Accuracy Enhancement and Feature Extraction for GNSS Daily Time Series Using Adaptive CEEMD-Multi-PCA-Based Filter
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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.In order to overcome the shortcoming of Principal Component Analysis(PCA) in feature extraction and dimension reduction,a method for extracting Gabor features of face images based on Gabor wavelet was presented.First,Gabor feature vectors were extracted from face images.After reduced by two-dimensioned PCA(2DPCA) algorithm,the features were reduced further by rough set.Then the nearest classifier was trained for classification.The experiments on AR human face image database show the presented method is superior to biomimetic pattern recgonition method and PCA algorithm.
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Empirical Mode Decomposition (EMD) is suitable to process the nonlinear and non-stationary time series for filtering noise out to extract the signals. The formal errors are provided along with Global Navigation Satellite System (GNSS) position time series, however, not being considered by the traditional EMD. In this contribution, we proposed a modified approach that called weighted Empirical Mode Decomposition (weighted EMD) to extract signals from GNSS position time series, by constructing the weight factors based on the formal errors. The position time series over the period from 2011 to 2018 of six permanent stations (SCBZ, SCJU, SCMN, HLFY, FJPT, SNXY) were analyzed by weighted EMD, as well as the traditional EMD. The results show that weighted EMD can extract more signals than traditional EMD from original GNSS position time series. Additionally, the fitting errors were reduced 14.52 %, 12.25 % and 8.06 % for North, East and Up components for weighted EMD relative to traditional EMD, respectively. Moreover, 100 simulations of four stations are further carried out to validate the performances of weighted EMD and traditional EMD. The mean Root Mean Squared Errors (RMSEs) are reduced from traditional EMD to weighted EMD with the reductions of 9.08 %, 9.63 % and 6.84 % for East, North and Up components, respectively, which highlights the necessity of considering the formal errors. Therefore, it reasonable to conclude that weighted EMD can extract the signals more than traditional EMD, which can be suggested to analyze GNSS position time series with formal errors.
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