Journal of Geodesy

The gravimetry measurements from the Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) mission provide an essential way to monitor changes in ocean bottom pressure ( \(p_b\) ), which is a critical variable in understanding ocean circulation. However, the coarse spatial resolution of the GRACE(-FO) fields blurs important spatial details, such as \(p_b\) gradients. In this study, we employ a self-supervised deep learning algorithm to downscale global monthly \(p_b\) anomalies derived from GRACE(-FO) observations to an equal-angle 0.25  \( ^{\circ }\) grid in the absence of high-resolution ground truth. The optimization process is realized by constraining the outputs to follow the large-scale mass conservation contained in the gravity field estimates while learning the spatial details from two ocean reanalysis products. The downscaled product agrees with GRACE(-FO) solutions over large ocean basins at the millimeter level in terms of equivalent water height and shows signs of outperforming them when evaluating short spatial scale variability. In particular, the downscaled \(p_b\) product has more realistic signal content near the coast and exhibits better agreement with tide gauge measurements at around 80% of 465 globally distributed stations. Our method presents a novel way of combining the advantages of satellite measurements and ocean models at the product level, with potential downstream applications for studies of the large-scale ocean circulation, coastal sea level variability, and changes in global geodetic parameters.

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission, launched by the European Space Agency, provided high-quality gravitational gradient data with near-global coverage, excluding polar regions. These data have been instrumental in regional gravity field modelling through various methods. One approach involves a mathematical model based on Fredholm’s integral equation of the first kind, which relates surface gravity anomalies to satellite gradient data. Solving this equation requires discretising a surface integral and applying further regularisation techniques to stabilise the numerical solution of a resulting system of linear equations. This study examines four methods for modifying the system of linear equations derived by discretising the Fredholm integral equation. The methods include direct inversion, remove-compute-restore, truncation reduction of the integral formula, and inversion of a modified integral for estimating surface gravity anomalies from satellite gradient data over a test area in Central Europe. Since the system of linear equations is ill-conditioned, the Tikhonov regularisation is applied to stabilise its numerical solution. To assess the precision and reliability of the estimated gravity anomalies, the study introduces mathematical models for estimation of biased and de-biased noise variance–covariance matrices of estimated surface gravity anomalies. The results indicate that the signal-to-noise ratio of reduced satellite gradient data in the remove-compute-restore method is smaller compared to other methods in the study, necessitating stronger stabilisation of the model to recover surface gravity anomalies. This, in turn, leads to a more optimistic uncertainty propagation than the other considered methods.

While integer ambiguity resolution (IAR) enables GNSS to achieve real-time sub-centimeter-level positioning in open-sky environments, it can be easily hindered if the involved receivers are situated in areas with limited satellite visibility, such as in dense city environments. In such GNSS-challenged cases, commercial Low Earth Orbit (LEO) communication satellites can potentially augment GNSS by providing additional measurements. However, LEO satellites often lack code measurements, mainly transmitting satellite-specific frequency-varying carrier phase signals. This contribution aims to study the ambiguity-resolved baseline positioning performance of such phase-only signals, addressing the extent to which LEO constellations can realize near real-time positioning in standalone and GNSS-combined modes. Through a simulation platform, we analyze the distinct response of each LEO constellation (Iridium, Globalstar, Starlink, OneWeb, and Orbcomm) to IAR under various circumstances. Although achieving single-receiver high-precision positioning can be challenged by inaccuracies in the LEO satellite orbit products, the relative distance between two receivers can help overcome this limitation. As a result, centimeter-level relative positioning over short baselines can be made possible, even with a satellite elevation cut-off angle of 50 degrees, making it suitable for GNSS-challenged environments. This can be achieved with high-grade receiver clocks over very short baselines ( \(\sim \) 5 km) and access to decimeter-level orbit products.

The stochastic representation of an uncertain shape model allows the dynamic evaluation of its induced gravity signal. This can be also applied for representing a time variable gravity field to model mass changes. The algorithm for estimating variations in gravitational potential is extended for the case of second-order derivatives. Two different harmonic synthesis formulas are used to derive the sought variations: one expressed in spherical coordinates using the traditional associated Legendre functions (ALF) and their derivatives up to the second order, while the other expressed in Cartesian coordinates by including the derived Legendre functions (DLF). The obtained variations are compared in terms of convergence with gravity signal differences referring to the specific shape changes using the line integral analytical approach for three asteroid shape models. Both approaches provide results that differ from the analytical method at a 1E−1 level, while the differences between them are at the 1E−15 level. The obtained results are highly influenced by the geometry of the examined shape model, with the ALF approach providing variations with closer agreement with the analytical method only for the almost spherical shape. Both harmonic synthesis expressions can be used to derive accurate results, as they differ at a very low level, and one can choose based on the convenience of their algorithmic characteristics.

