宋晓祥,,
李宁,
钱鹏
陆军工程大学通信工程学院 ??南京 ??210007
基金项目:国家自然科学基金(61571463, 61371124, 61472445)；江苏省自然科学基金(BK20171401)
详细信息
作者简介:郭艳：女，1971年生，教授，研究方向为大数据、信号处理、压缩感知
宋晓祥：男，1993年生，硕士生，研究方向为大数据、压缩感知
李宁：男，1967年生，副教授，研究方向为信号处理、认知无线电
钱鹏：男，1991年生，博士生，研究方向为压缩感知、无源目标定位
通讯作者:宋晓祥 guoyan_1029@sina.com
中图分类号:TN911.7计量
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被引次数:0
出版历程
收稿日期:2018-06-01
修回日期:2018-10-29
网络出版日期:2018-11-19
刊出日期:2019-04-01
Missing Data Prediction Based on Kronecker Compressing Sensing in Multivariable Time Series
Yan GUO,Xiaoxiang SONG,,
Ning LI,
Peng QIAN
Institute of Communications Engineering, Army Engineering University, Nanjing 210007, China
Funds:The National Natural Science Foundation of China (61571463, 61371124, 61472445), The Jiangsu Province Natural Science Foundation (BK20171401)
摘要
摘要:针对现有算法在预测多变量时间序列中的缺失数据时不适用或只适用于缺失数据较少的情况，该文提出一种基于克罗内克压缩感知的缺失数据预测算法。首先，利用多变量时间序列的时域平滑特性和序列之间的潜在相关性从时空两个方面设计了稀疏表示基，从而将缺失数据预测问题建模成稀疏向量恢复问题。模型求解部分，根据缺失数据的位置特点设计了适合当前应用场景且与稀疏表示基相关性低的观测矩阵。接着，从稀疏表示向量是否足够稀疏和感知矩阵是否满足有限等距特性两个方面验证了模型的性能。最后，仿真结果表明，所提算法在数据缺失严重的情况下具有良好的性能。
关键词:多变量时间序列/
缺失数据/
克罗内克压缩感知/
时域平滑特性/
潜在相关性
Abstract:In view of the problem that the existing methods are not applicable or are only feasible to the case where only a low ratio of data are missing in multivariable time series, a missing data prediction algorithm is proposed based on Kronecker Compressed Sensing (KCS) theory. Firstly, the sparse representation basis is designed to largely utilize both the temporal smoothness characteristic of time series and potential correlation between multiple time series. In this way, the missing data prediction problem is modeled into the problem of sparse vector recovery. In the solution part of the model, according to the location of missing data, the measurement matrix is designed suitable for the current application scenario and low correlation with the sparse representation basis. Then, the validity of the model is verified from two aspects: Whether the sparse representation vector is sufficiently sparse and the sensing matrix satisfies the restricted isometry property. Simulation results show that the proposed algorithm has good performance in the case where a high ratio of data are missing.
Key words:Multivariable time series/
Missing data/
Kronecker Compressing Sensing (KCS)/
Temporal smoothness characteristic/
Potential correlation
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