Journal of Geodesy最新文献

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 S_C/S_S 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.

For precise orbit determination (POD) and precise applications with POD products, one of the critical issues is the modeling of non-conservative forces acting on satellites. Since the official publication of Galileo satellite metadata in 2017, analytical models including the box-wing model and thermal thrust models have been established to absorb a substantial amount of solar radiation pressure (SRP) and thermal thrust. These models serve as the foundation for the best overall modeling approach, combining the analytical box-wing model and thermal thrust model with parameterization of the remaining non-conservative perturbing forces using various optimized Empirical CODE Orbit Models (ECOMs) of the Center for Orbit Determination in Europe (CODE). Firstly, we have demonstrated the significance of the second-order signals in the D direction and the first-order signals in the B direction through spectral analyses of the pure box-wing model, which are consistent with the currently recommended 7-parameter Empirical CODE Orbit Model 2 (ECOM2). In spite of this, we still found that degradation in orbit accuracy frequently occurs during deep eclipse seasons when using the ECOM2 model. We confirm a high-frequency signal existing in the fluctuating orbit overlap differences through the spectral analysis. Considering this, the ECOM2 force model should be extended to higher order and adapted to absorb the remaining effects of potential perturbing forces. After extending the ECOM2 force model to the sixth order in the Sun direction, we demonstrated the significance of fourth- and sixth-order sine terms for deep eclipses. Due to the higher-order periodic terms, the averaged RMS values of orbit overlap difference over deep eclipses can be reduced from 5.3, 10.8, and 23.8 cm to 3.2, 3.9, and 9.9 cm for in-orbit validation (IOV) satellites, from 5.0, 8.6, and 17.7 cm to 3.0, 3.0, and 7.1 cm for the first generation of full operational capability (FOC-1) satellites, and from 5.4, 8.6, and 19.0 cm to 3.6, 3.6, and 7.4 cm for the second generation of FOC (FOC-2) satellites, in the radial, cross-track, and along-track directions, respectively. Fluctuations with a peak amplitude of approximately 0.4 nm/s² in the bias in the solar panel axis (Y) direction (Y-bias) are effectively mitigated by the higher-order terms. Due to the higher-order terms, the vertical positioning errors during kinematic precise point positioning (PPP) convergence can be improved from 42.3 to 37.1 cm at the 95.5% confidence level. Meanwhile, a low correlation level of up to 0.02 is found between the newly introduced higher-order parameters and earth rotation parameters (ERPs).

Deformation phenomena on Earth are inherently three dimensional. With SAR interferometry (InSAR), in many practical situations the maximum number of observations is two (ascending and descending), resulting in an infinite number of possible displacement estimates. Here we propose a practical solution to this underdeterminancy problem in the form of the strapdown approach. With the strapdown approach, it is possible to obtain “3D-global/2D-local” solutions, by using minimal and largely undisputed contextual information, on the expected driving mechanisms and/or spatial geometry. It is a generic method that defines a local reference system with transversal, longitudinal, and normal (TLN) axes, with displacement occurring in the transversal-normal plane only. Since the orientation of the local frame is based on the physics of the problem at hand, the strapdown approach gives physically more relevant estimates compared to conventional approaches. Moreover, using an a-priori uncertainty approximation on the orientation of the local frame it is possible to assess the precision of the final estimates. As a result, appropriate cartographic visualization using a vector map with confidence ellipses enables an improved interpretation of the results.

This paper focuses on the retrieval of refractivity fields from GNSS measurements by means of least-squares collocation. Collocation adjustment estimates parameters that relate delays and refractivity without relying on a grid. It contains functional and stochastic models that define the characteristics of the retrieved refractivity fields. This work aims at emphasizing the capabilities and limitations of the collocation method in modeling refractivity and to present it as a valuable alternative to GNSS tomography. Initially, we analyze the stochastic models in collocation and compare the theoretical errors of collocation with those of tomography. We emphasize the low variability of collocation formal variances/covariances compared to tomography and its lower dependence on a-priori fields. Then, based on real and simulated data, we investigate the importance of station resolution and station heights for collocation. Increasing the network resolution, for example, from 10 to 2 km, results in improved a-posteriori statistics, including a 10% reduction in the error statistic for the retrieved refractivity up to 6 km. In addition, using additional stations at higher altitudes has an impact on the retrieved refractivity fields of about 1 ppm in terms of standard deviation up to 6 km, and a bias reduction of more than 3 ppm up to 3 km. Furthermore, we compare refractivity fields retrieved through tomography and collocation, where data of the COSMO weather model are utilized in a closed-loop validation mode to simulate tropospheric delays and validate the retrieved profiles. While tomography estimates are less biased, collocation captures relative changes in refractivity more effectively among the voxels within one height level. Finally, we apply tomography and collocation to test their capabilities to detect an approaching weather front. Both methods can sense the weather front, but their atmospheric structures appear more similar when the GNSS network has a well-distributed height coverage.

Carrier phase integer ambiguities must be determined for BDS-3/inertial navigation system (INS) tightly coupled (TC) integration to achieve centimetre-level positioning accuracy. However, cycle slip breaks the consistency of the integer ambiguities. Conventional multi-frequency cycle slip methods use the pseudorange; thus, requiring improvement when applied to kinematic situations. Furthermore, a concise and nonprior information-dependent model is crucial for real-time processing. In this study, an inertial-aided BDS-3 cycle slip detection and repair (I-CDR) method was developed. First, a BDS-3/INS TC model with I-CDR was created. The ionospheric delays were modelled as part of the TC states; therefore, they could be estimated and eliminated. Investigations were conducted on the effects of carrier phase noise, residual ionosphere delay, and INS-predicted position error on combined cycle slip detection (CCD) accuracy. The optimal CCDs under various frequency available configurations were determined. The effectiveness of I-CDR was demonstrated using land vehicle test data. The false alarm ratio was less than 1.0%, and the missed detection ratio was almost zero even in situations with challenging abundant 1-cycle slips in random epochs. Furthermore, the right determination ratio reached 100%. In addition, BDS-3 signal loss-recovery cases were simulated, and all cycle slips for all satellites could be repaired within 40s. I-CDR exhibits outstanding cycle slip detection and repair performance for dense 1-cycle slip and signal loss-recovery cases, demonstrating its suitability for BDS-3/INS TC integration.