Abstract
Global Navigation Satellite System (GNSS) coordinate time series contains obvious seasonal signals, which mainly manifest as a superposition of annual and semi-annual oscillations. Accurate extraction of seasonal signals is of great importance for understanding various geophysical phenomena. In this paper, a Weighted Nuclear Norm Minimization (WNNM) is proposed to extract the seasonal signals from the GNSS coordinate time series. WNNM assigns different weights to different singular values that enable us to estimate an approximate low rank matrix from its noisy matrix. To address this issue, the low rank characteristics of the Hankel matrix induced by GNSS coordinate time series was investigated first, and then the WNNM is applied to extract the seasonal signals in the GNSS coordinate time series. Meanwhile, the residuals have been analyzed, obtaining the estimation of the uncertainty of velocity. To demonstrate the effectiveness of the proposed algorithm, a number of tests have been carried out on both simulated and real GNSS dataset. Experimental results indicate that the proposed scheme offers preferable performances compared with many state-of-the-art methods.
Highlights
Global Navigation Satellite System (GNSS) coordinate time series often appear in many geophysical and geodetic applications
Weighted Nuclear Norm Minimization (WNNM) is the most gentle, followed by moving ordinary least squares (MOLS) and singular spectral analysis (SSA), which indicate that WNNM can achieve a better performance in extracting signals
The time series extracted by applying MOLS, wavelet decomposition (WD), SSA and WNNM are shown in Figure 9a–c, respectively, and the observed GNSS time series is illustrated for comparison
Summary
Global Navigation Satellite System (GNSS) coordinate time series often appear in many geophysical and geodetic applications. The common method for devising a linear model is least-squares (LS) fitting [14], LS lacks random changes in the estimation of signals, and only seasonal signals with constant amplitude can be obtained [3], which is not consistent with the true seasonal variations It has been suggested in several other studies to extract the periodic signals by data-driven methods, such as wavelet decomposition (WD) [13] and singular spectral analysis (SSA) [11,16,20]. To differentiate these seasonal components in GNSS coordinate time series, the WNNM is applied in this study to investigate the possibility of extracting seasonal signals from GNSS coordinate time series To circumvent this problem, the low-rank characteristics of the Hankel matrix induced by GNSS coordinate time series was investigated. The WNNM method was utilized to extract signals from the GNSS coordinate time series under different noise models and noise levels, and the results are compared with several state-of-the-art methods.
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