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Global positioning system (GPS) coordinate time series shows obvious seasonal oscillation, especially in the vertical direction. In order to separate tectonic movement from the other signals accurately and obtain reliable long-term movement trend, it is necessary to obtain accurate seasonal signal estimation. In this paper, seasonal signals in the GPS time series are modelled by time-varying sinusoidals, and the Atomic Norm Minimization (ANM) is used to extract the seasonal signals. To verify the efficiency of the proposed algorithm, a set of experiments is carried out on both the synthetic dataset and real GPS time series. The results of ANM are compared with the state-of-the-art methods under different noise levels. All the elicited results indicated that the ANM has certain advantages and can be used as an effective alternative way to extract the seasonal signals.

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.