Extended singular spectrum analysis for processing incomplete heterogeneous geodetic time series

The singular spectrum analysis (SSA) is a powerful tool to de-noise the geodetic time series and extract geophysical signals of interest. However, when missing data exists in geodetic time series, the ordinary SSA cannot be directly used to process them. Moreover, the heterogeneous properties of the geodetic time series are usually not considered in ordinary SSA, though their formal errors are provided beforehand. In this contribution, we develop an extended singular spectrum analysis (ESSA) to directly process the incomplete and heterogeneous geodetic time series. To validate the proposed approach, we select the 27 vertical position time series of GNSS permanent stations located in the Chinese mainland for analysis, and the results are compared with that of the improved SSA (ISSA, Shen et al. in Nonlinear Process Geophys 22(4):371-376, 2015) which is an effective approach for analyzing the time series with missing data. The results show that (i) our ESSA method performs faster than ISSA, with mean reductions in computation time by 40.14% for 27 stations; moreover, the time consumption of ISSA is more sensitive to the window size and the length of observations than that of ESSA; (ii) the ESSA method can extract more signals than ISSA in terms of fitting errors and root-mean-square ratios of extracted signals over residuals, specifically for the consideration of formal errors. The power spectrum analysis shows that the power of annual oscillation extracted by ESSA is stronger than that by ISSA; (iii) the repeated simulations based on the real data further demonstrate that the signals extracted by ESSA are closer to the true signals than ISSA, and the accuracy improvement is portal to the percentage of data missing.