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摘要:
针对经验的空间大气模型会在轨道预报中造成较大的误差，以某型号卫星作为基准航天器，提出2种不同精度的轨道预报模型作为仿真基础，以产生训练数据和测试数据。利用3种数据挖掘中的分类方法，如支持向量机（SVM）、神经网络（NN）、随机森林（RF）等方法，对空间大气模型在轨道预报时造成的误差进行监督学习，借此反演误差简化模型中大气模型的偏差并进行修正。分类器的训练结果表明，随机森林方法由于随机选择决策树、随机选择分类项目，按照最大概率反演的大气模型误差准确率高达99.99%，支持向量机次之，最大准确率仅为50.7%，前馈负向传播神经网络容易出现不学习的情况，应用效果最差。相比传统数理统计方法，本文方法具有快速处理大数据集、能够挖掘隐藏在轨道预报微小误差中的潜在信息等优势。
Abstract:The empirical atmospheric model would cause great error in orbital prediction. This paper, taking a typical satellite as the benchmark spacecraft, proposes two orbital prediction models with different precision to generate training data and test data. Using three supervised classification methods in data mining technology, i.e. support vector machine (SVM), neural network (NN), and random forest (RF), to learn the errors caused by atmospheric model in orbital prediction. In this way, the deviation between the atmospheric model and its real value can be recovered and then corrected. Classification training results show that due to the randomness and voting mechanism, RF makes the highest accuracy in recovering the known deviation of atmospheric model close to 99.99% through choosing maximum probability, which is followed by SVM with the maximum accuracy of 50.7%. It is often the case that feedforward backpropagation neural network fails to learn, so the application performance is poor. Compared with traditional statistical methods, the method proposed in this paper has the advantages of rapidly processing big datasets and the ability of mining potential knowledge in tiny orbital prediction errors.
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Key words:
- data mining /
- random forest /
- neural network /
- support vector machine /
- atmospheric model
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图 5 混淆矩阵和随机森林分类结果
Figure 5. Classification results of confusion matrix and random forest
表 1 精确模型与误差简化模型参数
Table 1. Parameters of accurate model and error simplified model
参数 精确模型 误差简化模型 地球形状 WGS84 WGS84 阶数 50×50 5×5 第三体引力摄动 太阳 太阳光压 精确地影预报 大气阻力 MSIS MSIS+(-100%~100%)误差 
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表 2 仿真初始状态
Table 2. Initial state of simulation
参数 数值 a/km 6 871.209 3 e 0.002 5 i/(°) 97.560 4 Ω/(°) -74.218 7 ω/(°) 95.295 7 M/(°) 21.168 3 rx/km -1 611.425 2 ry/km 2 731.717 4 rz/km 6 081.641 7 vx/(km·s-1) -1.426 1 vy/(km·s-1) 6.690 5 vz/(km·s-1) -3.372 2
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表 3 部分训练数据
Table 3. Partial training data
εi/% Δt/d a/km e i/(°) Ω/(°) ω/(°) M/(°) -50 0.301 6 871.102 0.002 5 97.565 -73.712 94.707 229.007 -40 0.600 6 871.051 0.002 5 97.563 -73.605 93.301 72.578 -30 0.300 6 871.102 0.002 5 97.565 -73.912 94.701 227.745 -20 0.600 6 871.048 0.002 5 97.563 -73.605 93.299 73.216 -10 0.500 6 871.142 0.002 5 97.561 -73.707 94.098 243.763 0 0.900 6 871.174 0.002 5 97.563 -73.301 93.709 278.117 10 0.800 6 871.061 0.002 5 97.565 -73.403 93.410 87.899 20 0.200 6 871.072 0.002 5 97.564 -74.014 95.067 39.982 30 0.300 6 871.096 0.0025 97.565 -73.912 94.703 228.378 40 0.500 6 871.135 0.002 5 97.561 -73.707 94.097 243.766 50 0.600 6 871.036 0.002 5 97.563 -73.605 93.298 73.220
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表 5 神经网络训练参数设置
Table 5. Training parameter setting of neural network
分类模型 神经网络层数 隐藏层神经元数 训练函数 适应性学习函数 最大验证失败次数 最小性能梯度 性能 神经网络 8 10 列文伯格算法 LEARNDM 10 1×10-9 均方差
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表 6 支持向量机训练参数设置
Table 6. Training parameter setting of SVM
分类模型 核函数 核尺度 特征选择 支持向量机 高斯 1.3 主成分分析法
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表 7 3种分类方法性能对比
Table 7. Performance comparison of three classification methods
分类模型 训练时长/s 精确度/% 随机森林 241.434 2 99.99 神经网络 2 102 0.011 6 支持向量机 29 167.627 4 50.7
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