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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (10): 1883-1891    DOI: 10.3785/j.issn.1008-973X.2020.10.003
    
Game strategy of resource allocation for phased array radar search and tracking
Yi-ming LIU(),Wen SHENG*()
Department of Air Defense Early Warning Equipment, Air Force Early Warning Academy, Wuhan 430019, China
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Abstract  

A resource allocation strategy based on game theory was proposed in order to solve the real-time problem of search and tracking (SAT) resource allocation (RA). The system model of search and tracking was established, and SATRA was modeled as a non-cooperative game problem. The resource allocation problem between the search subspace and the tracking multi-object in the model was regarded as the cooperative game relationship. The Shapley value was used to complete the corresponding problem, and the double objective optimization model of Nash equilibrium was given. The above double objective optimization model was transformed into a single objective optimization problem by using the dynamic weighted ideal point method in order to quickly find the distribution solution that meets the preference of decision maker. A parallel hybrid genetic particle swarm optimization (PHGAPSO) algorithm was proposed to solve the optimal allocation scheme of the above optimization problem. The simulation results verified the effectiveness and advancement of the game allocation strategy and the superiority of the performance of the hybrid algorithm. The method was compared with the Pareto bi-objective optimization method under the same conditions. The experimental results show that the game theory method has higher flexibility. The average search signal-to-noise ratio is increased by 1.02%, and the tracking target error is reduced by 1.55%.

Key words： phased array radar      search and tracking      resource allocation      game strategy      Shapley value      Nash equilibrium      hybrid genetic particle swarm optimization     
Received: 25 July 2019      Published: 28 October 2020
CLC:  TN 958  
Corresponding Authors: Wen SHENG     E-mail: ls.liu_yiming@whu.edu.cn;sheng_wen@263.net
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Yi-ming LIU
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Cite this article:

Yi-ming LIU,Wen SHENG. Game strategy of resource allocation for phased array radar search and tracking. Journal of ZheJiang University (Engineering Science), 2020, 54(10): 1883-1891.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.10.003     OR     http://www.zjujournals.com/eng/Y2020/V54/I10/1883


相控阵雷达搜索和跟踪资源博弈分配策略

为了解决搜索和跟踪（SAT）资源分配（RA）实时性的问题，提出博弈论视角下的资源分配策略. 建立搜索与跟踪的系统模型，将SATRA建模为非合作博弈问题，将模型中搜索子空域和跟踪多目标间的资源分配问题看作合作博弈关系，利用Shapley值完成相应资源的分配，给出纳什均衡求解的双目标优化模型；为了快速找到符合决策者偏好的分配解，将双目标优化模型通过动态加权的理想点法转化为单目标优化问题，提出并行混合遗传粒子群优化（PHGAPSO）算法求解上述优化问题最优分配方案，仿真验证了博弈分配策略的有效性和先进性以及混合算法性能的优越性. 在相同的条件下，与帕累托双目标优化方法进行对比. 实验结果表明，博弈论的方法具有更高的灵活性，平均搜索信噪比提高了1.02%，平均跟踪目标误差降低了1.55%.


关键词： 相控阵雷达,  搜索与跟踪,  资源分配,  博弈策略,  Shapley值,  纳什均衡,  混合遗传粒子群优化 
Fig.1 Flow chart of PHGAPSO algorithm implementation
空域序号 Rm,k / (103 km) φm,k / (°)
1 2.5 10
2 2.5 12
3 2.7 10
4 2.8 8
5 3.0 10
6 2.9 6
Tab.1 1-10 cycle search airspace 1 arrangement parameters
空域序号 Rm,k / (103 km) φm,k / (°)
1 2.4 6
2 2.4 8
3 2.6 8
4 2.8 8
5 3.0 16
6 3.0 10
7 2.7 6
8 2.5 8
Tab.2 11-20 cycle search airspace 2 arrangement parameters
Fig.2 Schematic diagram of target motion trajectory in radar area of responsibility
参数 数值 参数 数值
L 100 c1 2
Pc 0.4 c2 2
Pm 0.05 Pres 0~1.0
T 50 v 0.002~0.010
ω 0.7 PH(t) 0.5
Tab.3 Parameter design of PHGAPSO algorithms
Fig.3 Comparison of resource allocation results between GT and PBO methods
Fig.4 Comparison of search utility between GT and PBO methods
Fig.5 Comparison of track utility values between GT and PBO methods
Fig.6 Actual subspace resource allocation map at typical frame period
Fig.7 Actual multi-target resource allocation map at typical frame period
算法 Hmax tcom/s
PHGAPSO 0.007 368 3.505 643
GA 0.007 682 1.842 562
PSO 0.007 906 1.822 971
Tab.4 Statistical performance index of each algorithm
Fig.8 Comparison curve of performance curves of various optimization algorithms
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