Effective angular momentum (EAM) forecasts are widely used as an important input for predicting both polar motion and dUT1. So far, model predictions for atmosphere, ocean, and terrestrial hydrosphere utilized in Earth rotation research reach only 6-days into the future. GFZ’s oceanic and land-surface model forecasts are forced with operational 6-day high-resolution deterministic numerical weather predictions provided by the European Centre for Medium-range Weather Forecasts. Those atmospheric forecasts extend also further into the future with a reduced sampling rate of just 6 h but the prediction skill decreases rapidly after roughly one week. To decide about publishing 10-day instead of 6-day model-based EAM forecasts, we generated a test set of 454 individual 10-day forecasts and used it with GFZ’s EAM Predictor method to calculate Earth rotation predictions. Using 10-day instead of 6-day EAM forecasts leads to slight improvements in y-pole and dUT1 predictions for 10 to 30 days ahead. By introducing additional neural network models trained on the errors of the EAM forecasts when compared to their subsequently available analysis runs, Earth rotation prediction can be enhanced even further. A reduction of the mean absolute errors for polar motion and length-of-day prediction at a forecast horizon of 10 days of 26.8% in x-pole, 15.5% in y-pole, 27.6% in dUT1, and 47.1% in \(\Delta \) LOD is achieved. This test application successfully demonstrates the potential of the extended EAM forecasts for Earth rotation prediction although the success rate has to be further improved to arrive at robust routine predictions. GFZ publishes from October 2024 onwards raw uncorrected 10-day instead of 6-day EAM forecasts at www.gfz-potsdam.de/en/esmdata for the individual contributions of atmosphere, ocean, and terrestrial hydrosphere. Users interested in the summarized effect of all subsystems are advised to use the 90-day combined EAM forecast product that also makes use of the presented corrections to the EAM forecasts.

The geodetic community commonly challenges the composite hypotheses in the statistical testing of mathematical models. Since the composite hypotheses are not specified as opposed to their simple counterparts, they require a prior estimation of the model parameters. However, if the mathematical models are ill-conditioned, the regularized estimation is often applied for the parameters of interest. Due to the biased property, the regularized estimation does not rigorously originate in the principle of maximum likelihood (ML) estimation, which was the base for developing the theory of the generalized likelihood ratio (GLR) test. Since the regularized estimator of the parameters of interest is consequently inconsistent with the ML one, one cannot construct the GLR test, which is the uniformly most powerful invariant (UMPI) test. So far, only the bias correction approach has been suggested to solve this problem. In this contribution, an implicit representation of the regularized mathematical model is proposed. It eliminates the complete impact of regularized estimation on a mathematical model and delivers the misclosures analytically free from the influence of regularization. Thus, one can construct the GLR test, which belongs to the UMPI family, and then formulate the test statistic in terms of misclosures.

As a critical parameter in meteorological monitoring, precipitable water vapor (PWV) is widely used in short-term extreme weather forecasting and long-term climate change research. However, as PWV exhibits significant vertical attenuation, especially within 2 km, achieving accurate vertical interpolation is essential for comparisons and fusion across different measurement techniques, such as sampling water vapor at different heights. PWV vertical adjustment relies only on the empirical or time-varying lapse rate models (e.g., GPWV-H). The non-uniform vertical distribution of PWV and the uncertain variation trend in the low-latitude region still limit the accuracy. To address these issues, we propose the Spatially enhanced Vertical Adjustment Model for PWV (SPWV-H), taking into account the non-uniform distribution in the vertical direction based on the fifth-generation European Centre for Medium-Range Weather Forecasts Atmospheric Reanalysis (ERA5) products. The assessment, validated against the ERA5 benchmark, highlights the SPWV-H model’s superior performance with an RMSE of 1 mm and a bias of 0.03 mm, especially pronounced in the low-latitude region. Compared to global radiosonde datasets, the SPWV-H model achieves notable reductions in RMSE of 12%, 11%, and 18% when evaluated against the EPWV-H, GPWV-H, and GPT3-1 models, respectively. In spatial interpolation, the SPWV-H model achieves an RMSE of 1.22 mm, indicating an improvement of 10%, 9%, and 14% compared to the EPWV-H, GPWV-H, and GPT3-1 models, respectively. Therefore, the SPWV-H model can provide a reliable service for multi-source PWV fusion and real-time PWV monitoring by GNSS.

