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Joint Collaborative Radar Selection and Transmit Resource Allocation in Multiple Distributed Radar Networks with Imperfect Detection Performance
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摘要: 该文针对分布式相控阵多雷达网络的多目标跟踪场景，研究非理想检测条件下的节点选择与辐射资源联合优化分配算法。首先，根据分布式相控阵多雷达网络构成、目标运动模型、雷达量测模型以及雷达节点检测情况，推导非理想检测下以雷达节点选择、辐射功率和信号带宽为变量的贝叶斯克拉默-拉奥下界(BCRLB)闭式解析表达式，并以此作为多目标跟踪精度衡量指标。在此基础上，以最小化系统各雷达节点对所有目标的总辐射功率为优化目标，以满足目标跟踪精度门限以及给定的系统射频辐射资源限制为约束条件，建立非理想检测条件下多雷达网络节点选择与辐射资源联合优化分配模型，对各时刻雷达节点选择、辐射功率和信号带宽等参数进行联合优化设计，以提升多雷达网络的射频隐身性能。最后，针对上述非线性、非凸优化问题，采用基于障碍函数法和循环最小化算法的4步分解算法进行求解。仿真结果表明，与现有算法相比，所提算法能在满足给定多目标跟踪精度的条件下有效降低分布式相控阵多雷达网络的总辐射功率，至少降低了约32.3%，从而提升其射频隐身性能。
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关键词:
- 雷达资源分配 /
- 分布式多雷达网络 /
- 多目标跟踪 /
- 非理想检测 /
- 贝叶斯克拉默-拉奥下界
Abstract: In this study, a collaborative radar selection and transmit resource allocation strategy is proposed for multitarget tracking applications in multiple distributed phased array radar networks with imperfect detection performance. The closed-form expression for the Bayesian Cramér-Rao Lower Bound (BCRLB) with imperfect detection performance is obtained and adopted as the criterion function to characterize the precision of target state estimates. The key concept of the developed strategy is to collaboratively adjust the radar node selection, transmitted power, and effective bandwidth allocation of multiple distributed phased array radar networks to minimize the total transmit power consumption in an imperfect detection environment. This will be achieved under the constraints of the predetermined tracking accuracy requirements of multiple targets and several illumination resource budgets to improve its radio frequency stealth performance. The results revealed that the formulated problem is a mixed-integer programming, nonlinear, and nonconvex optimization model. By incorporating the barrier function approach and cyclic minimization technique, an efficient four-step-based solution methodology is proposed to solve the resulting optimization problem. The numerical simulation examples demonstrate that the proposed strategy can effectively reduce the total power consumption of multiple distributed phased array radar networks by at least 32.3% and improve its radio frequency stealth performance while meeting the given multitarget tracking accuracy requirements compared with other existing algorithms. -
图 1 多雷达网络多目标跟踪工作步骤
Figure 1. The working steps for multitarget tracking of multiple radar networks
图 2 基于本文所提算法的多雷达网络多目标跟踪闭环过程
Figure 2. The closed-loop process of proposed algorithm for multi-target tracking in multiple radar networks
图 3 仿真场景1多雷达网络分布与目标运动轨迹
Figure 3. Deployment of multiple radar networks and trajectories of moving targets in scenario 1
图 4 仿真场景1目标1的雷达节点选择与辐射资源优化分配结果
Figure 4. Radar node selection and transmit resource optimization results of target 1 in scenario 1
图 5 仿真场景1目标2的雷达节点选择与辐射资源优化分配结果
Figure 5. Radar node selection and transmit resource optimization results of target 2 in scenario 1
图 6 不同检测概率下的各目标BCRLB与跟踪精度阈值对比
Figure 6. The comparison between the BCRLB of targets and the specified tracking accuracy threshold
图 7 仿真场景1不同检测概率下各目标ARMSE对比结果
Figure 7. Comparison of the ARMSE of targets with different values of probability of detection in scenario 1
图 8 仿真场景1不同检测概率下总辐射功率消耗对比结果
Figure 8. Comparison of the total power consumption with different values of probability of detection in scenario 1
图 10 仿真场景2目标1的雷达节点选择与辐射资源优化分配结果
Figure 10. Radar node selection and transmit resource optimization results of target 1 in scenario 2
图 11 仿真场景2目标2的雷达节点选择与辐射资源优化分配结果
Figure 11. Radar node selection and transmit resource optimization results of target 2 in scenario 2
图 12 仿真场景2不同检测概率下各目标ARMSE对比结果
