 2005, 39(9): 1518–1521. doi: 10.16183/j.cnki.jsjtu.2005.09.030. HU Hongtao, JING Zhongliang, and HU Shiqiang. An unscented Kalman filter based multi-platform multi-sensor registration[J]. Journal of Shanghai Jiaotong University, 2005, 39(9): 1518–1521. doi: 10.16183/j.cnki.jsjtu.2005.09.030.
[79]	LI Wenling, JIA Yingmin, DU Junping, et al. Gaussian mixture PHD filter for multi-sensor multi-target tracking with registration errors[J]. Signal Processing, 2013, 93(1): 86–99. doi: 10.1016/j.sigpro.2012.06.030.
[80]	LI Minzhe, JING Zhongliang, PAN Han, et al. Joint registration and multi-target tracking based on labelled random finite set and expectation maximisation[J]. IET Radar,Sonar &Navigation, 2018, 12(3): 312–322. doi: 10.1049/iet-rsn.2017.0137.
[81]	LIAN Feng, HAN Chongzhao, LIU Weifeng, et al. Joint spatial registration and multi-target tracking using an extended probability hypothesis density filter[J]. IET Radar,Sonar &Navigation, 2011, 5(4): 441–448. doi: 10.1049/iet-rsn.2010.0057.
[82]	WANG Jun, ZENG Yajun, WEI Shaoming, et al. Multi-sensor track-to-track association and spatial registration algorithm under incomplete measurements[J]. IEEE Transactions on Signal Processing, 2021, 69: 3337–3350. doi: 10.1109/TSP.2021.3084533.
[83]	KANYUCK A J and SINGER R A. Correlation of multiple-site track data[J]. IEEE Transactions on Aerospace and Electronic Systems, 1970, AES-6(2): 180–187. doi: 10.1109/TAES.1970.310100.
[84]	BAR-SHALOM Y. On the track-to-track correlation problem[J]. IEEE Transactions on Automatic Control, 1981, 26(2): 571–572. doi: 10.1109/TAC.1981.1102635.
[85]	何友, 唐劲松, 王国宏. 多雷达跟踪系统中航迹质量管理的优化[J]. 现代雷达, 1995, 17(1): 14–19, 54. doi: 10.16592/j.cnki.1004-7859.1995.01.002. HE You, TANG Jinsong, and WANG Guohong. Optimal tracking-quality-management in multiradar tracking systems[J]. Modern Radar, 1995, 17(1): 14–19, 54. doi: 10.16592/j.cnki.1004-7859.1995.01.002.
[86]	黄晓冬, 何友, 赵峰. 几种典型情况下的航迹关联研究[J]. 系统仿真学报, 2005, 17(9): 2085–2088, 2174. doi: 10.3969/j.issn.1004-731X.2005.09.011. HUANG Xiaodong, HE You, and ZHAO Feng. Study of track association in typical cases[J]. Journal of System Simulation, 2005, 17(9): 2085–2088, 2174. doi: 10.3969/j.issn.1004-731X.2005.09.011.
[87]	齐林, 王海鹏, 刘瑜. 基于统计双门限的中断航迹配对关联算法[J]. 雷达学报, 2015, 4(3): 301–308. doi: 10.12000/JR14077. QI Lin, WANG Haipeng, and LIU Yu. Track segment association algorithm based on statistical binary thresholds[J]. Journal of Radars, 2015, 4(3): 301–308. doi: 10.12000/JR14077.
[88]	HONG Shuaixin, PENG Dongliang, and SHI Yifang. Track-to-track association using fuzzy membership function and clustering for distributed information fusion[C]. The 37th Chinese Control Conference, Wuhan, China, 2018: 4028–4032.
[89]	AZIZ A M. A new fuzzy clustering approach for data association and track fusion in multisensor-multitarget environment[C]. 2011 IEEE Aerospace Conference, Big Sky, USA, 2011: 1–10.
[90]	徐亚圣, 丁赤飚, 任文娟, 等. 基于直方统计特征的多特征组合航迹关联[J]. 雷达学报, 2019, 8(1): 25–35. doi: 10.12000/JR18028. XU Yasheng, DING Chibiao, REN Wenjuan, et al. Multi-feature combination track-to-track association based on histogram statistics feature[J]. Journal of Radars, 2019, 8(1): 25–35. doi: 10.12000/JR18028.
[91]	POORE A P and RIJAVEC N. A lagrangian relaxation algorithm for multidimensional assignment problems arising from multitarget tracking[J]. SIAM Journal on Optimization, 1993, 3(3): 544–563. doi: 10.1137/0803027.
[92]	POPP R L, PATTIPATI K R, and BAR-SHALOM Y. M-best S-D assignment algorithm with application to multitarget tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 2001, 37(1): 22–39. doi: 10.1109/7.913665.
[93]	BAR-SHALOM Y. On the sequential track correlation algorithm in a multisensor data fusion system[J]. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(1): 396–396. doi: 10.1109/TAES.2008.4517016.
[94]	宋文彬. 传感器数据空间配准算法研究进展[J]. 传感器与微系统, 2012, 31(8): 5–8. doi: 10.13873/j.1000-97872012.08.027. SONG Wenbin. Research progress of spatial registration algorithms for sensor data[J]. Transducer and Microsystem Technologies, 2012, 31(8): 5–8. doi: 10.13873/j.1000-97872012.08.027.
