Finding Probability of Submarine-Launched Acoustic Homing Torpedoes Based on Gaussian Process Regression
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摘要: 明确潜射声自导鱼雷的发现概率, 对相关战术制定具有显著作用。传统解析算法和统计算法无法平衡概率评估的快速性和精确性, 针对此问题, 文中提出了一种基于高斯过程回归的发现概率评估模型, 以及基于解析模型的训练数据集生成方法, 并在特定态势下开展了发现概率评估的数值仿真。结果显示, 文中所提方法具有很好的评估效果, 可为相关战场决策提供理论支撑。Abstract: The determination of the finding probability of submarine-launched acoustic homing torpedoes significantly affects tactical formulation. Conventional analytical and statistical algorithms fail to balance the speed and precision of probability assessment. In response to this issue, this paper introduced a model for assessing the finding probability based on Gaussian process regression. Additionally, a method was proposed for generating a training dataset based on the analytical model. Numerical simulations for assessing the finding probability were conducted within a specific battlefield scenario. The outcomes illustrate the superior assessment effect of the proposed method, offering theoretical support for decision-making in relevant battlefield contexts.
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图 1 初始雷目距离3 km处脱靶量采样值
Figure 1. The sampling values of miss distance at 3 km initial distance between torpedo and target
图 2 声自导鱼雷一次转角弹道水平面示意图
Figure 2. Diagram of trajectory of acoustic homing torpedo with one time rotating in horizonal plane
图 3 声自导鱼雷捕获目标极限情况态势
Figure 3. Diagram of limitary battlefield situation when acoustic homing torpedo finds target
图 8 发现概率预测与验证相对误差
Figure 8. Relative errors of prediction and validation of finding probability
表 1 战场态势参数设置
Table 1. Parameters setting of battlefield situation
名称 参数 初始雷目距离/km 10/5/50 初始目标舷角/(°) 0/10/180 鱼雷速度/kn 50 声自导探测距离/m 1 500 声自导探测扇面半角/(°) 50 鱼雷初始段航程/m 500 鱼雷回转半径/m 50 鱼雷初始发射提前角/(°) 20 目标速度/kn 20 目标航向/(°) 180 鱼雷速度误差标准差/kn 3 鱼雷航向误差标准差/(°) 1 探测目标速度误差标准差/kn 3 探测目标航向误差标准差/(°) 1 目标速度误差标准差/kn 3 目标航向误差标准差/(°) 1 目标初始方位探测误差标准差/(°) 1 目标初始距离探测误差标准差/m 1%初始距离 
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表 2 不同核函数均方根误差
Table 2. RMSE of different kernel functions
高斯核函数 RMSE RQK 0.010 640 SEK 0.011 284 MK5/2 0.010 881 EK 0.012 799
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表 3 需预测发现概率的新态势条件
Table 3. New situation for which the finding probability is needed to be predicted
编号 初始雷目距离/m 初始目标舷角/(°) 1 12 345 0~180(间隔1°) 2 34 567 0~180(间隔1°)
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表 4 预测和验证相对误差范围及态势占比
Table 4. Relative error range of prediction and validation and percentage of battlefield situation
类别 相对误差范围/% 态势占比/% 预测 0~1 97.24 0~2 100 验证 0~3 79.83 0~5 93.92
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