In February 2023, the International Laser Ranging Service started the tracking of additional medium Earth orbit satellites from the global BeiDou navigation satellite system (BDS) constellation, increasing the total number of tracked BDS satellites to 27. As an optical space geodesy technique, the Satellite Laser Ranging (SLR) provides another important measurement for BDS other than the microwave (L-band) one. Based on three years of data from June 2021 to May 2024, the potential benefits of introducing SLR data into BDS processing and analysis are investigated from three key aspects: orbit validation, precise orbit determination, and geodetic parameters estimation. The independent SLR validations of BDS precise orbit products from four analysis centers show that using the a priori box-wing model for solar radiation pressure (SRP) modeling can achieve superior performance than purely empirical models. The results also indicate the existence of SRP modeling deficiencies for some satellites such as C45 and C46 with Search and Rescue payloads. Given a sparse ground network with 5 stations, the introduction of SLR significantly stabilizes the SRP parameter estimates and improves the orbit accuracy by 44.4%. In terms of geodetic parameter estimation, the scatter of the Z-component geocenter motion can be effectively reduced with the inclusion of SLR data, presenting 10.9–15.3% smaller root mean square (RMS) values during February 2023 and May 2024, depending on the SRP models. In addition, the annual amplitudes of the Z-component geocenter motion are reduced by 7.2–48.2%. The improvement is more pronounced with a limited number of microwave stations, due to the greater strength of SLR observations in geocenter motion estimation. On the other hand, since the SLR observations are unhomogeneously distributed in both space and time, the incorporation of SLR does not evidently enhance the accuracy of Earth rotation parameters, and may even to some extent contaminate the results when the number of microwave stations is limited.

Trends in the deep-ocean M \(_2\) barotropic tide, deduced from nearly three decades of satellite altimetry and recently presented by Opel et al. (Commun Earth Environ 5:261, https://doi.org/10.1038/s43247-024-01432-5, 2024), are here updated with a slightly longer time series and with a focus on potential systematic errors. Tidal changes are very small, of order 0.2 mm/year or less, with a tendency for decreasing amplitudes, which is evidently a response to the ocean’s increasing stratification and an increasing energy loss to baroclinic motion. A variety of systematic errors in the satellite altimeter system potentially corrupt these small trend estimates. The Dynamic Atmosphere Correction (DAC), derived from an ocean model and used for de-aliasing, introduces a spurious trend (exceeding 0.1 mm/year in places) caused by changes in ECMWF atmospheric tides. Both operational and reanalysis atmospheric tides have spurious trends over the altimeter era. Tidally coherent errors in satellite orbits, including from use of inconsistent tidal geocenter models, are more difficult to bound, although differences between two sets of satellite ephemerides are found to reach 0.1 mm/year for M \(_2\) . Orbit errors are more deleterious for some other constituents, including the annual cycle. Tidal leakage in the “mesoscale correction,” needed here to suppress non-tidal ocean variability, is a known potential problem, and if the leakage changes over time, it impacts ocean-tide trend estimation. Tests show the error is likely small in the open ocean ( \(<0.04\)  mm/year) but large in some marginal seas ( \(>0.2\)  mm/year). Potential contamination from other altimeter corrections (e.g., ionospheric path delay) is likely negligible for M \(_2\) but can be difficult to bound.

Latest harmonic developments of the Earth tide-generating potential (TGP), e.g., HW95 (Hartmann and Wenzel in Geoph Res Lett 22:3553, 1995), RATGP95 (Roosbeek in Geophys J Int 126:197, 1996), KSM03 (Kudryavtsev in J Geodesy 77:829, 2004), include a number of terms caused by the joint effect of the Earth’s polar flattening (that can be numerically described by the \({J}_{2}\) geopotential coefficient) and the Moon/the Sun gravitational attraction. In the present study, we additionally consider the effect of the Earth’s equatorial flattening due to the Earth’s triaxiality. Explicit analytical expressions for the relevant part of the TGP are derived. New terms of the TGP development due to the Earth’s triaxial figure are found. Amplitudes of nineteen of them exceed the threshold level of 10–8 m2s−2 used by the modern tidal potential catalogs. Three of the new terms have the frequency sign opposite to that of the Earth rotation. It is not the case for any previously known term of the Earth TGP development. Every term has a new feature that an integer multiplier of the mean local lunar time used in its argument is not equal to the order of the spherical harmonic associated with the term. It necessitates a relevant modification of the standard HW95 format for representing the Earth TGP. The new terms are suggested for including in the current and future tidal potential catalogs.

