An enhanced singular spectrum analysis method for constructing nonsecular model of GPS site movement

Abstract

Abstract Many GPS time series contain offsets, sometimes nonsecular trends, and seasonal signals with time‐varying amplitudes due to several different types of geophysical phenomena. Therefore, the use of nonsecular models to depict the real geophysical movement of GPS sites is better than a linear model. In this study, an enhanced singular spectrum analysis (SSA) method for fitting GPS time series and predicting its coordinates is proposed. Simulation results show that the root‐mean‐square (RMS) of differences between the reconstructed and simulated signals is 1.7 mm; the RMS of the differences between the predicted coordinates and simulated signal is about 3 mm for the first half 1.5 years of testing period and decreases to 10 mm for the last half 1.5 years. Fitting results for three GPS time series are obtained using maximum likelihood estimation (MLE), which is used to fit the time series with a piecewise linear trend plus an annual/semiannual components, SSA, and state space model (SSM). Both SSA and SSM perform similarly and better than the MLE in extracting the nonsecular trend and annual/semiannual components from the GPS time series. The prediction results from SSA have higher coefficients with raw time series and lower power of annual/semiannual in their residuals than that from MLE for two case studies. The differences between the linear trend estimated by Plate Boundary Observatory and SSA nonsecular model for 16 GPS time series are all larger than 2 mm in up direction, which is not negligible for a high‐accuracy terrestrial reference frame construction.