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Resource Allocation and Precise Tracking Algorithm for Multiple Maneuvering Targets
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摘要: 雷达系统在对多机动目标进行跟踪时，跟踪性能会因为多雷达发射资源的非匹配预设和先验信息的不充分利用而下降。针对该问题，提出了一种面向多机动目标的资源分配与精细化跟踪算法，以期在同等资源消耗条件下获取更高的目标跟踪性能。首先，该文结合跟踪器反馈的目标预测信息，利用多模型交互的思想对目标预测位置分布函数进行拟合，建立了基于多模型交互的检测跟踪一体化方法，实现了系统对机动目标的精细化跟踪。而后，分析了多雷达发射资源和机动目标跟踪性能的耦合机理，结合机动目标贝叶斯克拉美罗下界的推导，建立了跟踪性能驱动的多模型加权资源分配框架。最后通过仿真验证了所提方法在相同资源消耗条件下，能够显著提升多机动目标的综合跟踪精度。Abstract: In radar systems that track multiple maneuvering targets, conventional approaches often suffer from performance degradation due to suboptimal resource allocation and insufficient utilization of prior information. To address this challenge and significantly enhance tracking performance under equivalent resource constraints, a resource allocation and precise tracking algorithm for multiple maneuvering targets is proposed. First, by integrating a multiple model interaction architecture with tracker feedback prediction, a probabilistic distribution model for target position prediction through multiple model interaction is constructed. This model establishes an integrated detection and tracking method based on multiple model interactions to achieve refined tracking of maneuvering targets. Subsequently, by analytically modeling the coupling mechanism between radar resources and tracking performance, and deriving the Bayesian Cramér-Rao Lower Bound (BCRLB) for maneuvering targets, a performance-driven multimodel weighted resource allocation framework is developed. Simulations validate that the proposed method can significantly enhance the overall tracking precision of multiple maneuvering targets under equivalent resource consumption.
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Key words:
- Maneuvering target /
- Resource allocation /
- Precise tracking /
- Prior information /
- Multiple model
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图 1 面向机动目标跟踪的资源分配与精细化目标跟踪处理框架
Figure 1. The processing framework of resource allocation and precise target tracking for maneuvering target tracking
图 7 雷达对目标距离波门检测门限系数曲线
Figure 7. Threshold coefficient of radar range gate detection for the target
1 基于内点法的雷达发射功率优化算法
1. The optimization algorithm based on interior point method
输入：内点可行域$D = \left\{ {{p_{i,q,k}}\left| {\displaystyle\sum\nolimits_{q = 1}^Q {{p_{i,q,k}}} \le p_{{\mathrm{total}}}^i,{\mathrm{lb}} \le {p_{i,q,k}} \le {\mathrm{ub}},\forall i,q} \right.} \right\}$，设置算法初始点，即
${\boldsymbol{p}}_{q,k}^{} = \left\{ {{p_{i,q,k}}\left| {{p_{i,q,k}} = {{p_{{\mathrm{total}}}^i} \mathord{\left/ {\vphantom {{p_{total}^i} Q}} \right. } Q},\forall i} \right.} \right\}$。设置迭代索引$j = 1$ ，设置算法终止条件为迭代步长$\varepsilon \le 0.000\;1$或迭代次数$\varphi \ge 100\;000$。(1) 构造罚函数优化问题如下 $ \mathop {\min }\limits_{{p_k}} {\text{ }}\displaystyle\sum\limits_{q = 1}^Q {{f_q}({{\boldsymbol{p}}_{q,k}})} + {\varsigma _q}{\varphi _D}({{\boldsymbol{p}}_{q,k}}) $ 其中，$ {\varsigma _q} > 0 $为惩罚因子，$ \varphi_{D}\left({\boldsymbol{p}}_{q, k}\right) $为罚函数，当$ {{\boldsymbol{p}}_{q,k}} \in D $时，$ {\varphi _D}({{\boldsymbol{p}}_{q,k}}) = 0 $，否则$ {\varphi _D}({{\boldsymbol{p}}_{q,k}}) = \infty $。 (2) 搜索罚函数优化问题的极小值点$ {\boldsymbol{p}}_{1, k}^{*}, {\boldsymbol{p}}_{2, k}^{*}, \cdots ,{\boldsymbol{p}}_{Q, k}^{*} $。 (3) 检验终止条件，并计算当前极小值点对应目标函数值，若符合终止条件，则算法终止，否则更新初始点为$ {\boldsymbol{p}}_{1, k}^{*}, {\boldsymbol{p}}_{2, k}^{*}, \cdots, {\boldsymbol{p}}_{Q, k}^{*} $,
$ {\varsigma _q} = 0.1{\varsigma _q} $，令$j = j + 1$并跳转至步骤(1)。输出：雷达节点对各个目标分配的发射功率结果$ {\boldsymbol{p}}_{1 k}, {\boldsymbol{p}}_{2 k}, \cdots, {\boldsymbol{p}}_{Q k} $。 
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表 1 雷达仿真参数表
Table 1. Radar parameters
参数 数值 采样间隔 2 s 发射信号带宽 2 MHz 发射信号波长 1 m 相关波门系数 8 初始模型概率 ${\mu _0} = [\begin{array}{*{20}{c}} {0.4}&{0.3}&{0.3} \end{array}]$ 天线孔径 10 m 虚警率 10–4 过程噪声强度 1 蒙特卡罗次数 1000 模型转移概率矩阵 ${{\boldsymbol{p}}_{ij}} = \left[ {\begin{array}{*{20}{c}} {0.80}&{0.10}&{0.10} \\ {0.05}&{0.90}&{0.05} \\ {0.05}&{0.05}&{0.90} \end{array}} \right]$
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表 2 雷达位置信息表
Table 2. Radar position information
雷达序号 雷达位置信息$(x,y,z)$ 雷达1 $( - 40000\;{\mathrm{m}},100000\;{\mathrm{m}},0\;{\mathrm{m}})$ 雷达2 $( - 80000\;{\mathrm{m}},50000\;{\mathrm{m}},1000\;{\mathrm{m}})$ 雷达3 $( - 100000\;{\mathrm{m}},10000\;{\mathrm{m}},0\;{\mathrm{m}})$ 雷达4 $( - 90000\;{\mathrm{m}}, - 30000\;{\mathrm{m}},0\;{\mathrm{m}})$ 雷达5 $( - 70000\;{\mathrm{m}}, - 70000\;{\mathrm{m}},2000\;{\mathrm{m}})$ 雷达6 $( - 50000\;{\mathrm{m}}, - 100000\;{\mathrm{m}},0\;{\mathrm{m}})$
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表 3 多机动目标状态数据
Table 3. Target parameters
序号 初始状态
(m, m/s, m, m/s, m, m/s)转弯率
$({\omega _1},{\omega _2})\;({}^{ \circ }/{\mathrm{s}})$目标1 $ ( - 10\;000,200,0,0,8\;000,0) $ (5,–5) 目标2 $(0,60,20\;000,180,8\;000,0)$ (3,–3) 目标3 $(5\;000,60,50\;000,180,8\;000,0)$ (3,–5) 目标4 $(10\;000, - 200, - 30\;000,0,8\;000,0)$ (3,–5)
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