Partial ambiguity resolution (PAR) has been widely adopted in real-time kinematic (RTK) and precise point positioning with augmentation from continuously operating reference station (PPP-RTK). However, current PAR methods, either in the position domain or the ambiguity domain, suffer from high false alarm and miss detection, particularly in challenging environments with poor satellite geometry and observations contaminated by non-line-of-sight (NLOS) effects, gross errors, biases, and high observation noise. To address these issues, a PAR method based on machine learning is proposed to significantly improve the correct fix rate and positioning accuracy of PAR in challenging environments. This method combines two support vector machine (SVM) classifiers to effectively identify and exclude ambiguities those are contaminated by bias sources from PAR without relying on satellite geometry. The proposed method is validated with three vehicle-based field tests covering open sky, suburban, and dense urban environments, and the results show significant improvements in terms of correct fix rate and positioning accuracy over the traditional PAR method that only utilizes ambiguity covariances. The fix rates achieved with the proposed method are 93.9%, 81.9%, and 93.1% with the three respective field tests, with no wrong fixes, compared to 72.8%, 20.9%, and 16.0% correct fix rates using the traditional method. The positioning error root mean square (RMS) is 0.020 m, 0.035 m, and 0.056 m in the east, north, and up directions for the first field test, 0.027 m, 0.080 m, and 0.126 m for the second field test, and 0.035 m, 0.042 m, and 0.071 m for the third field test. In contrast, only decimeter- to meter-level accuracy was obtainable with these datasets using the traditional method due to the high wrong fix rate. The proposed method provides a correct and fast time-to-first-fix (TTFF) of 3–5 s, even in challenging environments. Overall, the proposed method offers significant improvements in positioning accuracy and ambiguity fix rate with high reliability, making it a promising solution for PAR in challenging environments.

The development of optical clocks has experienced significant acceleration in recent years, positioning them as one of the most promising quantum optical sensors for next-generation gravimetric missions (NGGMs). This study investigates the feasibility of retrieving the temporal gravity field via improved optical clocks through a closed-loop simulation. It evaluates optical clock capabilities in temporal gravity field inversion by considering the clock noise characteristics, designing satellite formations, and simulating the performance of optical clocks. The results indicate that optical clocks exhibit higher sensitivity to low-degree gravity field signals. However, when the optical clock noise level drops below 1 × 10−19 \(/\sqrt{\uptau }\) (τ being the averaging time in seconds) in the satellite-to-ground (SG) mode or below 1 × 10−20 \(/\sqrt{\uptau }\) in the satellite-to-satellite (SS) mode, atmospheric and oceanic (AO) errors become the dominant source of error. At this noise level, optical clocks can detect time-variable gravity signals up to approximately degree 30. Compared to existing gravity measurement missions such as GRACE-FO, optical clocks exhibit consistent results in detecting signals below degree 20. If the orbital altitude is reduced to 250 km, the performance of optical clocks across all degrees aligns with the results of GRACE-FO. Furthermore, the study reveals that lowering the orbital altitude of satellite-based optical clocks from 485 to 250 km improves results by an average of 33%. Switching from the SS mode to the SG mode results in an average improvement of 51%, while each order-of-magnitude improvement in clock precision enhances results by an average of 60%. In summary, these findings highlight the tremendous potential of optical clock technology in determining Earth’s temporal gravity field and provide crucial technological support for NGGMs.

