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Joint Optimization of Transmit Power and Dwell Time for Asynchronous Multi-target Tracking in Heterogeneous Multiple Radar Networks with Imperfect Detection
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摘要: 该文针对异步多目标跟踪场景，研究了非理想检测下的异构多雷达网络功率时间联合优化问题。首先，将各融合采样间隔内得到的来自不同雷达节点的所有异步量测信息融合为复合量测信息，结合该复合量测信息推导了非理想检测下包含雷达节点选择、辐射功率和驻留时间等参数的异步目标跟踪误差贝叶斯克拉美罗下界(BCRLB)解析表达式，并将其作为异步多目标跟踪精度的衡量指标。在此基础上，建立了非理想检测下面向异步多目标跟踪的异构多雷达网络功率时间联合优化模型，即以最小化异步多目标跟踪误差为优化目标，以满足给定的系统辐射资源限制为约束条件，对不同雷达网络中雷达节点的选择方式、辐射功率和驻留时间等发射参数进行自适应联合优化设计，从而提升异构多雷达网络的异步多目标跟踪精度。最后，针对上述优化问题，结合序列二次规划(SQP)算法和循环最小法，采用四步分解算法进行求解。仿真结果表明，与现有算法相比，所提算法能够有效提升异构多雷达网络的异步多目标跟踪精度。Abstract: The joint optimization problem of transmit power and dwell time of radar for asynchronous multi-target tracking in heterogeneous multiple radar networks with imperfect detection is investigated. Firstly, all the asynchronous measurements from different radar node in each fusion sampling interval are fused into composite measurement, thus the Bayesian Cramér-Rao Lower Bound (BCRLB) analytical expression of the asynchronous target tracking error with parameters such as radar node selection, transmit power and dwell time with imperfect detection is derived and used as the asynchronous target tracking accuracy measure. Based on this, a joint optimization model of transmit power and dwell time for asynchronous multi-target tracking in heterogeneous multiple radar networks with imperfect detection is established, with the optimization objective of minimizing the asynchronous multi-target tracking error and the constraints of given system transmit resource limitations, the parameters such as radar node selection, transmit power and dwell time in different radar networks are designed adaptively and optimally so as to improve the asynchronous multi-target tracking accuracy of the heterogeneous multiple radar networks system. Finally, a four-step decomposition algorithm combined with the Sequential Quadratic Programming (SQP) algorithm and cyclic minimization method is used to solve the optimization problem. Simulation results demonstrate that the asynchronous multi-target tracking accuracy of the heterogeneous multiple radar networks outperforms existing algorithms.
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图 1 目标q在第k个融合采样间隔内的异步量测模型
Figure 1. Asynchronous measurement model of target q in the k-th fusion sampling interval
图 2 异构多雷达网络分布与目标运动轨迹
Figure 2. Deployment of heterogeneous multiple radar networks and trajectories of moving targets
图 3 目标1的雷达节点选择与功率时间优化结果
Figure 3. Radar node selection, power and dwell time optimization results of target 1
图 4 目标2的雷达节点选择与功率时间优化结果
Figure 4. Radar node selection, power and dwell time optimization results of target 2
图 5 不同检测概率下的各目标BCRLB
Figure 5. BCRLB of each target with different probabilities of detection
1 非理想检测下面向异步多目标跟踪的异构多雷达网络功率时间联合优化算法
1. Joint optimization of transmit power and dwell time for asynchronous multi-target tracking in heterogeneous multiple radar networks with imperfect detection
步骤1：根据功率和时间初始矩阵分配给各雷达节点相应的辐射
功率$ {\boldsymbol{\bar P}}_{{\text{t,}}k}^q $和驻留时间$ {\boldsymbol{\bar T}}_k^q $，松弛$ \mu _{n,m,k}^q $，采用SQP算法求
解式(21)，得到所有的雷达节点选择系数，降序排列后
依次选取$ {L_{\max }} $个雷达节点；步骤2：将优化模型(22)分解为两个子优化问题，采用SQP算法
依次迭代求解式(23)和式(24)，得到辐射功率和驻留时
间优化分配结果$ {\boldsymbol{\hat P}}_{{\text{t,}}k}^q $和$ {\boldsymbol{\hat T}}_k^q $；步骤3：异构多雷达网络系统指定下一个目标进行相应的资源优
化分配，重复步骤1和步骤2，直到照射所有目标；步骤4：利用循环最小法得到最优雷达节点选择和功率时间分配
结果。
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表 1 异构多雷达网络雷达节点发射参数设置
Table 1. Parameter settings of radar node in heterogeneous multiple radar networks
参数 数值 参数 数值 ${T_{{\text{fusion}}}}$ $6\;{\text{s} }$ ${ {\overline P_{\min } } }$ $100\;{\text{W}}$ ${ {\overline P_{ {} {\text{max} } } } }$ $1000\;{\text{ W} }$ $ {P_{{\text{PAR}}}} $ $300\;{\text{W}}$ $ {P_{{\text{MSR}}}} $ $300\;{\text{W} }$ ${ {\overline T_{\min } } }$ $0.003\;{\text{s}}$ ${ {\overline T_{\max } } }$ $0.03\;{\text{s} }$ $ {T_{{\text{CMIMO}}}} $ $0.006\;{\text{s}}$ $ {T_{{\text{MSR}}}} $ $0.006\;{\text{s}}$ $ \beta _k^q $ $1\;{\text{MHz}}$ $ P_{{\text{total}}}^q $ $1500\;{\text{W}}$ $ T_{{\text{total}}}^q $ $0.03\;{\text{s}}$
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表 2 目标具体运动轨迹参数
Table 2. Specific trajectory parameters of targets
目标编号 初始位置($ {\text{km}} $) 运动速度($ {{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. } {\text{s}}} $) 1 $ \left( { - 10,42.5} \right) $ $ \left( { - 125, - 340} \right) $ 2 $ \left( {30, - 35} \right) $ $ \left( {160,300} \right) $
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表 3 各雷达节点的初始采样时间和采样间隔
Table 3. Initial sampling time and sampling interval of each radar node
$ \left( {n,m} \right) $ $ t_{n,m,q}^{i{\text{ni}}} $ (s) $ T_{n,m,q}^0 $ (s) (1,1) 2 1 (2,1) 3 1 (3,1) 4 1 (4,1) 1 1 (5,1) 5 1 (1,2) 2 2 (2,2) 4 2 (3,2) 3 2 (4,2) 5 2 (5,2) 1 2 (1,3) 3 3 (2,3) 5 3
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