Air combat maneuver trajectory prediction of target based on Volterra series optimized by SABA algorithm
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摘要:
目标机动轨迹预测是空战态势感知和目标威胁评估的重要前提。针对传统目标机动轨迹预测模型复杂度大、预测精度低等问题，通过分析并结合目标机动轨迹时序数据所具备的混沌特性，引入Volterra泛函级数模型进行目标机动轨迹预测。为解决Volterra泛函级数模型中存在高阶核函数难以求解的问题，利用变异机制和自适应步长控制机制改进蝙蝠算法的寻优能力，进而构建了一种基于自适应蝙蝠算法（SABA）优化的Volterra泛函级数目标机动轨迹预测模型，并利用优化后不同阶数的Volterra泛函级数模型对目标未来机动轨迹进行预测。仿真实验中，通过与其他优化算法改进的Volterra泛函级数模型的预测精度对比，验证了所提预测模型的可行性，同时也说明了二阶Volterra泛函级数模型更加适用于目标机动轨迹预测。
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关键词:
- 轨迹预测 /
- Volterra泛函级数模型 /
- 核参数优化 /
- 自适应蝙蝠算法 /
- 截断阶数
Abstract:Target maneuver trajectory prediction is an important prerequisite for air combat situation awareness and target threat assessment. Aiming at the problems of high complexity and low prediction accuracy of traditional target maneuvering trajectory prediction model, Volterra functional series model was introduced to predict the target maneuvering trajectory by analyzing and combining the chaotic characteristics of target maneuvering trajectory time series data. To solve the problem that it is difficult to solve the high-order kernel function in Volterra functional series model, the mutation mechanism and adaptive step control mechanism were used to improve the optimization ability of bat algorithm. Then, a Volterra functional series target maneuver trajectory prediction model based on self-adaptive bat algorithm (SABA) optimization was constructed, and the future maneuvering trajectory of the target was predicted by using the optimized Volterra series model with different orders. In the simulation experiment, the feasibility of the prediction model is verified by comparing with the prediction accuracy of the Volterra series prediction model improved by other optimization algorithms, and the second-order Volterra series model is proved to bemore suitable for target maneuver trajectory prediction.
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图 1 基于SABA算法优化的Volterra泛函级数目标机动轨迹预测流程
Figure 1. Flow chart of target maneuver trajectory prediction based on Volterra functional series optimized by SABA algorithm
图 2 基于二、三阶Volterra模型目标空间预测结果对比
Figure 2. Comparison of target space prediction results based on second-order and third-order Volterra models
图 3 不同智能算法优化预测模型的空间适应度函数值比较
Figure 3. Comparison of spatial fitness function values of prediction models optimized by different intelligent algorithms
图 4 不同智能算法优化预测模型的运行时间对比
Figure 4. Comparison of running time of prediction models optimized by several intelligent algorithms
表 1 不同预测模型进行2步预测的性能对比
Table 1. Performance comparison of two-step prediction with different prediction models
算法 阶数 Mad Mse Mape Cor BA-Volterra 二阶 21.9137 6.563 3×102 0.0009 0.9983 BA-Volterra 三阶 30.5021 1.460 4×103 0.0012 0.9976 SABA-Volterra 二阶 15.4337 2.424 6×102 0.0006 0.9987 SABA-Volterra 三阶 25.1874 8.296 9×102 0.0010 0.9978 ACO-Volterra 二阶 24.4320 8.006 2×102 0.0010 0.9979 ACO-Volterra 三阶 112.5901 1.684 0×104 0.0043 0.9891 GA-Volterra 二阶 35.4252 1.355 7×103 0.0014 0.9975 GA-Volterra 三阶 202.4583 5.289 1×104 0.0080 0.9836 BPNN 83.7994 9.162 4×103 0.0033 0.9971 
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表 2 不同预测模型进行4步预测的性能对比
Table 2. Performance comparison of four-step prediction with different prediction models
算法 阶数 Mad Mse Mape Cor BA-Volterra 二阶 85.6052 8.851 1×103 0.0033 0.9899 BA-Volterra 三阶 134.2922 2.223 0×104 0.0053 0.9886 SABA-Volterra 二阶 27.9075 1.269 8×103 0.0011 0.9982 SABA-Volterra 三阶 27.9597 1.104 6×103 0.0011 0.9983 ACO-Volterra 二阶 30.5999 1.143 9×103 0.0013 0.9978 ACO-Volterra 三阶 114.2622 1.695 3×104 0.0045 0.9890 GA-Volterra 二阶 53.7130 3.015 4×103 0.0021 0.9970 GA-Volterra 三阶 210.4822 5.956 8×104 0.0082 0.9834 BPNN 221.7636 7.253 6×104 0.0087 0.9830
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表 3 不同预测模型进行8步预测的性能对比
Table 3. Performance comparison of eight-step prediction with different prediction models
算法 阶数 Mad Mse Mape Cor BA-Volterra 二阶 108.0024 1.475 9×104 0.0042 0.9887 BA-Volterra 三阶 125.6733 1.900 8×104 0.0049 0.9888 SABA-Volterra 二阶 39.5275 1.589 9×103 0.0015 0.9976 SABA-Volterra 三阶 71.7624 6.519 5×103 0.0028 0.9968 ACO-Volterra 二阶 294.7023 1.395 2×105 0.0114 0.9811 ACO-Volterra 三阶 545.3952 3.806 3×105 0.0212 0.9689 GA-Volterra 二阶 100.6532 1.049 8×104 0.0039 0.9890 GA-Volterra 三阶 430.5977 2.278 4×105 0.0167 0.9753 BPNN 369.8697 1.923 3×105 0.0144 0.9773
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