﻿ 基于神经网络算法的卫星轨道预报
 舰船科学技术  2020, Vol. 42 Issue (10): 146-151    DOI: 10.3404/j.issn.1672-7649.2020.10.028 PDF

1. 中国人民解放军91054部队，北京 102442;
2. 战略支援部队航天工程大学，北京 101416;
3. 中国人民解放军91776部队，北京 100161

Research on satellite orbit forecast based on neural network algorithm
LUO Fei1, REN Hao-li2, ZHAO Bing3
1. No. 91054 Unit of the PLA, Beijing 102442, China;
2. Strategic Support Force Aerospace Engineering University, Beijing 101416, China;
3. No. 91776 Unit of the PLA, Beijng 100161, China
Abstract: It is necessary to predict the orbit of foreign military satellites in order to effectively evade the reconnaissance and surveillance of Chinese naval ship targets by foreign military reconnaissance satellitesor to carry out interference countermeasures. The limitation and low prediction accuracy of the satellite orbitprediction model is the problems currently existing in this field. Aiming at the existing problem of the traditional method, this paper proposes a satellite orbit prediction algorithm based on neural network algorithm, and obtain the track change rules by training historical TLE data, which forecast satellite orbit. the preliminary experimental results show that the proposed algorithm is feasible.
Key words: satellite orbit     TLE     neural network     algorithm
0 引　言

1 卫星轨道数据

SSN每天不定时会发布一条针对卫星的TLE轨道数据，随着时间T变化，TLE两行轨道六要素也发生改变，直观上来看，TLE轨道六要素的变化和时间T之间应存在某种对应关系。TLE轨道六要素的物理含义详细说明见表1，使用神经网络进行轨道预测将使用六要素，如表1所示。

2 基于神经网络的轨道预报算法 2.1 构建LSTM预测模型

var = {eiΩωM0n0TD}。

 图 1 基于LSTM预测轨道参数要素的神经网络模型 Fig. 1 Neural network model based on LSTM to predict orbital parameter elements

1）输入层：TLE轨道预报八要素数据。

2）LSTM层：获取TLE轨道预报八要素数据的高维度特征。

3）全连接层（Full-connect）：对获取到的高维度特征进行整合。

4）输出层：计算目标要素的预测值并输出。

 $J\left(\theta \right) =\sqrt{\frac{1}{m}\sum\limits _{i=1}^{m}{({y}_{i}-{\tilde {y}}_{i})}^{2}} {\text{。}}$

 $f\left({w}_{1},\cdots ,{w}_{n},b\right)=y=w\cdot t+b+\epsilon \text{。}$

2.2 构建LSTM-CNN网络模型

 图 2 基于LSTM_CNN神经网络和线性回归预测TLE轨道六要素示意图 Fig. 2 Six elements of TLE orbit prediction based on LSTM_CNN neural network and linear regression

 ${{t}{l}{e}}_{{s}}={TLE}_{m-n-1}^{m}\text{，}$
 ${{T}{L}{E}}_{{m}}=\{{{i}}_{{m}},{\omega }_{m},{M}_{m},{i}_{m},{e}_{m},{n}_{m},{t}_{m},\Delta {t}_{m}\}\text{，}$
 $\Delta {{t}}_{{m}}={t}_{m+1}-{t}_{m}\text{。}$

 ${\tilde {{i}}}_{{m}+1}=LSTM\_CN{N}_{1}\left({TLE}_{m-n-1}^{m}\right)\text{，}$
 ${\tilde {{e}}}_{{m}+1}=LSTM\_CN{N}_{2}\left({TLE}_{m-n-1}^{m}\right)\text{，}$
 ${\tilde {{n}}}_{{m}+1}=LSTM\left({TLE}_{m-n-1}^{m}\right)\text{，}$
 ${\tilde {{\Omega }}}_{{m}+1}=LR\left({TLE}_{m-n-1}^{m}\right) \text{，}$
 ${\tilde {{\omega }}}_{{m}+1}=LR({TLE}_{m-n-1}^{m}\text{，}$
 ${\tilde {{M}}}_{{m}+1}=LR\left({TLE}_{m-n-1}^{m}\right) \text{。}$

 $\begin{split} & {\tilde {{T}{L}{E}}}_{{m}+1}=\{{\tilde {{i}}}_{{m}+1},{\tilde {\omega }}_{m+1},{\tilde {M}}_{m+1},{\tilde {i}}_{m+1},{\tilde {e}}_{m+1},{\tilde {n}}_{m+1},{t}_{m+1},\Delta {t}_{m+1}\}\\ &\Delta {{t}}_{{m}+1}={t}_{m+2}-{t}_{m+1*} \text{，}\\[-10pt] \end{split}$

 ${{T}{L}{E}}_{m-n-2}^{m+1}={{T}{L}{E}}_{m-n-2}^{m}\oplus {\widetilde {{T}{L}{E}}}_{m+1} \text{。}$

2.3 模型衡量指标

1）根据模型预测的TLE数据和真实的TLE数据的绝对误差作为衡量指标，来衡量模型预测TLE数据的精度:

 ${{m}{e}{t}{r}{i}{c}}_{1}=\left|\right|{{T}{L}{E}}_{{p}}-{{T}{L}{E}}_{{t}}\left|\right| \text{，}$

2）传统的动力学模型的衡量指标是在同一时刻模型预测空间飞行物体的状态，例如速度和位置，与星历数据观察值的绝对误差，绝对误差越小说明其精度越高。为了能和传统的动力学模型比较，采用速度和位置的绝对误差作为模型的另一衡量指标。

 ${metric}_{2}^{position}=\sqrt{{\left({p}_{x}^{t}-{p}_{x}^{p}\right)}^{2}+{\left({p}_{y}^{t}-{p}_{y}^{p}\right)}^{2}+{\left({p}_{z}^{t}-{p}_{z}^{p}\right)}^{2}} \text{，}$
 ${metric}_{2}^{velocity}=\sqrt{{\left({v}_{x}^{t}-{v}_{x}^{p}\right)}^{2}+{\left({v}_{y}^{t}-{v}_{y}^{p}\right)}^{2}+{\left({v}_{z}^{t}-{v}_{z}^{p}\right)}^{2}} \text{。}$

3 初步实验结果 3.1 实验数据

3.2 模型参数设置

3.3 实验结果与分析

1）LSTM_CNN模型替换LSTM模型

LSTM模型对应的3个元素使用LSTM_CNN模型来训练和预测，分别记录在20 d内轨道离心率、轨道倾角和平均运动的误差及在20 d内速度位置上的误差。

4 结　语

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