An enhanced singular spectrum analysis method for constructing non-linear model of GPS site movement

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