GNSS Coordinate Time Series Denoising Method Based on Parameteroptimized Variational Mode Decomposition

  Objectives:   In order to effectively filter out complex noise components in GNSS coordinate time series and extract effective signals, this paper constructs a denoising method based on parameteroptimized variational modal decomposition (VMD).   Methods:   The method uses the permutation entropy combined with mutual information as the fitness function, and uses the gray wolf optimization (GWO) algorithm to adaptively obtain the optimal parameter combination of the number of mode decompositions K and the quadratic penalty factor α of VMD, decomposes the GNSS coordinate time series into K intrinsic mode function components, and uses the sample entropy to determine the effective mode components and reconstructs them into effective signals, so as to realize the effective separation of signal and noise. Finally, the GWO-VMD method is compared and analyzed with the empirical mode decomposition (EMD), wavelet denoising (WD) and IVMD methods by using the simulated signal and the measured data from 20 reference stations of the Crustal Movement Observation Network of China (CMONOC) for experiments.   Results:   The simulated signal experiments show that the three denoising evaluation indexes of root mean square error, correlation coefficient and signal-to-noise ratio of GWOVMD denoising signal are better than EMD, WD and IVMD methods. The experiments on the measured data show that the GWO-VMD method can reduce the amplitude of noise significantly; in terms of the velocity uncertainty of the reference station, the overall GWO-VMD method reduces the velocity uncertainty better than the EMD, WD and IVMD methods.   Conclusions:   the GWO-VMD method can more effectively remove the noise from GNSS coordinate time series and better preserve the original characteristics of the signal, providing reliable data for subsequent analysis and processing.