频谱共存下面向多目标跟踪的组网雷达功率时间联合优化算法

时晨光; 董璟; 周建江

doi:10.12000/JR22146

频谱共存下面向多目标跟踪的组网雷达功率时间联合优化算法

DOI: 10.12000/JR22146

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，副教授，主要研究方向为飞行器射频隐身技术、网络化雷达资源管理，多平台传感器协同等

董　璟，硕士生，主要研究方向为网络化雷达多目标跟踪与协同资源管理

周建江，教授，主要研究方向为飞行器射频隐身技术、雷达目标特性分析、航空电子信息技术等

通讯作者:
时晨光 scg_space@163.com

责任主编：严俊坤 Corresponding Editor: YAN Junkun
中图分类号: TN957
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出版历程
- 收稿日期: 2022-07-13
- 修回日期: 2022-08-24
- 网络出版日期: 2022-09-01
- 刊出日期: 2023-06-28

Joint Transmit Power and Dwell Time Allocation for Multitarget Tracking in Radar Networks under Spectral Coexistence

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

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Corresponding author: SHI Chenguang, scg_space@163.com

摘要

摘要: 该文针对频谱共存环境下多目标跟踪资源分配问题，提出了组网雷达功率时间联合优化算法。首先，推导了包含雷达节点选择、发射功率和驻留时间等射频辐射参数的预测贝叶斯克拉默-拉奥下界(BCRLB)，以此作为多目标跟踪精度的衡量指标；在此基础上，以最小化多目标跟踪BCRLB为优化目标，以满足给定的组网雷达射频资源和预先设定的通信基站最大可容忍干扰能量阈值为约束条件，建立了频谱共存下面向多目标跟踪的组网雷达功率时间联合优化分配模型，对雷达节点选择、发射功率和驻留时间进行自适应联合优化配置；然后，针对上述优化问题，采用两步分解法将其分解为多个子凸问题，并结合半正定规划(SDP)算法和循环最小化算法进行求解。仿真结果表明，与现有算法相比，所提算法能够在保证通信基站正常工作的条件下，有效提高组网雷达的多目标跟踪精度。
- 资源分配 /
- 组网雷达 /
- 多目标跟踪 /
- 频谱共存
Abstract: For the resource allocation problem of multitarget tracking in a spectral coexistence environment, this study proposes a joint transmit power and dwell time allocation algorithm for radar networks. First, the predicted Bayesian Cramér-Rao Lower Bound (BCRLB) with the variables of radar node selection, transmit power and dwell time is derived as the performance metric for multi-target tracking accuracy. On this basis, a joint optimization model of transmit power and dwell time allocation for multitarget tracking in radar networks under spectral coexistence is built to collaboratively optimize the radar node selection, transmit power and dwell time of radar networks, This joint optimization model aims to minimize the multitarget tracking BCRLB while satisfying the given transmit resources of radar networks and the predetermined maximum allowable interference energy threshold of the communication base station. Subsequently, for the aforementioned optimization problem, a two-step decomposition method is used to decompose it into multiple subconvex problems, which are solved by combining the Semi-Definite Programming (SDP) and cyclic minimization algorithms. The simulation results showed that, compared with the existing algorithms, the proposed algorithm can effectively improve the multitarget tracking accuracy of radar networks while ensuring that the communication base station works properly.
- Resource allocation /
- Radar networks /
- Multitarget tracking /
- Spectral coexistence

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图 1 组网雷达布阵及多目标运动轨迹图

Figure 1. Deployment of radar networks and trajectories of multiple targets

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图 2 雷达节点选择与功率时间资源优化分配结果

Figure 2. Radar node selection and allocation results of power and dwell time resources

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图 3 RCS不变场景下ARMSE对比结果

Figure 3. Comparison results of ARMSE with same RCS

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图 4 各目标RCS数值

Figure 4. RCS values of each target

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图 5 RCS变化场景下雷达节点选择与功率时间资源优化分配结果

Figure 5. Radar node selection and allocation results of power and dwell time resources with various RCS

