面向目标跟踪的机载组网雷达辐射参数与航迹规划联合优化算法

时晨光; 王奕杰; 代向荣; 周建江

doi:10.12000/JR22005

面向目标跟踪的机载组网雷达辐射参数与航迹规划联合优化算法

doi: 10.12000/JR22005

南京航空航天大学雷达成像与微波光子技术教育部重点实验室南京 210016

基金项目: 国家自然科学基金(62271247, 61801212)，国家部委基金，航空科学基金(20200020052005, 20200020052002)，南京航空航天大学前瞻布局科研专项资金

详细信息

作者简介:
时晨光，博士，副教授，硕士生导师，研究方向为飞行器射频隐身技术、组网雷达协同感知、多传感器信息融合与管理等

王奕杰，硕士生，主要研究方向为飞行器射频隐身技术

代向荣，硕士生，主要研究方向为飞行器射频隐身技术

周建江，博士，教授，博士生导师，研究方向为隐身技术、雷达目标特性分析与特征控制等

通讯作者:
时晨光 scg_space@163.com

责任主编：易伟 Corresponding Editor: YI Wei
中图分类号: TN957
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出版历程
- 收稿日期: 2022-01-07
- 修回日期: 2022-02-27
- 网络出版日期: 2022-03-21
- 刊出日期: 2022-10-28

Joint Transmit Resources and Trajectory Planning for Target Tracking in Airborne Radar Networks

Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Funds: The National Natural Science Foundation of China (62271247, 61801212), The National Ministries Foundation, The National Aerospace Science Foundation of China (20200020052005, 20200020052002), The Fund of Prospective Layout of Scientific Research for Nanjing University of Aeronautics and Astronautics

More Information

Corresponding author: SHI Chenguang, scg_space@163.com

摘要

摘要: 该文针对机载组网雷达，在单目标跟踪场景下，研究了雷达辐射参数与航迹规划联合优化问题。首先，推导了包含各雷达辐射功率、驻留时间、发射信号高斯脉冲长度和信号带宽等射频辐射参数以及各载机速度、朝向角等平台运动参数的贝叶斯克拉默-拉奥下界(BCRLB)表达式，以此作为表征目标跟踪精度的衡量指标；推导了含有各雷达辐射功率、驻留时间等射频辐射参数以及各载机速度、朝向角等平台运动参数的机载组网雷达被截获概率，以此作为表征机载组网雷达射频隐身性能的衡量指标。在此基础上，建立了面向目标跟踪的机载组网雷达辐射参数与航迹规划联合优化模型，以最小化机载组网雷达的目标估计误差BCRLB为优化目标，以满足给定的系统射频资源、载机机动能力和预先设定的被截获概率阈值为约束条件，对各载机飞行速度、朝向角以及各机载雷达辐射功率、驻留时间、发射信号高斯脉冲长度和信号带宽进行联合优化设计，以提升机载组网雷达的目标跟踪精度。最后，针对上述优化问题，结合粒子群算法，采用5步分解迭代算法进行求解。仿真结果表明，与现有算法相比，所提算法能够在满足一定射频隐身性能要求的条件下，有效提升机载组网雷达的目标跟踪精度。
- 辐射资源控制 /
- 航迹规划 /
- 机载组网雷达 /
- 射频隐身 /
- 目标跟踪
Abstract: This paper investigates the joint optimization problem of transmit resources and trajectory planning for target tracking in airborne radar networks. First, the analytical expression for the Bayesian Cramér-Rao Lower Bound (BCRLB) with the variables of the radar transmit power, dwell time, transmit signal Gaussian pulse length and signal bandwidth, and speed and heading angle of airborne nodes is derived and adopted as the metric function to evaluate the target tracking accuracy. In addition, the analytical expression of intercept probability with the variables of the radar transmit power, dwell time, and speed and heading angle of airborne nodes is also derived and utilized as the metric function to gauge the radio frequency stealth performance of the overall system. On this basis, a joint optimization model of transmit resources and trajectory planning for target tracking in airborne radar networks is established to jointly optimize the radar transmit power, dwell time, transmit signal Gaussian pulse length and signal bandwidth, and speed and heading angle of airborne nodes. This is done to minimize the target estimation error BCRLB under the constraints of given system resources, aircraft maneuvering and intercept probability threshold, thereby improving the target tracking accuracy of airborne radar network. Subsequently, a five-step decomposition iterative algorithm incorporating the particle swarm algorithm is used to solve the underlying optimization problem. The simulation results demonstrate that the target tracking accuracy of the proposed algorithm outperforms other existing approaches.
- Transmit resources control /
- Trajectory planning /
- Airborne radar network /
- Radio frequency stealth /
- Target tracking

