Journal of Geodesy最新文献

BeiDou Global Navigation Satellite System (BDS-3) PPP-B2b service greatly promotes the real-time precise point positioning applications. However, previous research works have revealed that a nonnegligible satellite-specific clock bias (SCB) exists in the PPP-B2b clock offset, causing the degradation of PPP-B2b positioning performance. In this paper, a single-station-augmented PPP-B2b considering the SCB via BDS-3 short-message communication (SMC) is proposed. Specifically, an easy-to-implement real-time extraction method of single-differenced (SD) SCB is proposed using a single reference station. Then, based on the extracted SCB augmentation information, a new full-rank estimable SCB-weighted model is proposed to enhance the PPP-B2b positioning. In addition, to effectively transmit the SCB augmentation information without regard to Internet, a delicate design of encoding and broadcast strategy is developed via the BDS-3 SMC function. The results show that the extracted SD SCB series of each satellite is highly stable over a certain period of observation arc. The precision of extracted SD SCB series of each satellite varies from 0.11 to 0.28 ns with a mean value of 0.18 ns. In addition, compared with the traditional PPP-B2b model, the proposed SCB-weighted model improves the positioning performance in the static and kinematic applications. Specifically, for the static application, the positioning accuracy of SCB-weighted model exhibits 35.3%, 66.7%, and 48.2% improvements in east, north, and up directions, respectively; the convergence time exhibits a 39.7% improvement. For the kinematic vehicle application, the SCB-weighted model exhibits a faster re-convergence speed. The positioning accuracy is improved from 0.421 to 0.208 m with a 50.6% improvement. In conclusion, the proposed single-station-augmented PPP-B2b using the SCB-weighted model is highly appreciated for enhancing the PPP-B2b positioning performance.

The prolate spheroidal harmonic series is a well-suited tool for gravity modeling of elongated bodies. In this work, the prolate spheroidal harmonic algorithms for forward modeling of the gravitational field of homogeneous polyhedral bodies are presented. The line integral forms of the prolate spheroidal harmonic coefficients are given using the Gauss divergence and the Stokes theorems, and the discontinuities of the prolate spheroidal coordinates are considered in the integral conversions from the volume integrals of the coefficients into the surface and line integrals. The line integral algorithms with normalizations are numerically stable for high- and ultra-high-degree coefficients and both the small and the large eccentric bodies. The method extending exponent of floating-point numbers may need to be applied for ultra-high-degree coefficients. The good convergences and numerical accuracies of the prolate spheroidal harmonic expansions and the numerical stabilities of the line integral algorithms are verified by the numerical experiments for the gravitational field of the homogeneous comet Hartley 2 with 1752 triangular faces shape model, where the harmonic coefficients and expansions are computed up to the truncated degree/order (d/o) 300. Compared with the spherical harmonic expansions, the prolate spheroidal harmonic converges faster for external observation points.

Various vertical reference levels are used in the coastal zone, for various purposes. Being able to transform accurately and efficiently between them is of increasing interest since the need for seamless data over sea and land is growing due to sea-level rise, coastal engineering, and more frequent storm surges. We present a method for simultaneous calculation of models linking the ellipsoid, the geoid, and mean sea level using least-squares collocation. The method includes calculations of interpolated model surfaces together with associated standard error surfaces that provide estimates of the models’ uncertainty. We have applied the method on data from Norway, including sea level data and GNSS/levelling points, and calculated a mean sea surface and a dynamic ocean topography model. The estimated formal errors of the models range 0.4–1.8 cm and 0.5–3.5 cm, respectively. To assess the dynamic ocean topography model, we compared it with satellite altimetry-based datasets. Depending on which dataset used for comparison, we obtained mean differences between −3.2 and (1.2~textrm{cm}) and standard deviations between 4.2 and 5.0 cm at the outer limit of the domain of the estimated models where the distances to the observations are at their longest.