[95]	TIAN Wei, WANG Yue, SHAN Xiuming, et al. Track-to-track association for biased data based on the reference topology feature[J]. IEEE Signal Processing Letters, 2014, 21(4): 449–453. doi: 10.1109/LSP.2014.2305305.
[96]	TIAN Wei. Reference pattern-based track-to-track association with biased data[J]. IEEE Transactions on Aerospace and Electronic Systems, 2016, 52(1): 501–512. doi: 10.1109/TAES.2015.140433.
[97]	LI Zhenhua, CHEN Siyue, LEUNG H, et al. Joint data association, registration, and fusion using EM-KF[J]. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(2): 496–507. doi: 10.1109/TAES.2010.5461637.
[98]	田威, 王钺, 山秀明, 等. 稳健的联合航迹关联与系统误差估计[J]. 清华大学学报:自然科学版, 2013, 53(7): 946–950. doi: 10.16511/j.cnki.qhdxxb.2013.07.009. TIAN Wei, WANG Yue, SHAN Xiuming, et al. Robust method for joint track association and sensor bias estimation[J]. Journal of Tsinghua University:Science and Technology, 2013, 53(7): 946–950. doi: 10.16511/j.cnki.qhdxxb.2013.07.009.
[99]	LEVEDAHL M. Explicit pattern matching assignment algorithm[C]. The SPIE of 4728, Signal and Data Processing of Small Targets 2002, Orlando, USA, 2002: 461–469.
[100]	SHI Yue, WANG Yue, and SHAN Xiuming. A novel fuzzy pattern recognition data association method for biased sensor data[C]. The 9th International Conference on Information Fusion, Florence, Italy, 2006: 1–5.
[101]	CHAIR Z and VARSHNEY P K. Optimal data fusion in multiple sensor detection systems[J]. IEEE Transactions on Aerospace and Electronic Systems, 1986, AES-22(1): 98–101. doi: 10.1109/TAES.1986.310699.
[102]	SINGER R A and KANYUCK A J. Computer control of multiple site track correlation[J]. Automatica, 1971, 7(4): 455–463. doi: 10.1016/0005-1098(71)90096-3.
[103]	ROECKER J A and MCGILLEM C D. Comparison of two-sensor tracking methods based on state vector fusion and measurement fusion[J]. IEEE Transactions on Aerospace and Electronic Systems, 1988, 24(4): 447–449. doi: 10.1109/7.7186.
[104]	BAR-SHALOM Y and CAMPO L. The effect of the common process noise on the two-sensor fused-track covariance[J]. IEEE Transactions on Aerospace and Electronic Systems, 1986, AES-22(6): 803–805. doi: 10.1109/TAES.1986.310815.
[105]	UHLMANN J K. General data fusion for estimates with unknown cross covariances[C]. The SPIE of 2755, Signal Processing, Sensor Fusion, and Target Recognition V, Orlando, USA, 1996: 536–547.
[106]	HURLEY M B. An information theoretic justification for covariance intersection and its generalization[C]. The 5th International Conference on Information Fusion, Annapolis, USA, 2002: 505–511.
[107]	CHANG K C, TIAN Zhi, and MORI S. Performance evaluation for MAP state estimate fusion[J]. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(2): 706–714. doi: 10.1109/TAES.2004.1310015.
[108]	DRUMMOND O E. Track fusion with feedback[C]. The SPIE of 2759, Signal and Data Processing of Small Targets 1996, Orlando, USA, 1996: 342–360.
[109]	DRUMMOND O E. Hybrid sensor fusion algorithm architecture and tracklets[C]. The SPIE of 3163, Signal and Data Processing of Small Targets 1997, San Diego, USA, 1997: 512–524.
[110]	ZHU Yunmin, YOU Zhisheng, ZHAO Juan, et al. The optimality for the distributed Kalman filtering fusion with feedback[J]. Automatica, 2001, 37(9): 1489–1493. doi: 10.1016/S0005-1098(01)00074-7.
[111]	YUAN Ting, BAR-SHALOM Y, and TIAN Xin. Heterogeneous track-to-track fusion[C]. The 14th International Conference on Information Fusion, Chicago, USA, 2011: 1–8.
[112]	CHANG K C, SAHA R K, and BAR-SHALOM Y. On optimal track-to-track fusion[J]. IEEE Transactions on Aerospace and Electronic Systems, 1997, 33(4): 1271–1276. doi: 10.1109/7.625124.
[113]	TIAN Xin. Track-to-track fusion configurations and association in a sliding window[J]. Journal of Advances in Information Fusion, 2009, 4(2): 146–164.
[114]	LI Tiancheng, FAN Hongqi, GARCÍA J, et al. Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking[J]. Information Fusion, 2019, 51: 233–243. doi: 10.1016/j.inffus.2019.02.009.