Figure 12. Comparison of the ARMSE of targets with different values of probability of detection in scenario 2
图 13 仿真场景2不同检测概率下总辐射功率消耗对比结果
Figure 13. Comparison of the total power consumption with different values of probability of detection in scenario 2
图 14 仿真场景3多雷达网络分布与目标运动轨迹
Figure 14. Deployment of multiple radar networks and trajectories of moving targets in scenario 3
图 15 仿真场景3目标1的雷达节点选择与辐射资源优化分配结果
Figure 15. Radar node selection and transmit resource optimization results of target 1 in scenario 3
图 16 仿真场景3目标2的雷达节点选择与辐射资源优化分配结果
Figure 16. Radar node selection and transmit resource optimization results of target 2 in scenario 3
图 17 仿真场景3不同检测概率下各目标ARMSE对比结果
Figure 17. Comparison of the ARMSE of targets with different values of probability of detection in scenario 3
图 18 仿真场景3不同检测概率下总辐射功率消耗对比结果
Figure 18. Comparison of the total power consumption with different values of probability of detection in scenario 3
图 19 仿真场景4目标1的雷达节点选择与辐射资源优化分配结果
Figure 19. Radar node selection and transmit resource optimization results of target 1 in scenario 4
图 20 仿真场景4目标2的雷达节点选择与辐射资源优化分配结果
Figure 20. Radar node selection and transmit resource optimization results of target 2 in scenario 4
图 21 仿真场景4不同检测概率下各目标ARMSE对比结果
Figure 21. Comparison of the ARMSE of targets with different values of probability of detection in scenario 4
图 22 仿真场景4不同检测概率下总辐射功率消耗对比结果
Figure 22. Comparison of the total power consumption with different values of probability of detection in scenario 4
图 23 不同场景下本文所提算法与穷举法的计算耗时对比
Figure 23. Comparison of computational time consumption between the proposed algorithm and the exhaustive method in different scenarios
1 非理想检测下基于障碍函数法的雷达节点选择算法
1. Radar node selection algorithm based on barrier function method with imperfect detection
输入：x令$ {g_1} = {\kern 1pt} \mathbb{F}\left( {{\boldsymbol{\mu }}_k^q,{\boldsymbol{\hat P}}_{{\text{t}},k}^q,{\boldsymbol{\hat \beta }}_k^q} \right) - {\eta ^q} $, $ {g_2} = {\kern 1pt} - \mu _{1,1,k}^q $,
$ {g_3} = {\kern 1pt} - \mu _{2,1,k}^q $, ···, $ {g_{{N_1} + 1}} = {\kern 1pt} - \mu _{{N_1},1,k}^q $, ···,
$ {g_{\sum\limits_{m = 1}^M {{N_m}} + 1}} = {\kern 1pt} - \mu _{{N_M},M,k}^q $, $ {g_{\sum\limits_{m = 1}^M {{N_m}} + 2}} = {\kern 1pt} \mu _{1,1,k}^q - 1 $,
$ {g_{\sum\limits_{m = 1}^M {{N_m}} + 3}} = {\kern 1pt} \mu _{2,1,k}^q - 1 $, ···, $ {g_{2\sum\limits_{m = 1}^M {{N_m}} + 1}} = {\kern 1pt} \mu _{{N_M},M,k}^q - 1 $，
设置迭代索引$ \varphi = 1 $；设置可行域$ D = \left\{ {\mu _{n,m,k}^q\left| {{g_a}\left( {\mu _{n,m,k}^q} \right) \le 0,a = 1,2, \cdots ,2\displaystyle\sum\limits_{m = 1}^M {{N_m}} + 1} \right.} \right\} $，
其中$ {g_a}\left( {\mu _{n,m,k}^q} \right) = {g_a} $；设置$ \varepsilon \gt 0 $为算法终止指标，$ {\xi ^{\left( \varphi \right)}} \gt 0 $,
$ e \ge 2 $。步骤1：取$ {\left( {\mu _{n,m,k}^q} \right)^{\left( {\varphi - 1} \right)}} \in D $为初始点； 步骤2：求解如下问题：
$\begin{gathered} \min {\kern 1pt} {\mathbb{G}_1} - {\xi ^{\left( \varphi \right)} }\left[ {\frac{1}{ { {g_1} } } + \frac{1}{ { {g_2} } } + \cdots + \frac{1}{ { {g_{2 \sum\limits_{m = 1}^M { {N_m} } + 1} } } } } \right], \\ {\text{s} }{\text{.t} }{\text{.} }{\kern 1pt} {\kern 1pt} {\kern 1pt} \mu _{n,m,k}^q \in D. \\ \end{gathered}$式中，${\mathbb{G}_1}$表示优化模型(23)中的目标函数； 步骤3：令上述问题的极小值点为$ {\left( {\mu _{n,m,k}^q} \right)^{\left( \varphi \right)}} $； 步骤4：检验终止条件，若
$ - {\xi ^{\left( \varphi \right)}}\left[ {\dfrac{1}{{{g_1}}} + \dfrac{1}{{{g_2}}} + , \cdots , + \dfrac{1}{{{g_{2\sum\limits_{m = 1}^M {{N_m}} + 1}}}}} \right] \lt \varepsilon $，算法终止；若
未满足终止条件，令${\left( {\mu _{n,m,k}^q} \right)^{\left( {\varphi + 1} \right)} } \leftarrow \dfrac{ { { {\left( {\mu _{n,m,k}^q} \right)}^{\left( \varphi \right)} } } }{e}$,
$ \varphi \leftarrow \varphi + 1 $。输出：雷达节点最优选择结果。 
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