Radio Frequency Stealth-based Optimal Radio Frequency Resource Allocation Algorithm for Multiple-target Tracking in Radar Network
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摘要: 针对组网雷达系统多目标跟踪场景，该文提出一种面向射频(RF)隐身的组网雷达射频辐射资源优化分配算法。首先，采用目标跟踪误差的贝叶斯克拉美-罗下界(BCRLB)作为目标跟踪性能指标。其次，以各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，以BCRLB不大于给定目标跟踪精度阈值及系统射频辐射资源作为约束条件，建立了包含雷达节点分配方式、驻留时间和辐射功率3个优化变量的优化模型。然后，采用两步分解法对上述优化模型进行了求解，即先固定雷达节点选择，利用内点法对简化后的非凸非线性优化模型进行求解，之后再通过匈牙利算法确定最佳雷达节点分配方式。仿真结果表明，相较于辐射资源均匀分配算法，所提算法可以有效降低组网雷达的射频资源消耗，提升系统射频隐身性能。Abstract: In the scenario of multi-target tracking by a radar network system, a Radio Frequency (RF) stealth-based optimal RF resource allocation algorithm in radar network is proposed. Firstly, the Bayesian Cramer-Rao Lower Bound (BCRLB) of target tracking error is used as the target tracking performance index. Secondly, the optimization model is established which includes three optimization variables: radar node selection, dwell time and radiation power. In this model, the objective function is the weighted sum of the dwell time resources and radiation power resources of each radar, the constraint condition can be conclude that the BCRLB must be less than the given threshold and the system RF radiation resources must be between the upper and lower limits. Then, the two-step decomposition method is used to solve the above optimization model. The radar node selection is fixed first, then the interior point method is used to solve the simplified non-convex nonlinear optimization model, and then the Hungarian algorithm is used to determine the best radar node selection mode. The simulation results show that compared with uniform resource allocation algorithm, the proposed algorithm can effectively reduce the RF resource consumption of the radar network and improve the RF stealth performance of the system.
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表 1 固定雷达分配方式的辐射资源优化控制算法
步骤 1 令${g_1} = {\kern 1pt} F_{k\left| {k - 1} \right.}^s - {F_{\max }}$,${g_2} = {\kern 1pt} {T_{{\rm{d,min}}}} - T_{{\rm{d}},1,k}^s$, ${g_3} = {\kern 1pt} {T_{{\rm{d,min}}}} - T_{{\rm{d}},2,k}^s$,···, ${g_{M + 1}} = {T_{{\rm{d,min}}}} - {\kern 1pt} T_{{\rm{d}},M,k}^s$, ${g_{M + 2}} = {\kern 1pt} T_{{\rm{d}},1,k}^s - {T_{{\rm{d,max}}}}$,
${g_{M + 3}} = {\kern 1pt} T_{{\rm{d}},2,k}^s - {T_{{\rm{d,max}}}}$,···, ${g_{2M + 1}} = {\kern 1pt} T_{{\rm{d}},M,k}^s - {T_{{\rm{d,max}}}}$, ${g_{2M + 2}} = {\kern 1pt} {P_{\min }} - P_{1,k}^s$, ${g_{2M + 3}} = {\kern 1pt} {P_{\min }} - P_{2,k}^s$,···, ${g_{3M + 1}} = {\kern 1pt} {P_{\min }} - P_{M,k}^s$,
${g_{3M + 2}} = P_{1,k}^s - {P_{\max }}$,···, ${g_{4M + 1}} = P_{M,k}^s - {P_{\max }}$，设置可行域：$D = \left\{ T_{ {\rm{d} },m,k}^s,P_{m,k}^s\left| {g_a}\left( {T_{ {\rm{d} },m,k}^s,P_{m,k}^s} \right) \le 0,a = 1,2, ··· ,4M + 1,\right.\right.$
$\left.1 \le m \leq M \right\}$其中，${g_a}\left( {T_{{\rm{d}},m,k}^s,P_{m,k}^s} \right) = {g_a},a = 1,2, ··· ,4M + 1$，取${\left( {T_{{\rm{d}},m,k}^s,P_{m,k}^s} \right)^{\left( 0 \right)}} \in D\left( {1 \le m \le M} \right)$为初始点，$\varepsilon > 0$为算法终
止指标，${\xi _1} > 0$, $c \ge 2$，令$l = 1$；
步骤 2 以${\left( {T_{{\rm{d}},m,k}^s,P_{m,k}^s} \right)^{\left( {l - 1} \right)}}$为初始点求解如下子问题：$\min {\kern 1pt} {F_1} - {\xi _1}\left[ {\frac{1}{ { {g_1} } } + \frac{1}{ { {g_2} } } + ··· + \frac{1}{ { {g_{2M + 2} } } } } \right], {\rm{s} }{\rm{.t} }{\rm{.} }{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} T_{ {\rm{d} },m,k}^s,P_{m,k}^s \in D$，其中，${F_1}$表
示式(7)中的优化目标函数，令上述问题的极小值点为${\left( {T_{{\rm{d}},m,k}^s,P_{m,k}^s} \right)^{\left( l \right)}}$；步骤 3 检验终止条件，若$- {\xi _l}\left[ {\dfrac{1}{ { {g_1} } } + \dfrac{1}{ { {g_2} } } + ··· + \dfrac{1}{ { {g_{4M + 1} } } } } \right] < \varepsilon$，算法终止；否则，令${\xi _{l + 1} } \leftarrow \dfrac{ { {\xi _l} } }{c}$, $l \leftarrow l + 1$，转入步骤2。 
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