[115]	LI Tiancheng, WANG Xiaoxu, LIANG Yan, et al. On arithmetic average fusion and its application for distributed multi-Bernoulli multitarget tracking[J]. IEEE Transactions on Signal Processing, 2020, 68: 2883–2896. doi: 10.1109/TSP.2020.2985643.
[116]	LI Tiancheng and HLAWATSCH F. A distributed particle-PHD filter using arithmetic-average fusion of Gaussian mixture parameters[J]. Information Fusion, 2021, 73: 111–124. doi: 10.1016/j.inffus.2021.02.020.
[117]	LI Tiancheng, CORCHADO J M, and SUN Shudong. Partial consensus and conservative fusion of Gaussian mixtures for distributed PHD fusion[J]. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(5): 2150–2163. doi: 10.1109/TAES.2018.2882960.
[118]	TIAN Xin, BAR-SHALOM Y, YUAN Ting, et al. A generalized information matrix fusion based heterogeneous track-to-track fusion algorithm[C]. The SPIE 8050, Signal Processing, Sensor Fusion, and Target Recognition XX, Orlando, USA, 2011: 805015.
[119]	TIAN Xin, YUAN Ting, and BAR-SHALOM Y. Track-to-track Fusion in Linear and Nonlinear Systems[M]. CHOUKROUN D, OSHMAN Y, THIENEL J, et al. Advances in Estimation, Navigation, and Spacecraft Control. Berlin, Heidelberg: Springer, 2015: 21–41.
[120]	MALLICK M, CHANG K C, ARULAMPALAM S, et al. Heterogeneous track-to-track fusion in 3-D using IRST sensor and air MTI radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(6): 3062–3079. doi: 10.1109/TAES.2019.2898302.
[121]	MENEGAZ H M T, ISHIHARA J Y, and KUSSABA H T M. Unscented Kalman filters for riemannian state-space systems[J]. IEEE Transactions on Automatic Control, 2019, 64(4): 1487–1502. doi: 10.1109/TAC.2018.2846684.
[122]	YEE D, REILLY J P, KIRUBARAJAN T, et al. Approximate conditional mean particle filtering for linear/nonlinear dynamic state space models[J]. IEEE Transactions on Signal Processing, 2008, 56(12): 5790–5803. doi: 10.1109/TSP.2008.929660.
[123]	BATTISTELLI G, CHISCI L, FANTACCI C, et al. Distributed peer-to-peer multitarget tracking with association-based track fusion[C]. The 17th International Conference on Information Fusion, Salamanca, Spain, 2014: 1–7.
[124]	CHONG C Y, MORI S, and CHANG K C. Information fusion in distributed sensor networks[C]. American Control Conference, Boston, USA, 1985: 830–835.
[125]	CORALUPPI S, RAGO C, CARTHEL C, et al. Distributed MHT with passive sensors[C]. The 24th International Conference on Information Fusion, Sun City, South Africa, 2021: 1–8.
[126]	ÜNEY M, CLARK D E, and JULIER S J. Distributed fusion of PHD filters via exponential mixture densities[J]. IEEE Journal of Selected Topics in Signal Processing, 2013, 7(3): 521–531. doi: 10.1109/JSTSP.2013.2257162.
[127]	BATTISTELLI G, CHISCI L, FANTACCI C, et al. Consensus CPHD filter for distributed multitarget tracking[J]. IEEE Journal of Selected Topics in Signal Processing, 2013, 7(3): 508–520. doi: 10.1109/JSTSP.2013.2250911.
[128]	WANG Bailu, YI Wei, HOSEINNEZHAD R, et al. Distributed fusion with multi-Bernoulli filter based on generalized covariance intersection[J]. IEEE Transactions on Signal Processing, 2017, 65(1): 242–255. doi: 10.1109/TSP.2016.2617825.
[129]	FANTACCI C, VO B N, VO B T, et al. Robust fusion for multisensor multiobject tracking[J]. IEEE Signal Processing Letters, 2018, 25(5): 640–644. doi: 10.1109/LSP.2018.2811750.
[130]	LI Suqi, BATTISTELLI G, CHISCI L, et al. Multi-sensor multi-object tracking with different fields-of-view using the LMB filter[C]. The 21st International Conference on Information Fusion, Cambridge, UK, 2018: 1201–1208.
[131]	LI Suqi, YI Wei, HOSEINNEZHAD R, et al. Robust distributed fusion with labeled random finite sets[J]. IEEE Transactions on Signal Processing, 2018, 66(2): 278–293. doi: 10.1109/TSP.2017.2760286.
[132]	GAO Lin, BATTISTELLI G, and CHISCI L. Multiobject fusion with minimum information loss[J]. IEEE Signal Processing Letters, 2020, 27: 201–205. doi: 10.1109/LSP.2019.2963817.
[133]	GAO Lin, BATTISTELLI G, and CHISCI L. Fusion of labeled RFS densities with minimum information loss[J]. IEEE Transactions on Signal Processing, 2020, 68: 5855–5868. doi: 10.1109/TSP.2020.3028496.

