A regularized static gravity field estimation from GOCE, GRACE and Swarm observations based on full signal variance–covariance regularization matrix

SUMMARY: 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.