Extracting Seasonal Signal in GNSS Position Time Series via Nuclear Norm Minimization

Abstract:

Global Navigation Satellite System (GNSS) position time series usually show obvious seasonal signals, which may be caused by seasonal temperature changes, surface mass loading, GNSS system errors etc. Accurately detection and extraction of seasonal signals is not only conducive to improving the estimation accuracy of velocity and its uncertainty, but is also helpful to reasonably explaining various geophysical phenomena. In addressing this issue, a novel detection scheme exploiting the low-rank characteristics of Hankel matrix constructed by the GNSS time series has been proposed in this paper. Seasonal signals in the GNSS time series are modeled by a superposition of the annual and semi-annual sinusoids. The nuclear norm minimization is applied in this study to investigate the possibility of extracting seasonal signals from GNSS position time series. To circumvent this problem, the low-rank characteristic of the Hankel matrix induced by GNSS time series was investigated first. And then, the NNM method was used to extract seasonal signals from the GNSS coordinate time series under different noise models and noise levels. NNM is an optimization task with constraints that can be constructed for recovering low rank matrix X from the noisy data matrix Y. In the optimization task, we minimize the l2 norm of Y-X and the nuclear norm of X, which can be reformulated as a convex optimization problem and can be solved by off-the-art convex optimization toolkit. Finally, the residual was analyzed, and the corresponding parameters, including trend uncertainty, noise amplitude and spectral indices, were calculated. Extensive experiments are carried out on both synthetic data and real GNSS time series to demonstrate the effectiveness of the proposed method. The results are compared to those of other conventional methods such as Moving Ordinary Least Squares (MOLS), Wavelet Decomposition (WD), and Singular Spectrum Analysis (SSA). All the elicited results indicated that the NNM has certain advantages and can be employed as an effective way to detect the seasonal signals.