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1. 引言
2. 空间目标逆合成孔径雷达成像雷达方程
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
3.2 关于Δr求解的模型误差
3.3 空间目标ISAR成像雷达方程分析
4. 仿真实验分析
4.1 目标轨道高度变化对回波信号接收功率的影响
4.2 目标轨道高度变化对成像质量的影响
4.3 实验总结
5. 结束语

1. 引言
2. 空间目标逆合成孔径雷达成像雷达方程
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
3.2 关于Δr求解的模型误差
3.3 空间目标ISAR成像雷达方程分析
4. 仿真实验分析
4.1 目标轨道高度变化对回波信号接收功率的影响
4.2 目标轨道高度变化对成像质量的影响
4.3 实验总结
5. 结束语

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分布式多传感器多目标跟踪方法综述

DOI: 10.12000/JR22111

通讯作者:
魏少明 shaoming.wei@buaa.edu.cn

计量

Review of the Method for Distributed Multi-sensor Multi-target Tracking（in English）

Corresponding author: WEI Shaoming, shaoming.wei@buaa.edu.cn

1. 引言

2. 空间目标逆合成孔径雷达成像雷达方程

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

3.2 关于Δr求解的模型误差

3.3 空间目标ISAR成像雷达方程分析

4. 仿真实验分析

4.1 目标轨道高度变化对回波信号接收功率的影响

4.2 目标轨道高度变化对成像质量的影响

4.3 实验总结

5. 结束语

期刊类型引用(2)

其他类型引用(1)

计量

目录

1. 引言

2. 空间目标逆合成孔径雷达成像雷达方程

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

3.2 关于Δr求解的模型误差

3.3 空间目标ISAR成像雷达方程分析

4. 仿真实验分析

4.1 目标轨道高度变化对回波信号接收功率的影响

4.2 目标轨道高度变化对成像质量的影响

4.3 实验总结

5. 结束语

期刊介绍

联系我们

分布式多传感器多目标跟踪方法综述

DOI: 10.12000/JR22111

通讯作者: 魏少明 shaoming.wei@buaa.edu.cn

计量

出版历程

Review of the Method for Distributed Multi-sensor Multi-target Tracking（in English）

Corresponding author: WEI Shaoming, shaoming.wei@buaa.edu.cn

1. 引言

2. 空间目标逆合成孔径雷达成像雷达方程

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

3.2 关于Δr求解的模型误差

3.3 空间目标ISAR成像雷达方程分析

4. 仿真实验分析

4.1 目标轨道高度变化对回波信号接收功率的影响

4.2 目标轨道高度变化对成像质量的影响

4.3 实验总结

5. 结束语

期刊类型引用(2)

其他类型引用(1)

计量

出版历程

目录

1. 引言

2. 空间目标逆合成孔径雷达成像雷达方程

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

3.2 关于Δr求解的模型误差

3.3 空间目标ISAR成像雷达方程分析

4. 仿真实验分析

4.1 目标轨道高度变化对回波信号接收功率的影响

4.2 目标轨道高度变化对成像质量的影响

4.3 实验总结

5. 结束语

期刊介绍

联系我们

通讯作者:
魏少明 shaoming.wei@buaa.edu.cn