An L1 norm regularization model for signal extraction from GNSS coordinate time series

Accurate signal extraction from Global Navigation Satellite System (GNSS) coordinate time series is crucial for geophysical studies. Primary focus of this paper lies in the recovery of trend and seasonal signals from observed GNSS coordinate time series. To achieve this, this paper presents a novel Modified L1-norm Regularization Rank-1 Matrix Completion (ML1MC) method, ML1MC leverages the low-rank property of Hankel matrices and incorporates automatic rank estimation and Block Coordinate Descent (BCD) to effectively handle noise and avoid overfitting, which provides a more comprehensive rank-1 matrix representation than Singular Value Decomposition (SVD) based low-rank matrix recovery methods. Extensive experiments on simulated and real GNSS datasets demonstrate ML1MC's superior performance in comparison to several State-Of-The-Art (SOTA) methods. Specifically, compared to the SOTA methods, ML1MC achieves over 7.8\% misfit reduction and reduces trend uncertainty error by more than 45.9\% under normal noise conditions.