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

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. © 2024 SinoMaps Press. All rights reserved.