Finding Probability of Submarine-Launched Acoustic Homing Torpedo 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 probability associated with submarine-launched acoustic homing torpedoes significantly influences tactical formulation. Conventional analytical and statistical algorithms encounter challenges in balancing the trade-off between the speed and precision of probability assessment. In response to this issue, this paper introduces a novel estimation model for assessing the probability of detection based on Gaussian process regression. Additionally, a methodology is proposed for generating training data using an analytical model. Subsequently, numerical simulations were conducted within a specific battlefield scenario. The outcomes illustrate the superior performance of the proposed method, offering valuable theoretical insights for informed decision-making in relevant battlefield contexts.
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图 1 初始雷目距离3 km处脱靶量2次采样值
Figure 1. The two sampling 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 声自导鱼雷恰好捕获目标态势示意图
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 1500 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 function
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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