Extraction of Time-Varying Signals in GNSS and Geophysical Interpretation: Methods, Advances, and Challenges.

Precise signal extraction and geophysical interpretation of Global Navigation Satellite System (GNSS) coordinate time series constitute the core foundation for establishing the International Terrestrial Reference Frame (ITRF) and inverting surface mass redistribution. This paper reviews major advances in this field across four dimensions: model framework, signal characteristics, extraction methods, and geophysical mechanisms. Key findings include: (1) Maximum Likelihood Estimation (MLE) has become the recognized standard for linear trend extraction: by jointly estimating deformation parameters and the noise covariance, it corrects the up to 5-10-fold underestimation of velocity uncertainty that arises in conventional least-squares analyses when colored noise is present but a white-noise covariance is assumed; (2) in CMONOC benchmark tests reported by Wu et al., Variational Mode Decomposition (VMD) achieves an average 69.8% residual RMS reduction at 97.9% of stations-results that are promising but not yet independently replicated on other networks-while the self-supervised model GNSS-FM (currently an unreviewed preprint) represents an emerging intelligent analysis paradigm; (3) the combined effect of atmospheric, non-tidal ocean and hydrological loading explains about 42% of the residual power of the annual vertical signal globally after pole tide correction and reduces the weighted mean vertical annual amplitude from 4.19 mm to 3.19 mm, while for horizontal components the fraction explained by current loading models is much smaller (amplitude ratio, explained variance and RMS/WRMS reduction are distinct metrics and are not directly interchangeable). This paper further highlights that the annual period was reported to fluctuate between 363 and 367 days at the ten CMONOC stations analyzed by Li et al.-a time variability that, if general, challenges fixed-frequency signal separation methods, although apparent period changes may also arise from amplitude/phase modulation, spectral leakage, finite-record effects, colored noise or data gaps-and it identifies thermoelastic deformation (TED) as a long-neglected but potentially quantifiable component, based on a recently released preprint dataset that has not yet undergone peer review. Finally, key research prospects are outlined, including physics-informed fusion methods, self-supervised foundation models, and a unified multi-source inversion framework.