Echo state network-based data recovery method for low-low satellite-to-satellite tracking missions in laser interferometry
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摘要:
作为低低跟踪重力卫星GRACE任务的后续任务，激光干涉重力卫星任务GRACE Follow On双星之一的加速度计载荷在运行一个月后出现了异常，造成了关键科学测量数据的缺失，同时在GRACE服役期最后阶段也出现了类似情况。由此，加速度计数据恢复技术对GRACE尤其是GRACE Follow On任务探测目标的实现极为重要。本文提出了一种基于机器学习的回声状态网络模型来实现加速度计数据恢复与重建的全新方法。基于回声状态网络模型，构建双星之间加速度计数据的映射关系，并通过贝叶斯优化提高网络性能，可实现对缺失加速度计数据的高精度高效率重建。通过实测数据的实验比对，在重力场探测信号频段，模型预测结果在沿轨道方向和径向两个高灵敏轴可达到（甚至部分频段优于）
$ {10}^{-8} $ m∙s−2/$ \sqrt{H\textit{z}} $ 量级水平，在轨道法向低灵敏轴到达$ {10}^{-8} $ m∙s−2/$ \sqrt{H\textit{z}}\sim{10}^{-7} $ m∙s−2/$ \sqrt{H\textit{z}} $ 水平。这一重建精度达到甚至部分优于GRACE官方数据移植精度，可初步应用于重力场反演，实现低低跟踪任务加速度计高精度数据产品恢复。-
关键词:
- 激光干涉测距重力卫星 /
- 低低跟踪 /
- 机器学习 /
- 数据处理
Abstract:As a follow-on mission to the GRACE low-low satellite-to-satellite tracking gravity mission, one of the twin satellites of laser ranging interferometer gravity mission GRACE Follow-On experienced an anomaly in its accelerometer payload after one month of operation. This anomaly resulted in the loss of scientific measurement data, a situation similar to the final phase of the GRACE. Therefore, research on accelerometer data recovery is important to achieve the detection objectives of both GRACE and GRACE Follow-On. This paper proposes a novel method for accelerometer data recovery and reconstruction based on the Echo State Network in machine learning. By constructing a mapping relationship of accelerometer data between the twin satellites using the Echo State Network and improving the network performance through Bayesian optimization, this method can achieve high-precision and high-efficiency reconstruction of missing accelerometer data. Through experimental comparison with measured data, in the frequency band of gravity field detection, the prediction results in the along-track and radial directions have been shown to reach the level of
$ {10}^{-8} $ m∙s−2/$ \sqrt{H\textit{z}} $ . In the cross-track direction, the results reach levels between$ {10}^{-8}$ m∙s−2/$ \sqrt{H\textit{z}} $ ~${10}^{-7} $ m∙s−2/$\sqrt{H\textit{z}} $ . This reconstruction accuracy is comparable to, or even partially superior to, the official GRACE data transplant accuracy, making it preliminarily applicable to gravity field inversion. This research achieves high-precision accelerometer data recovery for low-low satellite-to-satellite tracking missions using machine learning methods. -
图 2 回声状态网络加速度计数据预测流程图
Figure 2. Flowchart of accelerometer data prediction by echo state network
图 4 回声状态网络模型数据预测总体结果。（a）沿轨道方向；（b）轨道法线方向；（c）沿轨道径向
Figure 4. Prediction results of ESN Model data. (a) Along orbit direction; (b) along orbit plane normal direction; (c) along orbit radial direction
图 5 模型预测三轴方向具体结果。（a）沿轨道方向；（b）轨道法方向；（c）沿轨道径向
Figure 5. Detailed results along the three axes. (a) Along orbit direction; (b) along orbit plane normal direction; (c) along orbit radial direction
图 6 GRACE任务加速度计预测结果残差振幅谱密度。（a）沿轨道方向；（b）轨道法方向；（c）沿轨道径向
Figure 6. Amplitude spectral density of residual acceleration for GRACE mission. (a) Along orbit direction; (b) along orbit plane normal direction; (c) along orbit radial direction
图 7 GFO任务加速度预测结果残差振幅谱密度。（a）沿轨道方向；（b）轨道法方向；（c）径向
Figure 7. Amplitude spectral density of residual acceleration for GFO mission. (a) Along orbit direction; (b) along orbit plane normal direction; (c) along orbit radial direction
表 1 回声状态网络训练数据来源
Table 1. Training data source
文件名 数据标识 数据描述 ACC1B lin_accl_x、lin_accl_y、lin_accl_z 线性加速度 GNV1B xpos、ypos、zpos GPS坐标 SCA1B quatangle、quaticoeff、quatjcoeff、quatkcoeff 四元数 
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表 2 回声状态网络超参数设定
Table 2. Hyperparameter settings of ESN
超参数名称 参数范围 设定值 储层神经元个数 [150, 500] 347 谱半径 [0.5, 1.6] 0.95 输入缩放因子 [0.1, 0.5] 0.25 泄露率 [0.05, 0.6] 0.30
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