基于FGSR的GPS坐标时间序列重构  

GPS Coordinate Time Series Reconstruction Based on FGSR

作　　者：周杨 陈刚 边家文[1] Zhou Yang;Chen Gang;Bian Jiawen(School of Mathematics and Physics,China University of Geosciences,Wuhan Hubei 430074,China;College of Marine Science and Technology,China University of Geosciences,Wuhan Hubei 430074,China)

机构地区：[1]中国地质大学(武汉)数学与物理学院,湖北武汉430074 [2]中国地质大学(武汉)海洋学院,湖北武汉430074

出　　处：《工程地球物理学报》2025年第2期285-295,共11页Chinese Journal of Engineering Geophysics

基　　金：国家自然科学基金(编号:42274012)。

摘　　要：全球定位系统(Global Positioning System,GPS)坐标时间序列被广泛应用于诸多领域,如地壳形变、地震、海啸预警和板块运动监测等。但是由于受到某些地球物理效应以及相关技术误差的影响,使得GPS坐标时间序列中不可避免地包含大量噪声及缺失数据,因此精确地重构GPS坐标时间序列具有重要意义。针对该问题,本文利用低秩矩阵补全的方法对由观测的GPS坐标时间序列构造的Hankel矩阵进行矩阵补全。由于秩函数的估计和求解是NP(Non-deterministic Polynomial,NP)难问题,本文用因子组稀疏正则化(Factor Group-Sparse Regularization,FGSR)替代秩函数的估计。相对于加权核范数最小化(Weighted Nuclear Norm Minimization,WNNM)用核范数来替代秩函数,FGSR能避免在每次迭代时进行奇异值分解(Single Value Decomposition,SVD),节省计算成本。尤其是在重构较大规模的矩阵时FGSR的用时,比WNNM快了3~4倍。通过模拟数据实验,本文将FGSR方法与小波分解方法(Wavelet Decomposition,WD)、奇异谱分析方法(Singular Spectrum Analysis,SSA)、滑动最小二乘方法(Moving Ordinary Least Squares,MOLS)、WNNM和Hankel矩阵补全(Hankel Matrix Completion,HMC)进行比较。实验结果表明,FGSR可以更加有效地重构GPS坐标时间序列:在低噪声情况下,FGSR的Misift比所比较方法小2%~3%;在高噪声情况下,FGSR的Misift比所比较方法小0.8%~17%;此外,FGSR分离出的噪声与加入的噪声在谱指数、振幅以及速度不确定度都是最接近的。Global positioning system(GPS)coordinate time series are widely used in many fields,such as crustal deformation,earthquake and tsunami early warning,and plate motion monitoring.However,due to certain geophysical effects and related technical errors,GPS coordinate time series inevitably contain a large amount of noise and missing data.Therefore,accurately reconstructing GPS coordinate time series is of great significance.To address this problem,this paper uses the low-rank matrix completion method to complete the Hankel matrix constructed from the observed GPS coordinate time series.Since the estimation and solution of the rank function is an NP(non-deterministic polynomial)-hard problem,this paper replaces the estimation of the rank function with factor group-sparse regularization(FGSR).Compared with weighted nuclear norm minimization(WNNM),which uses the nuclear norm to replace the rank function,FGSR can avoid performing singular value decomposition(SVD)in each iteration,saving computational cost.Especially when reconstructing large-scale matrices,FGSR is 3 to 4 times faster than WNNM.Through experiments with simulated data,this paper compares the FGSR method with the Wavelet decomposition(WD)method,the singular spectrum analysis(SSA)method,the moving ordinary least squares(MOLS)method,WNNM,and the Hankel matrix completion(HMC).The experimental results show that FGSR can reconstruct GPS coordinate time series more effectively.In the case of low noise amplitude,the Misift of FGSR is 2%to 3%smaller than that of the other compared methods;in the case of high noise amplitude,the Misift of FGSR is 0.8%to 17%smaller than that of the other compared methods.In addition,the noise separated by FGSR is the closest to the added noise in terms of spectral index,amplitude,and velocity uncertainty.

关 键 词：GPS时间序列 信号重构 FGSR 低秩 

分 类 号：P228[天文地球—大地测量学与测量工程]