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图 6 RCS变化场景下ARMSE对比结果

Figure 6. Comparison results of ARMSE with various RCS

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图 7 ${E_{\max }} = 3{\text{ J}}$时雷达节点选择与功率时间资源优化分配结果

Figure 7. Radar node selection and allocation results of power and dwell time resources with ${E_{\max }} = 3{\text{ J}}$

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图 8 不同${E_{\max }}$条件下ARMSE对比结果

Figure 8. Comparison results of ARMSE under different ${E_{\max }}$ conditions

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算法 1 频谱共存下面向多目标跟踪的组网雷达功率时间联合优化算法求解流程
Alg. 1 Solution flow of joint transmit power and dwell time allocation for multitarget tracking in radar networks under spectral coexistence
初始化：$ \Im \left( 0 \right) $为给定常数，定义发射功率和驻留时间初始值　　　　　$\hat P_{n,k}^q$, $\hat T_{n,k}^q$；
步骤1 选定运动目标q，求解SDP问题(18)，求出k时刻雷达权重　矢量$ {\boldsymbol{\alpha }}_k^q $，获得$ \left( {{\partial _{\max }} - 1} \right) $种雷达节点选择备选方案。
步骤2 对于 $s = 1,2, \cdots ,({\partial _{\max } } - 1 )$：
1. 设定方案s选择的雷达节点权重系数$\bar \alpha _{n,k,s}^q = 1$，其余节点　　　权重系数均初始化为0；
2．求解SDP问题(19)，得到雷达节点选择$ {\boldsymbol{\alpha }}_{k,s}^q $、发射功率　　　 $ {\boldsymbol{P}}_{k,s}^q $、驻留时间$ {\boldsymbol{T}}_{k,s}^q $以及目标跟踪误差$ \Im _{k,s}^q $；
步骤3 选取步骤2所有方案中的最小跟踪误差$ \Im _k^q $及其对应雷达节　点选择方案和资源分配方案作为备选方案；
如果$\left\| {\Im _k^q - \Im \left( 0 \right)} \right\| \le \varepsilon $且$\Im _k^q < \Im \left( 0 \right)$：选取$ \Im _k^q $和其对应的雷达　　节点权重集合、发射功率集合和驻留时间集合作为k时刻跟踪　　目标q的资源分配方案；
否则：$\Im \left( 0 \right) = \min \left( {\Im \left( 0 \right),\Im _k^q} \right)$，并保存其对应的雷达节点选　　择和资源分配方案，跳转至步骤1；
步骤4 输出原问题(17)的最终雷达节点选择、发射功率、驻留时　间结果$ {\boldsymbol{\alpha }}_k^q $, $ {\boldsymbol{P}}_k^q $, $ {\boldsymbol{T}}_k^q $，并确定下一个跟踪目标，跳转至步骤1，直　到所有的运动目标跟踪方案都完成优化。

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表 1 仿真参数设置

Table 1. Simulation parameter settings

参数	数值	参数	数值
$ {G_{\text{t}}} $	$ 36{\text{ dB}} $	$ \beta $	$ 1{\text{ MHz}} $
$ {G_{\text{r}}} $	$ 35{\text{ dB}} $	$ {F_{\text{r}}} $	$ 3{\text{ dB}} $
$ {G_{{\text{RP}}}} $	$ 45 $	k	$1.38 \times {10^{ - 23} }\;{ {\text{J} } \mathord{\left/ {\vphantom { {\text{J} } {\text{K} } } } \right. } {\text{K} } }$
$ {P_{\min }} $	$ 100{\text{ W}} $	$ {P_{\max }} $	$ 600{\text{ W}} $
${T_{ {\text{min} } } }$	$ 0.01{\text{ s}} $	$ {T_{\max }} $	$ 0.08{\text{ s}} $
$ {P_{{\text{total}}}} $	$ 700{\text{ W}} $	$ {T_{{\text{total}}}} $	$ 0.1{\text{ s}} $

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