An efficient improved singular spectrum analysis for processing GNSS position time series with missing data

Abstract

Summary The improved SSA (ISSA) method is widely recognized for directly extracting signals from gappy time series without requiring prior interpolation. However, it is rather time consuming, particularly for long time series with large window sizes, such as Global Navigation Satellite System (GNSS) position time series. This study proposes an efficient ISSA method that yields equivalent results to the ISSA method while significantly reducing computation time. Both methods aim to minimize the quadratic norm of principal components, while our method has fewer unknown parameters in the principal component computation than those of the ISSA method. We evaluate the performance of the proposed method using real GNSS position time series from 27 permanent stations located in mainland China. Results show that the proposed method can effectively reduce computation time than the ISSA method and the improvement depends on the chosen window size, the time series length, and the percentage of missing data. This efficient approach can be naturally extended to principal component analysis (PCA) and multi-channel SSA (MSSA) for processing multiple incomplete time series, improving computational efficiencies compared to the modified PCA and the improved MSSA while maintaining unchanged results. We also compare the ISSA method with the modified SSA (SSAM) and the iterative SSA methods using both real and synthetic time series data. Results indicate that the ISSA method outperforms the SSAM method, and when conducted iteratively, also surpasses the iterative SSA method.