A truncated reweighting nuclear norm regularization model for signal extraction from GNSS coordinate time series

A B S T R A C T Extracting seasonal signals accurately from Global Navigation Satellite System (GNSS) coordinate time series is essential for investigating geophysical processes such as crustal deformation and plate motion. The coexistence of time-varying periodic signals and colored noise with fluctuating amplitudes significantly complicates this task, rendering flexible and robust methods imperative. Leveraging the low-rank property of the Hankel matrix constructed from noise-free signals, this paper proposes a Truncated Reweighted Nuclear Norm Minimization (TRNM) method for reconstructing GNSS coordinate time series. TRNM integrates truncation and reweighting strategies to better approximate the rank of the original matrix, and employs a modified Accelerated Proximal Gradient (APG) technique incorporating an adaptive momentum updating criterion and Reweighting Singular Value Thresholding (RSVT) to reduce computational cost induced by full SVD. Simulation experiments and real data analysis are conducted by comparing TRNM with five State Of The Art (SOTA) methods. It is observed that TRNM performs as well as the SOTA methods for low noise level condition while outperforms the compared methods for high noise level condition with respect to residual spectral index, residual amplitude, Trend Uncertainty (TU), and misfit. Moreover, TRNM demonstrates the minimal deviation of TU from theoretical values across all evaluation metrics for missing rates ranging from 0.1 to 0.5 or data length increasing from 1000 to 6000 days, while keeping nearly the smallest misfit value, without requiring data interpolation. Finally, real GNSS time series experiments show that the residual analysis results are consistent with those obtained by simulation experiments, and TRNM exhibits robustness against noise with varying levels. Therefore, this paper proposes a competitive and robust method for reconstructing GNSS coordinate time series.