Abstract
Coordinate time series determined using the global positioning system (GPS) contain annual and semiannual periods that are routinely modeled by periodic signals with time-varying amplitudes. The accurate extraction of seasonal signals is of great importance to improve the accuracy of the velocity and understand various geophysical phenomena. However, when the amplitude of noise is larger than or close to those of seasonal signals, fully extracting the seasonal signals is difficult. It is necessary to develop new characteristics by which the seasonal signal can be distinguished from the noise. In this study, a low-rank Hankel matrix completion (HMC) method is proposed to extract the noise-free GPS coordinate time series. Specifically, a Hankel matrix induced by the observed GPS time series is constructed and proved to be low-rank; subsequently, singular value decomposition and singular value curvature spectrum (SVCS) are applied on the Hankel matrix to recover the low-rank part, namely, the trend and seasonal signals of the Hankel matrix from the observations. Notably, HMC utilizes the differences in the rank of the Hankel matrix constructed by the trend and seasonal signals and those constructed by the noise, and the rank is approximated by the SVCS. Meanwhile, parameter estimation and residual analysis are conducted to evaluate the performance of reconstruction, including the amplitude, spectral index, and power spectral density of the residual. Finally, several tests are conducted on both simulated and real GPS datasets to verify the effectiveness of the proposed method. Experimental results indicate that the proposed method shows competitive performance compared with several state-of-the-art methods.
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Acknowledgements
The authors would like to thank the anonymous reviewers for their effort reviewing our paper and for their valuable suggestions and feedback. This work is supported by the National Natural Science Foundation of China (nos. 42274012 and 42374174). The authors would like to thank Francisco Javier Alonso Sanchez, University of Extremadura, Spain, for providing the SSA code, the SOPAC for providing the real GPS coordinate time series (http://sopacftp.ucsd.edu/pub/timeseries/) and data analysis tool supported by Hector (http://segal.ubi.pt/hector/).
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Gong, J., Chen, G., Bian, J. et al. Reconstruction of GPS Coordinate Time Series Based on Low-Rank Hankel Matrix Recovery. Math Geosci 56, 923–948 (2024). https://doi.org/10.1007/s11004-023-10117-2
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DOI: https://doi.org/10.1007/s11004-023-10117-2