Journal of Geodesy最新文献

We describe a model that accounts for the phase rotation that occurs when a receiver or transmitter changes orientation while observing or emitting circularly polarized electromagnetic waves. This model extends work detailing Global Navigation Satellite Systems (GNSS) carrier phase wind-up to allow us to describe the interaction of changing satellite orientation with phase rotation in observing radio telescopes. This development is motivated by, and a critical requirement of, unifying GNSS and Very Long Baseline Interferometry (VLBI) measurements at the observation level. The model can be used for either stationary choke ring antennas or steerable radio telescopes observing either natural radio sources or satellites. Simulations and experimental data are used to validate the model and to illustrate its importance. In addition, we rigorously lay out the feed rotation correction for radio telescopes with beam waveguide and full Nasmyth focuses and validate the correction by observing the effect with dual polarization observations. Using this feed rotation model for beam waveguide telescopes, we produce the first phase delay solution for the VLBI baseline WARK30M–WARK12M. We provide a practical guide to using the feed rotation model in Appendix D.

The International Association of Geodesy defined the International Height Reference System (IHRS) in 2015. IHRS will be realised through the International Height Reference Frame (IHRF) primarily by geopotential numbers. On the global scale, a sparse core reference network is utilised to realise the IHRS, but denser realisations (or densifications) are needed to ensure local access and height datum unification. ITRF ellipsoidal heights and a gravimetric (quasi-) geoid model form the basis for a model-based IHRS realisation, which can be enhanced by levelling to improve local accessibility to the global frame and relative uncertainty. This study investigates incorporating levelling observations in the IHRS realisation process and explores potential improvements. A case study over Sweden using an initial model-based IHRS realisation and precise levelling observations from the Baltic Levelling Ring (BLR) project was performed. The levelling network was adjusted relative to the model-based IHRF geopotential numbers using three approaches regarding the a priori variance–covariance matrix for weighting of the observations: constrained adjustment, weighted adjustment with realistic a priori uncertainties, and weighted adjustment with Variance Component Estimation (VCE) to iteratively tune the variance–covariance matrix. It is shown that the model-based IHRS realisation improves significantly. Both the estimated standard uncertainty of the adjusted IHRF geopotential numbers and the relative standard uncertainty between nodal benchmarks are reduced by approximately 40 per cent in the Swedish case. To fully exploit precise levelling observations in the IHRS realisation process, a weighted adjustment, preferably using VCE to optimally combine the initial model-based geopotential numbers and the levelling observations is recommended.

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.