Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

Abstract

The daily position time series derived by Global Navigation Satellite System (GNSS) contain nonlinear signals which are suitably extracted by using wavelet analysis. Considering formal errors are also provided in daily GNSS solutions, a weighted wavelet analysis is proposed in this contribution where the weight factors are constructed via the formal errors. The proposed approach is applied to process the position time series of 27 permanent stations from the Crustal Movement Observation Network of China (CMONOC), compared to traditional wavelet analysis. The results show that the proposed approach can extract more exact signals than traditional wavelet analysis, with the average error reductions are 13.24%, 13.53% and 9.35% in north, east and up coordinate components, respectively. The results from 500 simulations indicate that the signals extracted by proposed approach are closer to true signals than the traditional wavelet analysis.Remote Sens. 2020, 12, 992 2 of 16 filter (AWF) [28]. Wavelet analysis (WA) is one of the data-driven approaches to analyzing the non-linear time series. It was initially proposed by Morlet et al. [29,30] to analyze the seismic signals in geophysics and was popularized by Grossmann and Morlet [31] and Goupillaud et al. [32]. Nowadays, WA becomes a new mathematical approach and is widely applied in geodesy and geophysics [33,34], remote sensing [35,36] and hydrology [37,38]. Unlike the Fourier transform (FT) [39] which maps a time series from time domain to frequency domain, the wavelet transform (WT) can simultaneously describe the time-frequency characteristics of a time series, which is one of the most important properties of the wavelets [40]. As a time-frequency analysis method, the WT can decompose the time series into different components according to frequency, and then map the decomposed components at different scales to obtain the information of time series at different resolutions, which is named as multiresolution analysis (MRA) [41]. Due to its superior performance on signal processing, it has also been employed to analyze the GNSS position time series. For preprocessing of GNSS position time series, Wu et al. [42] proposed an improved 3σ method of outlier detection based on WA. Borghi et al. [43] introduced WT to detect discontinuity in GNSS position time series. For noise analysis, Kaczmarek and Kontny [44] identified the noise model using WA and demonstrated that the nature of noise did not depend on the method of modeling the time series. Wu et al. [45] proposed a wavelet-based hybrid approach to remove white noise and flicker noise originating from GNSS position time series. Li et al. [46] introduced a WT-based multiscale multiway principle component analysis (MSMPCA) to eliminate noise in high-rate GNSS data including high-frequency random noise, low-frequency errors and common mode error (CME). For signal analysis, Kaczmarek and Kontny [17] applied wavelet power spectrum analysis to position time series and found that annual signal is more significant than other pe...

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