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@ARTICLE{2026GeoJI.246..210C,
       author = {{Chen}, Jianhua and {Chen}, Qiujie and {Shen}, Yunzhong and {Zhang}, Xingfu and {Xuan}, Jianhao and {Flury}, Jakob},
        title = "{A regularized static gravity field estimation from GOCE, GRACE and Swarm observations based on full signal variance--covariance regularization matrix}",
      journal = {Geophysical Journal International},
     keywords = {Geopotential theory, Satellite gravity, Joint inversion, Numerical modeling},
         year = 2026,
        month = aug,
       volume = {246},
       number = {2},
          eid = {ggag210},
        pages = {ggag210},
     abstract = "{Advances in satellite gravimetry technologies have enabled the
        integration of increasingly diverse mission data sets for high-
        resolution static gravity field modelling. However, during the
        construction of regularization matrices for stabilizing
        spherical harmonic coefficients (SHCs), conventional
        regularization methods generally neglect significant
        correlations among SHCs, primarily due to heterogeneous noise
        characteristics of observations from different missions. To
        address this limitation, we propose a full signal
        variance--covariance (FSVC) regularization method by constructing
        a full regularization matrix based on a priori gravity anomaly
        signal amplitudes. Applying this method to combined normal
        equations integrating GOCE SGG, GRACE and Swarm observations
        yield three solutions under different constraint strategies: a
        Kaula diagonal constrained solution (Tongji-GMMG2025S-KLA), a
        diagonal signal variance--covariance (DSVC) regularized solution
        (Tongji-GMMG2025S-DSVC) derived from the diagonal elements of
        the FSVC matrix, and the FSVC-regularized solution (Tongji-
        GMMG2025S-FSVC). Our analyses demonstrate that: Based on FSVC
        analysis, the proposed FSVC regularization method exhibits
        overall superior performance compared to the diagonal
        regularization approach, particularly when the prior model
        incorporates terrestrial gravity data. Even when using the
        Kaula-constraint solution as the prior model, quantitative
        evaluations in both spectral and spatial domains demonstrate
        that the FSVC-regularized solution still exhibits significantly
        improved performance relative to diagonal regularization
        schemes. In the degree range 151--300, the Tongji-GMMG2025S-FSVC
        model reduces cumulative geoid error degree variances by 9.28
        per cent and 9.58 per cent compared to the Tongji-GMMG2025S-KLA
        and Tongji-GMMG2025S-DSVC solutions, respectively, indicating
        more effective suppression of medium- to high-degree noise.
        Spatial comparisons with the XGM2019 model further show reduced
        gravity anomaly discrepancies, with the FSVC solution achieving
        the lowest global standard deviation (4.94 mGal). Notably, this
        improvement is particularly evident in the Indonesia region,
        which is characterized by complex land--sea distributions.
        Independent validation using GNSS/Levelling data demonstrates
        that the FSVC-regularized solution overall higher accuracy than
        the diagonal-constrained solutions. In particular, the Tongji-
        GMMG2025S-FSVC model exhibits a distinct advantage, achieving
        noise reductions of 9.15 per cent and 8.53 per cent relative to
        the Tongji-GMMG2025S-KLA and Tongji-GMMG2025S-DSVC solutions in
        the Canadian region, respectively. In conclusion, the proposed
        FSVC regularization approach proves highly effective in
        suppressing high-degree noise and enhancing the accuracy of
        satellite-only static gravity field solutions. This improvement
        highlights the potential applicability of the proposed approach
        for future multisatellite gravity mission integration.}",
          doi = {10.1093/gji/ggag210},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2026GeoJI.246..210C},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}