Thu Oct 08, F. Flechtner
• Sorted by Date • Sorted by Last Name of First Author •
Li, Xiangjun, Wu, Shuguang, Li, Houpu, Liu, Bing, Bian, Shaofeng, and He, Yuefan, 2026. Extraction of Time–Varying Signals in GNSS and Geophysical Interpretation: Methods, Advances, and Challenges. Sensors, 26(17):5557, doi:10.3390/s26175557.
• from the NASA Astrophysics Data System • by the DOI System •
@ARTICLE{2026Senso..26.5557L,
author = {{Li}, Xiangjun and {Wu}, Shuguang and {Li}, Houpu and {Liu}, Bing and {Bian}, Shaofeng and {He}, Yuefan},
title = "{Extraction of Time-Varying Signals in GNSS and Geophysical Interpretation: Methods, Advances, and Challenges}",
journal = {Sensors},
keywords = {GNSS coordinate time series, time-varying signal extraction, environmental loading deformation, geophysical interpretation, multi-source data fusion},
year = 2026,
month = sep,
volume = {26},
number = {17},
eid = {5557},
pages = {5557},
abstract = "{What are the main findings? Maximum Likelihood Estimation (MLE) has
become the standard for GNSS linear trend extraction because it
jointly estimates trend parameters and stochastic noise
covariance; by doing so, it corrects the up to 5--10-fold
underestimation of velocity uncertainty that occurs when
temporally correlated (colored) noise is present but a white-
noise covariance is assumed. In large-sample benchmark tests on
the CMONOC network reported by Wu et al., Variational Mode
Decomposition (VMD) yields positive residual RMS improvement at
97.9\% of stations (mean 69.8\%), outperforming SSA (90.5\% of
stations); these results originate from the authors' prior work
and await independent replication on other networks before
generalization (See relevant sections in the manuscript for
metric-related caveats). Li et al. reported interannual
fluctuations of the annual period between 363 and 367 days at
ten CMONOC stations; if such period drift proves widespread, it
challenges signal separation methods built on fixed-frequency
assumptions. Maximum Likelihood Estimation (MLE) has become the
standard for GNSS linear trend extraction because it jointly
estimates trend parameters and stochastic noise covariance; by
doing so, it corrects the up to 5--10-fold underestimation of
velocity uncertainty that occurs when temporally correlated
(colored) noise is present but a white-noise covariance is
assumed. In large-sample benchmark tests on the CMONOC network
reported by Wu et al., Variational Mode Decomposition (VMD)
yields positive residual RMS improvement at 97.9\% of stations
(mean 69.8\%), outperforming SSA (90.5\% of stations); these
results originate from the authors' prior work and await
independent replication on other networks before generalization
(See relevant sections in the manuscript for metric-related
caveats). Li et al. reported interannual fluctuations of the
annual period between 363 and 367 days at ten CMONOC stations;
if such period drift proves widespread, it challenges signal
separation methods built on fixed-frequency assumptions. What
are the implications of the main findings? If the reported
period drift of seasonal signals is confirmed on wider networks,
future GNSS signal processing should move beyond fixed-frequency
assumptions; time-varying frequency models (e.g.,
UKF\_Amp\_Period) offer a viable path forward. Multi-source
fusion (GNSS + InSAR + GRACE) is essential for separating
coupled geophysical signals that cannot be resolved by any
single technique. Self-supervised foundation models (e.g., GNSS-
FM, currently an unreviewed preprint) point to a possible
paradigm shift in GNSS time series analysis, but their
geographic fairness and physical interpretability remain
unvalidated. If the reported period drift of seasonal signals is
confirmed on wider networks, future GNSS signal processing
should move beyond fixed-frequency assumptions; time-varying
frequency models (e.g., UKF\_Amp\_Period) offer a viable path
forward. Multi-source fusion (GNSS + InSAR + GRACE) is essential
for separating coupled geophysical signals that cannot be
resolved by any single technique. Self-supervised foundation
models (e.g., GNSS-FM, currently an unreviewed preprint) point
to a possible paradigm shift in GNSS time series analysis, but
their geographic fairness and physical interpretability remain
unvalidated. 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.}",
doi = {10.3390/s26175557},
adsurl = {https://ui.adsabs.harvard.edu/abs/2026Senso..26.5557L},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
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