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A Fast Power Allocation Algorithm in a Collocated MIMO Radar under Low Interception Backgrounds
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摘要: 针对集中式MIMO雷达同时跟踪多批机动目标场景，该文提出一种低截获背景下的快速功率分配算法。首先，将目标机动过程建模为自适应当前统计(ACS)模型，并采用粒子滤波对各目标状态进行估计。其次，对条件克拉默-拉奥下界(PC-CRLB)进行推导，并基于目标运动特性和电磁特性构建目标综合威胁度评估模型。随后，将目标跟踪误差评估指数和雷达未被截获概率的加权和作为优化目标，建立了关于发射功率的优化模型，利用目标函数单调递减性质，提出了一种基于序列松弛的求解算法进行模型求解。最后，通过仿真验证所提算法的有效性和时效性。结果表明，所提算法能够有效提高目标跟踪精度和雷达系统低截获性能，相比采用内点法求解运算速度提高近50%。
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关键词:
- 集中式MIMO雷达 /
- 功率分配 /
- 机动跟踪 /
- 低截获性能 /
- 条件克拉默-拉奥下界(PC-CRLB)
Abstract: This study proposes a fast power allocation algorithm under a low interception background for a collocated MIMO radar that simultaneously tracks multiple maneuvering targets. First, the target maneuver process is modeled as an Adaptive Current Statistical (ACS) model, and a particle filter is used to estimate the state of each target. Second, the Predicted Conditional Cramer-Rao Lower Bound (PC-CRLB) is derived, and the target comprehensive threat assessment model is constructed based on the target motion and electromagnetic characteristics. Subsequently, an optimization model with respect to transmitting power is established by developing the weighted sum of the target tracking error evaluation index and the unintercepted probability of radar as the optimization objective. Thereafter, to solve the model using the monotonically decreasing property of the objective function, a solving algorithm based on sequence relaxation is proposed. Finally, a simulation is conducted to verify the effectiveness and timeliness of the proposed algorithm. The results indicate that the proposed algorithm can effectively improve the target tracking accuracy and low interception performance of the radar system. Further, its run speed is increased by nearly 50% compared with that of the interior point method. -
图 1 集中式MIMO雷达同时多波束工作模式
Figure 1. Simultaneous multi-beam working mode of the collocated MIMO radar
图 9
$ {\ell _1} $ 模型下的目标跟踪轨迹Figure 9. Target tracking trajectory in model
$ {\ell _1} $ 
图 10
$ {\ell _2} $ 模型下的目标跟踪轨迹Figure 10. Target tracking trajectory in model
$ {\ell _2} $ 
图 11 各算法关于最差情况的PC-CRLB性能对比
Figure 11. PC-CRLB performance comparison of each algorithm on the worst case
图 12 各算法关于最差情况的RMSE性能对比
Figure 12. RMSE performance comparison of each algorithm on the worst case
图 13 各算法关于最大截获概率的性能对比
Figure 13. Performance comparison of each algorithm for maximum intercept probability
图 14
$ {\ell _1} $ 模型中的雷达功率分配结果Figure 14. Results of radar power allocation in model
$ {\ell _1} $ 
图 15
$ {\ell _2} $ 模型中的雷达功率分配结果Figure 15. Results of radar power allocation in model
$ {\ell _2} $ 表 1 功率快速求解算法
Table 1. Fast power solving algorithm
步骤1 应用式(30)计算$ {D_k} $； 步骤2 定义${{\boldsymbol{Q}}_0}$为集合${\boldsymbol{Q}} = \{ 1,2,\cdots,Q\}$中所有满足不等式
${D_k} > {{\rm{fun}}_q}(\arg \min ({\bf{1} }_Q^{\text{T} }{ {\boldsymbol{P} }_k}))$元素的集合。若${{\boldsymbol{Q}}_0} \ne \varnothing$，则进入
步骤3；否则，令${P_{k,q,{\text{opt} } } } = {\bar P_{\min } }$, ${ {\boldsymbol{Q} }_0} = { {\boldsymbol{Q} }_0} \cup \{ q\}$,
${\boldsymbol{Q}} = {\boldsymbol{Q}}\backslash \{ q\}$，并返回步骤1；步骤3 令对目标q进行功率分配结果的最优解为
${P_{k,q,{\text{opt} } } } = {\rm{fun}}_q^{ - 1}({D_k})$；步骤4 令最优解对应函数值为$ {D_{k,{\text{opt}}}} = {D_k} $。 
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表 2 仿真参数设置
Table 2. Simulation parameter setting
参数 取值 参数 取值 $ {p_{{\text{fa}}}} $ 10–8 $ {G_{\text{t}}} $ 30 dB $ {G_{\text{I}}} $ 6 dB $ {G_{{\text{IP}}}} $ 3 dB $ {\beta _{k,q}} $ 1 MHz $ {T_{k,q}} $ 1 ms $ \lambda $ 0.3 m $ \eta $ 45 m ${T_{\rm{s}}}$ 1 s $ {P_{{\text{total}}}} $ 5 kW $ {\bar P_{{\text{max}}}} $ 4 kW $ {\bar P_{\min }} $ 0.5 kW
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表 3 初始时刻目标运动参数
Table 3. Initial target motion parameters
目标编号 位置(km) 速度(m/s) 加速度(m/s2) 最大加速度(m/s2) 1 (9.6, 84.1) (–494.2, –1346.1) (–19.4, 20.7) 80 2 (89.7, 24.4) (533.2, 468.5) (14.6, 0.9) 50 3 (66.9, 72.4) (–257.1, 695.1) (9.6, 7.7) 60
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