Accuracy Enhancement and Feature Extraction for GNSS Daily Time Series Using Adaptive CEEMD-Multi-PCA-Based Filter

Global navigation satellite system (GNSS) positions include various useful signals and some unmodeled errors. In order to enhance the accuracy and extract the features of the GNSS daily time sequence, an improved method of complete ensemble empirical mode decomposition (CEEMD) and multi-PCA (MPCA) based on correlation coefficients and block spatial filtering was proposed. The results showed that the mean standard deviations of the raw residual time sequence were 1.09, 1.20 and 4.79 mm, while those of the newly proposed method were 0.15, 0.20 and 2.86 mm in north, east and up directions, respectively. The proposed method outperforms wavelet decomposition (WD)-PCA and empirical mode decomposition (EMD)-PCA in effectively eliminating low- and high-frequency noise, and is suitable for denoising nonlinear and nonstationary GNSS position sequences. Furthermore, feature extraction of the denoised GNSS daily time series was based on CEEMD, which is superior to WD and EMD. Results of noise analysis suggested that the noise components in the original and denoised GNSS time sequence are complex. The advantages of the proposed method are the following: (i) it fully exploits the merits of CEEMD and WD, where CEEMD is first used to obtain the limited intrinsic modal functions (IMFs) and then to extract seasonal and trend features; (ii) it has good adaptive processing ability via WD for noise-dominant IMFs; and (iii) it fully considers the correlation between the different components of each station and the non-uniform behavior of common mode error on a spatial scale.