Most present-day bathymetric prediction solely addresses the linear mapping relationship between gravity signals and bathymetric data, disregarding nonlinearity’s effects, despite a probable nonlinear mapping between gravity signals and the seafloor topography. This paper investigates the consequences of excluding nonlinear terms in predicting bathymetry and reaches focused conclusions for different types of seafloor topography. The nonlinear effects were assessed by modelling the gravity signals generated by seafloor topographies with different topographic relief, topographic sizes, and basal depths. The results demonstrate that the nonlinear effect is more pronounced in shallow seas compared to deep seas for the same topographic relief. Furthermore, the consequences of ignoring nonlinear terms become more significant as topographic relief increases and topographic sizes decrease. The experiment on topographic sensitivity demonstrates that nonlinear gravity signals are able to detect small-scale topography more acutely, with higher orders corresponding to smaller sensitive topographic sizes. Using the Emperor seamount chain as an illustrative example, the nonlinear mapping is created by employing the eXtreme Gradient Boosting. The prediction accuracy of bathymetry using gravity anomalies has increased by 13%, whereas the predictive precision through vertical gravity gradient anomalies has risen by 7%. These results confirm the conclusions drawn from the simulation experiment. In addition, the results of the global nonlinear effects indicate that the regions most impacted are situated in the trenches along the plate boundaries, the eastern Pacific, and the Atlantic Ridge. The prediction of bathymetry will benefit from the consideration of nonlinear relationships, particularly for shallow sea and small-scale topography.

Space missions to small bodies like asteroids, comets, and moons rely on physics-based simulations to test guidance and control systems. However, accurately modeling their gravitational fields is challenging due to their highly irregular shapes and limited knowledge of their internal structures, complicating orbit planning and landing maneuvers. This study presents a new approach to model realistic density distributions based on Voxel-shaped mass concentrations. We apply body-specific constraints to three-dimensional Perlin noise, supplemented with normalization and segmentation techniques. Additionally, various structural elements can be incorporated into the density distribution. These include centralized and decentralized shells of different thicknesses and densities, as well as anomalies of varying sizes and shapes. Normalization techniques ensure the body’s total mass conservation. We validate our method by calculating the gravitation of a cube and sphere with constant density and comparing it with its analytical solution. We further compare our method with other mascon approaches and the polyhedral method at different Voxel resolutions and conduct additional performance evaluations of our method using test scenarios with focus on geophysical parameters such as the moments of inertia tensor and the gravity field’s spherical harmonics expansion. Our results demonstrate the method’s ability to account for realistic density distributions and to accurately compute the corresponding gravitational fields and geophysical properties.

Ionospheric sporadic E (Es) layers are thin layers with enhanced ionospheric electron densities (IEDs) which occur frequently in ionospheric E region. Previous detecting method based on ground-based global navigation satellite system (GNSS) observations can only obtain the horizontal maps rather than the vertical distributions and structures of Es layers. This study proposes a computerized ionospheric tomography (CIT) method with constraints from GNSS radio occultation data for the reconstruction of three-dimensional (3-D) structure and evolution of Es layers. The strong Es layers that occurred in Australia on January 11, 2021, and in North America on August 4, 2021, are chosen for reconstruction, and the COSMIC-2 IED profiles in the reconstruction region and its surrounding area are used as constraints in the CIT process. The IED distribution in F region is reconstructed at first by using only slant total electron content (STEC) without significant sudden disturbances, and then the E region contribution to STEC is estimated by subtracting the F region contribution, based on which the 3-D structures of Es layers with high spatial and temporal resolutions are reconstructed consequently. The reconstructed results in F and E regions are assessed separately, which show good consistence with GNSS STEC, global ionospheric maps, or ionosonde observations. The evolution of Es layer structures in the reconstructed region is further analyzed, and the large-scale Es structure spanning over more than 10° in longitude and the movement of Es patches are clearly revealed. Particularly, the reconstruction results successfully trace the vertical variation in the altitudes of Es layers.