Lateral inhomogeneity in the Earth’s mantle affects the tidal response. The current study reformulates the expressions for estimating the lateral inhomogeneity effects on tidal gravity with respect to the unperturbed Earth and supplements some critical derivation process to enhance the methodology. The effects of lateral inhomogeneity are calculated using several real Earth models. By considering the collective contributions of seismic wave velocity disturbances and density disturbance, the global theoretical changes of semidiurnal gravimetric factor are obtained, which vary from − 0.22 to 0.22% compared to those in a layered Earth model, about 1/2 of the ellipticity’s effect. The gravity changes caused by lateral-inhomogeneous disturbances are also computed and turn out to be up to 0.16% compared to the changes caused by tide-generating potential. The current study compares the influences of lateral inhomogeneity with rotation and ocean tide loading. The results indicate that the rotation and ellipticity on tidal gravity are the most dominant factors, the ocean tide loading is the moderate one, and the lateral inhomogeneity in the mantle has the least significant influence. Moreover, an anti-correlation between the effective elastic thickness and gravimetric factor change caused by lateral inhomogeneity is found, implying that it is difficult to generate tidal response at regions with high rigidity. We argue that the gravimetric factor change can be used as an effective indicator for lithospheric strength.

The regional sea level budget and interannual sea level changes around Taiwan and Philippines are studied using altimetry, GRACE, and in-situ hydrographic data during 1993‒2021. Results show that the average sea level trend around Taiwan and Philippines during 1993–2021 derived from the altimetric data is 3.6 ± 0.2 mm/yr. Over 2002–2021, the study shows closure of sea level budget in the eastern ocean of Taiwan and Philippines within the observed data uncertainties, and the ocean mass accounts for 88%–100% of the observed sea level rise. In contrast, the sea level budget is not closed in the western ocean of Taiwan and Philippines, probably due to the lack of complete coverage by in-situ ocean observing systems. In addition, both regional sea level anomalies and their steric component around Taiwan and Philippines exhibit pronounced interannual and decadal variabilities. The trade wind stress associated with El Niño–Southern Oscillation and Pacific Decadal Oscillation offers a compelling explanation for the interannual and decadal signals of sea level anomalies in the southern ocean of Taiwan, with negative correlations of − 0.78 to − 0.64, indicating that trade wind stress makes a negative contribution to interannual-to-decadal sea level variability. In the northwestern ocean of Taiwan, the sea level variation is strongly influenced by the local monsoon system and shallow bathymetry with an annual amplitude of 90.3 ± 2.9 mm, larger than those in other regions around Taiwan and Philippines, where ocean mass is dominant with a high correlation with the sea level (+ 0.75 to + 0.78).

Numerical methods, like the finite element method (FEM) or finite volume method (FVM), are widely used to provide solutions in many boundary value problems. In previous studies, these numerical methods have also been applied in geodesy but demanded extensive computations because the upper boundary condition was usually set up at the satellite orbit level, hundreds of kilometers above the Earth. The relatively large distances between the lower boundary of the Earth's surface and the upper boundary exacerbate the computation loads because of the required discretization in between. Considering that many areas, such as the US, have uniformly distributed airborne gravity data just a few kilometers above the topography, we adapt the upper boundary from the satellite orbit level to the mean flight level of the airborne gravimetry. The significant decrease in the domain of solution dramatically reduces the large computation demand for FEM or FVM. This paper demonstrates the advantages of using FVM in the decreased domain in simulated and actual field cases in study areas of interest. In the simulated case, the FVM numerical results show that precision improvement of about an order of magnitude can be obtained when moving the upper boundary from 250 to 10 km, the upper altitude of the GRAV-D flights. A 2–3 cm level of accurate quasi-geoid model can be obtained for the actual datasets depending on different schemes used to model the topographic mass. In flat areas, the FVM solution can reach to about 1 cm precision, which is comparable with the counterparts from classical methods. The paper also demonstrates how to find the upper boundary if no airborne data are available. Finally, the numerical method provides a 3D discrete representation of the entire local gravity field instead of a surface solution, a (quasi) geoid model.