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图 1 载机运动模型示意图

Figure 1. Schematic diagram of the movement model of the carrier aircraft

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图 2 目标跟踪场景

Figure 2. Target tracking scene

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图 3 飞行速度优化结果

Figure 3. Flight speed optimization results

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图 4 飞行朝向角优化结果

Figure 4. Flight heading angle optimization results

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图 5 辐射功率优化结果

Figure 5. Transmit power optimization results

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图 6 驻留时间优化结果

Figure 6. Dwell time optimization results

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图 7 发射信号高斯脉冲长度优化结果

Figure 7. Transmit signal Gaussian pulse length optimization results

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图 8 发射信号带宽优化结果

Figure 8. Transmit signal bandwidth optimization results

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图 9 ARMSE对比结果

Figure 9. Comparison results of ARMSE

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图 10 不同被截获概率阈值的RMSE对比结果

Figure 10. Comparison results of RMSE with different intercept probability thresholds

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表 1 粒子群算法求解模型(23)

Table 1. Particle swarm algorithm to solve the model (23)

　步骤1：初始化$ Q $个粒子的初始位置和速度，初始位置代表各载
　　　　机飞行速度和朝向角；定义权重系数$ \zeta $，常数$ {c_1} $和$ {c_2} $，最
　　　　大迭代次数$ {L_{\max }} $；

　步骤2：根据机载组网雷达辐射参数与各载机飞行参数之间的关
　　　　系，在满足约束条件${p_{n,k} } \le {p_{ {\text{th} } } },\forall n$情况下，计算每个粒
　　　　子当前位置下的最优雷达辐射参数；
　步骤3：根据优化目标$\mathbb{F}\left( {{\boldsymbol{X}}_{\left. k \right|k - 1}^{ {\text{tgt} } }{{,} }{{\boldsymbol{P}}_{ {\text{t} },k} }{{,} }{{\boldsymbol{T}}_{ {\text{d} },k} } } \right){\text{ } }$计算粒子适应度；

　步骤4：更新全局最优粒子和个体最优粒子：
　步骤5：根据式(28)更新粒子的速度与位置；

　步骤6：检验结束条件，若结果收敛或达到最大迭代次数，则迭
　　　　代结束，输出全局最优粒子；否则令$ l = l + 1 $，转入步
　　　　骤2，继续迭代循环。

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表 2 机载组网雷达参数设置

Table 2. Parameter setting of airborne radar network

参数	数值	参数	数值
$ {G_{\text{t}}} $	$36\;{\text{dB} }$	$ {B_{\text{r}}} $	$1\;{\text{MHz} }$
$ {G_{\text{r}}} $	$35\;{\text{dB} }$	$ {F_{\text{r}}} $	$ 3\;{\text{dB}} $
$ {G_{{\text{RP}}}} $	$ 45 $	$ {f_{\text{c}}} $	$ 12\;{\text{GHz}} $
${\bar P _{\min } }$	$ 0 $	$ {\bar P _{\max }} $	$ 5\;{\text{kW}} $
${\bar \theta _{\max } }$	$ {15^ \circ } $	$ k $	$ 1.38 \times {10^{ - 23}}{{\text{J}} \mathord{\left/ {\vphantom {{\text{J}} {\text{K}}}} \right. } {\text{K}}} $
${\bar v _{\min } }$	$0.1\;{ { {\text{km} } } / {\text{s} } }$	$ {\bar v _{\max }} $	$0.4\;{ { {\text{km} } } / {\text{s} } }$
$ {T_{\text{r}}} $	$5 \times {10^{ - 4} }\;{\text{s} }$	$ {\bar T _{\max }} $	$2.5 \times {10^{ - 2} }\;{\text{s} }$

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表 3 截获接收机参数设置

Table 3. Parameter setting of intercept receiver

参数	数值	参数	数值
$p'_{{\rm{fa} } }$	$ {10^{ - 8}} $	$ {G_{{\text{IP}}}} $	$ 2 $
$ {F_{\text{I}}} $	$6\;{\text{dB} }$	$ {T_{\text{I}}} $	$2\;{\text{s} }$
$ {G_{\text{I}}} $	$10\;{\text{dB} }$	$ {B_{\text{I}}} $	$40\;{\text{GHz} }$

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表 4 机载组网雷达初始状态

Table 4. The initial state of airborne radar network

雷达编号	初始位置(km)	初始速度(km/s)	初始朝向角(°)
机载雷达1	[110,0]	0.4	0
机载雷达2	[10,0]	0.4	0
机载雷达3	[0,10]	0.4	90
机载雷达4	[0,150]	0.4	90

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