GNSS integer ambiguity precision point positioning (IPPP) with satellite integer clock products is currently one of the most precise techniques for time and frequency transfer. However, a challenging issue that hampered the long-term performance of IPPP is the day-boundary discontinuity (DBD) that manifests at UTC (Coordinated Universal Time) midnights during the processing of multi-day GNSS observations. Users’ remedy to eliminate such receiver clock DBDs is to identify the integer offset of ambiguities across days, but residual DBDs could still potentially exceed 100 ps. In this study, we propose an alternative but more efficient approach to eliminate the DBDs of satellite orbit/clock/bias products as an integral, while users would directly achieve receiver clocks without DBDs rather than being troubled to fix them through carrier-phase ambiguity connection. Such a post-processing alignment approach is applicable to IGS satellite integer products processed in daily batches and does not rely on the respective smoothness of orbits or clocks. After application to the rapid multi-GNSS Experiment (MGEX) product at Wuhan University, the residual discontinuities of satellite integer clocks for each GPS/Galileo/BDS-3 satellite typically do not exceed 0.05 cycles of narrow-lane wavelengths. In continuous time and frequency transfer over a 31-day period, DBDs in all nine IPPP time links are smaller than 25 ps with a standard deviation of 10 ps, compared to 60–90 ps for the legacy strategy and unaligned products. This day-boundary alignment approach is suitable for common satellite integer products in the International GNSS Service (IGS) and has been routinely implemented in Wuhan University’s rapid MGEX satellite orbit/clock/bias products since January 1, 2023.

In recent years, the fundamental quantity of the gravitational field has been extended from gravitational potential, gravitational vector, and gravitational gradient tensor to gravitational curvature with its first measurement along the vertical direction in laboratory conditions. Previous studies numerically identified the near-zone and polar-region problems for gravitational curvature of a tesseroid, but these issues remain unresolved. In this contribution, we derive the new third-order central and single-sided difference formulas with one, two, and three arguments using the finite difference method. To solve these near-zone and polar-region problems, we apply a numerical approach combining the conditional split, finite difference, and double exponential rule based on these newly derived third-order difference formulas when the computation point is located below, inside, and outside the tesseroid. Numerical experiments with a spherical shell discretized into tesseroids reveal that the accuracy of gravitational curvature is about 4–8 digits in double precision. Numerical results confirm that when the computation point moves to the surface of the tesseroid, the relative and absolute errors of gravitational curvature do not change much, i.e., the near-zone problem can be adequately solved using the numerical approach in this study. When the latitude of the computation point increases, the relative and absolute errors of gravitational curvature do not increase, which solves the polar-region problem with this stable numerical approach. The provided Fortran codes at https://github.com/xiaoledeng/xtessgc-xqtessgc will help with potential applications for the gravitational field of different celestial bodies in geodesy, geophysics, and planetary sciences.

The paper presents 3D numerical modelling of the altimetry-derived marine gravity data with the high horizontal resolution 1 × 1 arc min. The finite volume method (FVM) as a numerical method is used to solve the altimetry–gravimetry boundary-value problem. Large-scale parallel computations result in the disturbing potential in every finite volume of the discretized 3D computational domain between an ellipsoidal approximation of the Earth’s surface and an upper boundary chosen at altitude of 200 km. Afterwards, the first, second or higher derivatives of the disturbing potential in different directions can be numerically derived using the finite differences. A crucial impact on achieved accuracy has the process of preparing the Dirichlet boundary conditions over oceans/seas. It is based on nonlinear filtering of the geopotential generated on a mean sea surface (MSS) from a GRACE/GOCE-based satellite-only global geopotential model. The paper presents different types of the altimetry-derived marine gravity data obtained on the DTU21_MSS as well as at higher altitudes of the 3D computational domain. The altimetry-derived gravity disturbances on the DTU21_MSS are compared with those from recent datasets like DTU21_GRAV or SS_v31.1. Standard deviations of the residuals are about 2.7 and 2.9 mGal, respectively. The obtained altimetry-derived gravity disturbances at higher altitudes are compared with airborne gravity data from the GRAV-D campaign in US showing accuracy about 3 mGal. In addition, the gravity disturbing gradients as the second derivatives or the third derivatives are provided with the same high resolution on the DTU21_MSS as well as at different altitudes.