Objectives In order to effectively filter out complex noise components in GNSS coordinate time series and extract effective signals, we construct a denoising method based on parameter-optimized variational modal decomposition (VMD).

Methods First, the combination of permutation entropy and mutual information is used as fitness function, and the optimal parameter combination of the mode decomposition number $K$ and the quadratic penalty factor $\alpha$ of VMD is obtained by using grey wolf optimization algorithm(GWO). Then the GNSS coordinate time series is decomposed into $K$ eigen mode function components by VMD. Finally, the sample entropy is used to determine the effective modal component, which is reconstructed as an effective signal, so as to realize the effective separation of signal and noise.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 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 GWO-VMD 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, which can provide reliable data for subsequent analysis and processing.