基于变分模态分解的GNSS高程时间序列时变信号提取

Extraction of time-varying signals from GNSS height time series by variational mode decomposition

针对GNSS坐标时间序列中的时变信号难以由现有最小二乘、最大似然估计(MLE)等参数化方法准确提取的问题,本文采用变分模态分解(VMD)方法将中国内地构造环境监测网络(CMONOC)测站的高程时间序列分解为一系列本征模态函数(IMF),进而重构出测站位置时间序列中含有的时变信号。结果表明,相对于MLE方法,VMD方法在97.9%的测站上均方根误差(RMSE)改进率为正值,因此该方法有助于绝大多数测站精确提取出时变信号,减弱高程时间序列中的非线性形变。另外,从相关系数和信噪比的角度来看,VMD方法得到的重构序列与原始序列之间的相关系数更高,信噪比也更大,表明降噪效果较好。通过特定测站的分析表明,VMD方法能有效探测出GNSS高程时间序列预处理中包含遗漏的阶跃信号的测站,表现为较大的RMSE改进率,这在大批量测站的阶跃信号探测中具有一定的实用价值。VMD方法相对于小波分解(WD)经验模态分解(EMD)具有更好的自适应性,但IMF分量个数仍然需要针对具体测站进行逐一确定,当分解个数和重构分量选取恰当时,VMD方法在GNSS高程时间序列中的应用效果可进一步提高。

To solve the problem that the time-varying signals in GNSS coordinate time series are difficult to be accurately extracted by the existing parametric methods,such as least square fitting and maximum likelihood estimation(MLE),this paper adopts the variational mode decomposition(VMD)method to decompose the height time series at stations of the Crustal Movement Observation Network of China(CMOMOC)into a series of intrinsic mode functions(IMF),and then reconstruct the time-varying signals contained in stations’position.The results show that the root mean square error(RMSE)improvement rates of VMD method are positive in 97.9%of CMONOC stations compared with MLE method,indicating that VMD method is helpful to extract time-varying signals from most stations and reduce the nonlinear deformation in GNSS height time series.In addition,from the perspective of correlation coefficient and signal-to-noise ratio,the reconstructed series derived from VMD method obtains higher correlation coefficients with the original series than the fitting series,and the reconstructed series also has a stronger signal-to-noise ratio.The analysis of some specific stations shows that the VMD method can effectively detect the stations with missing offsets in the preprocessing of the original GNSS coordinate time series,which presents a large RMSE improvement rate.It proves that the VMD method has a certain practical value in the offset detection of a large number of stations.Compared with wavelet decomposition(WD)and empirical mode decomposition(EMD),VMD method has better self-adaptability,but the number of its IMF components still needs to be determined one by one for specific stations.When the numbers of decomposition and reconstructed components are carefully selected,the application effect of VMD method in GNSS height time series can be further improved.