The Kalman filter stands as one of the most widely used methods for recursive parameter estimation. However, its standard formulation typically assumes that all state parameters avail initial values and dynamic models, an assumption that may not always hold true in certain applications, particularly in global navigation satellite system (GNSS) data processing. To address this issue, Teunissen et al. (2021) introduced a generalized Kalman filter that eliminates the need for initial values and allows linear functions of parameters to have dynamic models. This work proposes a least-squares approach to reformulate the generalized Kalman filter, enhancing its applicability to GNSS data processing when the parameter dimension varies with satellite visibility changes. The reformulated filter, named generalized least-squares filter, is equivalent to the generalized Kalman filter when all state parameters are recursively estimated. In this case, we demonstrate how both the generalized Kalman filter and the generalized least-squares filter adaptatively manage newly introduced or removed parameters. Specifically, when estimation is limited to parameters with dynamic models, the generalized least-squares filter extends the generalized Kalman filter by allowing the dimension of estimated parameters to vary over time. Moreover, we introduce a new element of least-squares smoothing, creating a comprehensive system for prediction, filtering, and smoothing. To verify, we conduct simulated kinematic and vehicle-borne kinematic GNSS positioning using the proposed generalized least-squares filter and compare the results with those from the standard Kalman filter. Our findings show that the generalized least-squares filter delivers better results, maintaining the positioning errors at the centimeter level, whereas the Kalman-filter-based positioning errors exceed several decimeters in some epochs due to improper initial values and dynamic models. Moreover, the normal equation reduction strategy employed in the generalized least-squares filter improves computational efficiency by 23% and 32% in simulated kinematic and vehicle-borne kinematic positioning, respectively. The generalized least-squares filter also allows for the flexible adjustment of smoothing window lengths, facilitating successful ambiguity resolution in several epochs. In conclusion, the proposed generalized least-squares filter offers flexibility for various GNSS data processing scenarios, ensuring both theoretical rigor and computational efficiency.

Vertical land motion and the redistribution of masses within and on the surface of the Earth affect the Earth’s gravity field. Hence, studying the ratio between temporal changes of the surface gravity \(\left( {\dot{g}} \right)\) and height ( \(\dot{h}\) ) is important in geoscience, e.g., for reduction of gravity observations, assessing satellite gravimetry missions, and tuning vertical land motion models. Sjöberg and Bagherbandi (2020) estimated a combined ratio of \(\dot{g}/\dot{h}\) in Fennoscandia based on relative gravity observations along the 63 degree gravity line running from Vågstranda in Norway to Joensuu in Finland, 688 absolute gravity observations observed at 59 stations over Fennoscandia, monthly gravity data derived from the GRACE satellite mission between January 2003 and August 2016, as well as a land uplift model. The weighted least-squares solution of all these data was \(\dot{g}/\dot{h}\)  =  − 0.166 ± 0.011 μGal/mm, which corresponds to an upper mantle density of about 3402 ± 95 kg/m3. The present note includes additional GRACE data to June 2017 and GRACE Follow-on data from June 2018 to November 2023. The resulting weighted least-squares solution for all data is \(\dot{g}/\dot{h}\)  =  − 0.160 ± 0.011 μGal/mm, yielding an upper mantle density of about 3546 ± 71 kg/m3. The outcomes show the importance of satellite gravimetry data in Glacial Isostatic Adjustment (GIA) modeling and other parameters such as land uplift rate. Utilizing a longer time span of GRACE and GRACE Follow-on data allows us to capture fine variations and trends in the gravity-to-height ratio with better precision. This will be useful for constraining and adjusting GIA models and refining gravity observations.

LARES-2 is a new geodetic satellite designed for high-accuracy satellite laser ranging. The orbit altitude of LARES-2 is similar to that of LAGEOS-1, whereas the inclination angle of 70° complements the LAGEOS-1 inclination of 110°; hence, both satellites form the butterfly configuration for the verification of the Lense–Thirring effect. Although the major objective of LARES-2 is testing general relativity, LARES-2 substantially contributes to geodesy in terms of the realization of terrestrial reference frames, recovery of the geocenter motion, pole coordinates, length-of-day, and low-degree gravity field coefficients. We analyze the first 1.5 years of LARES-2 data and test different empirical orbit models for LARES-2 with and without co-estimating low-degree gravity field coefficients to find the best combination strategy with LAGEOS satellites. We found that LARES-2 orbit determination is more accurate than that of LAGEOS-1/2 due to a different satellite construction consisting of a solid sphere with no inner structure. Neither the correction for D0 nor the empirical once-per-revolution along-track accelerations SC/SS have to be estimated for LARES-2 when co-estimating gravity field coefficients. The only empirical parameter needed for LARES-2 is the constant along-track acceleration S0 to compensate for the Yarkovsky–Schach effect. On the contrary, for LAGEOS-1/2, the non-gravitational perturbations affect C30 and Z geocenter estimates when once-per-revolution parameters are not estimated. LARES-2 does not face this issue. LARES-2 improves the formal errors of the Z geocenter component by up to 59% and C20 by up to 40% compared to the combined LAGEOS-1/2 solutions and provides C30 estimates unaffected by thermal orbit modeling issues.