COA–VMPE–WD: A Novel Dual-Denoising Method for GPS Time Series Based on Permutation Entropy Constraint

To address the challenge of effectively filtering out noise components in GPS coordinate time series, we propose a denoising method based on parameter-optimized variational mode decomposition (VMD). The method combines permutation entropy with mutual information as the fitness function and uses the crayfish (COA) algorithm to adaptively obtain the optimal parameter combination of the number of modal decompositions and quadratic penalty factors for VMD, and then, sample entropy is used to identify effective mode components (IMF), which are reconstructed into denoised signals to achieve effective separation of signal and noise The experiments were conducted using simulated signals and 52 GPS station data from CMONOC to compare and analyze the COA–VMPE–WD method with wavelet denoising (WD), empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) methods. The result shows that the COA–VMPE–WD method can effectively remove noise from GNSS coordinate time series and preserve the original features of the signal, with the most significant effect on the U component. The COA–VMPE–WD method reduced station velocity by an average of 50.00%, 59.09%, 18.18%, and 64.00% compared to the WD, EMD, EEMD, and CEEMDAN methods. The noise reduction effect is higher than the other four methods, providing reliable data for subsequent analysis and processing.