Missing Telemetry Data Prediction Algorithm via Tensor Factorization
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摘要:
卫星健康状况监测是卫星安全保障的重要基础，而卫星遥测数据又是卫星健康状况分析的唯一数据来源。因此，卫星遥测缺失数据的准确预测是卫星健康分析的重要前瞻性手段。针对极轨卫星多组成系统、多仪器载荷以及多监测指标形成的高维数据特点，该文提出一种基于张量分解的卫星遥测缺失数据预测算法(TFP)，以解决当前数据预测方法大多面向低维数据或只能针对特定维度的不足。所提算法将遥测数据中的系统、载荷、指标以及时间等多维因素作为统一的整体进行张量建模，以完整、准确地表达数据的高维特征；其次，通过张量分解计算数据模型的成分特征，通过成分特征可对张量模型进行准确重构，并在重构过程中对缺失数据进行准确预测；最后，提出一种高效的优化算法实现相关的张量计算，并对算法中最优参数设置进行严格的理论推导。实验结果表明，所提算法的预测准确度优于当前大部分预测算法。
Abstract:Satellite health monitoring is an important concern for satellite security, for which satellite telemetry data is the only source of data. Therefore, accurate prediction of missing data of satellite telemetry is an important forward-looking approach for satellite health diagnosis. For the high-dimensional structure formed by the satellite multi-component system, multi-instrument and multi-monitoring index, the Tensor Factorization based Prediction (TFP) algorithm for missing telemetry data is proposed. The proposed algorithm surpasses most existing methods, which can only be applied to low-dimensional data or specific dimension. The proposed algorithm makes accurate predictions by modeling the telemetry data as a Tensor to integrally utilize its high-dimensional feature; Computing the component matrixes via Tensor Factorization to reconstruct the Tensor which gives the predictions of the missing data; An efficient optimization algorithm is proposed to implement the related tensor calculations, for which the optimal parameter settings are strictly theoretically deduced. Experiments show that the proposed algorithm has better prediction accuracy than the most existing algorithms.
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Key words:
- Satellite /
- Telemetry data /
- Missing data prediction /
- Tensor factorization
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算法1：TFP算法 输入：数据集$ {\cal X}\in {{\mathbb{R}}^{{{I}_{1}}\times {{I}_{2}}\times \cdots \times {{I}_{N}}}}$； 输出：训练后的成分矩阵$ {{ A}^{\left(j \right)}}$ (j=1 to N) 随机初始化成分矩阵$ {{ A}^{\left( j \right)}}$(j=1 to N) Repeat For each $ { A}_{{i_j}r}^{\left( j \right)}\left( {1 \le j \le N,1 \le {i_j} \le {I_j},1 \le r \le R} \right)$ If $ g_{{i_j}r}^{\left( j \right)}{|_t} \cdot g_{{i_j}r}^{\left( j \right)}{|_{t - 1}} > 0$ $ \delta _{ {i_j}r}^{\left( j \right)}{|_t} = {\rm{min} }\left( {\delta _{ {i_j}r}^{\left( j \right)}{|_{t - 1} } \cdot {\eta ^ + },{\rm{MaxSize}}} \right)$ $ { A}_{{i_j}r}^{\left( j \right)}{|_{t + 1}} = { A}_{{i_j}r}^{\left( j \right)}{|_t} - {\rm{sign}}\left( {g_{{i_j}r}^{\left( j \right)}{|_t}} \right) \cdot \delta _{{i_j}r}^{\left( j \right)}{|_t}$ Else If $ g_{{i_j}r}^{\left( j \right)} \cdot g_{{i_j}r}^{\left( j \right)}{\rm{'}} < 0$ $ \delta _{ {i_j}r}^{\left( j \right)}{|_t} = {\rm{max} }\left( {\delta _{ {i_j}r}^{\left( j \right)}{|_{t - 1} } \cdot {\eta ^ - },{\rm {MinSize}}} \right)$ If $ L{|_t} > L{|_{t - 1}}$ $ { A}_{{i_j}r}^{\left( j \right)}{|_{t + 1}} = { A}_{{i_j}r}^{\left( j \right)}{|_t} + {\rm{sign}}\left( {g_{{i_j}r}^{\left( j \right)}{|_{t - 1}}} \right) \cdot \delta _{{i_j}r}^{\left( j \right)}{|_{t - 1}}$ $ L{|_t} = 0$ End If Else $ \delta _{{i_j}r}^{\left( j \right)}{|_t} = \delta _{{i_j}r}^{\left( j \right)}{|_{t - 1}}$ $ { A}_{{i_j}r}^{\left( j \right)}{|_{t + 1}} = { A}_{{i_j}r}^{\left( j \right)}{|_t} - {\rm{sign}}\left( {g_{{i_j}r}^{\left( j \right)}{|_t}} \right) \cdot \delta _{{i_j}r}^{\left( j \right)}{|_t}$ End If End For Until $ L \le \varepsilon $ or maximum iterations exhausted 
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表 1 TFP算法与其它5个方法的对比
方法 数据密度5% 数据密度10% 数据密度20% 数据密度50% MAE RMSE MAE RMSE MAE RMSE MAE RMSE NMF 0.6175 1.5789 0.6007 1.5485 0.5986 1.5233 0.4870 1.4847 PMF 0.5687 1.4792 0.4984 1.2842 0.4492 1.1855 0.4006 1.0820 UPCC 0.6204 1.4010 0.5513 1.3139 0.4875 1.2343 0.3114 1.0749 IPCC 0.6886 1.4278 0.5908 1.3245 0.4454 1.2094 0.2895 1.1724 TA 0.6239 1.4058 0.5360 1.3045 0.4496 1.2030 0.2106 1.0988 TFP 0.3815 0.9469 0.3073 0.7597 0.2270 0.5619 0.1235 0.3150
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