Journal of Geodesy最新文献

The Helmert’s second condensation method is usually used to condense the topographical masses outside the boundary surface in the determination of the geoid and quasi-geoid based on the boundary-value theory. The condensation of topographical masses produces direct and indirect topographical effects. Nowadays, the Remove-Compute-Restore (RCR) technique has been widely utilized in the boundary-value problems. In view of spectral consistency, high-frequency direct and indirect topographical effects should be used in the Hotine-Helmert/Stokes–Helmert integral when the Earth gravitational model serves as the reference model in determining the (quasi-) geoid. Thus, the algorithms for high-frequency topographical effects are investigated in this manuscript. First, the prism methods for near-zone direct and indirect topographical effects are derived to improve the accuracies of near-zone effects compared with the traditional surface integral methods. Second, the Molodenskii spectral methods truncated to power H⁴ are put forward for far-zone topographical effects. Next, the "prism + Molodenskii spectral-spherical harmonic" combined algorithms for high-frequency topographical effects are further presented. At last, the effectiveness of the combined algorithms for the high-frequency topographical effects are verified in a mountainous test area.

The European Space Agency (ESA) is preparing a satellite mission called GENESIS to be launched in 2027 as part of the FutureNAV program. GENESIS co-locates, for the first time, all four space geodetic techniques on one satellite platform. The main objectives of the mission are the realization of the International Terrestrial Reference Frames and the mitigation of biases in geodetic measurements; however, GENESIS will remarkably contribute to the determination of the geodetic parameters. The precise GENESIS orbits will be determined through satellite-to-satellite tracking, employing two GNSS antennas to observe GPS and Galileo satellites in both nadir and zenith directions. In this research, we show results from simulations of GENESIS and Galileo-like constellations with joint orbit and clock determination. We assess the orbit quality of GENESIS based on nadir-only, zenith-only, and combined nadir–zenith GNSS observations. The results prove that GENESIS and Galileo joint orbit and clock determination substantially improves Galileo orbits, satellite clocks, and even ground-based clocks of GNSS receivers tracking Galileo satellites. Although zenith and nadir GNSS antennas favor different orbital planes in terms of the number of collected observations, the mean results for each Galileo orbital plane are improved to a similar extent. The 3D orbit error of Galileo is improved from 27 mm (Galileo-only), 23 mm (Galileo + zenith), 16 mm (Galileo + nadir), to 14 mm (Galileo + zenith + nadir GENESIS observations), i.e., almost by a factor of two in the joint GENESIS + Galileo orbit and clock solutions.

Physical geodesy applies potential theory to study the Earth’s gravitational field in space outside and up to a few km inside the Earth’s mass. Among various tools offered by this theory, boundary-value problems are particularly popular for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the nineteenth century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable; the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice.

With the support of inter-satellite link technology, GNSS can theoretically achieve the distributed autonomous orbit determination (AOD) function. Traditional AOD operation generally utilizes the forecast ephemeris uploaded by operational control segment (OCS) as the filter reference orbits or to constrain the orbit systematic errors, especially for constellation overall rotation effects in Earth-centered inertial (ECI) coordinate system. To get rid of the dependency on forecast trajectories for saving the OCS workload and also reduce the onboard storage and computation burden, we use a sequential extended Kalman filter to estimate the orbit parameters and consider main perturbation forces acting on satellites in the AOD solution. In particular, for modeling solar radiation pressure (SRP), an empirical prediction function derived by historical SRP estimates is introduced. Using the proposed scheme, the orbit 3D accuracy and user range error (URE) of the first 180-day distributed AOD solution for BeiDou-3 MEOs with precise Earth rotation parameters (ERPs) can reach about 2.10 and 0.43 m, respectively. The constellation rotation errors implied in AOD orbits around the X-, Y- and Z-axis of ECI system are less than 15.0, 11.7 and 15.2 mas, respectively. For real-world AOD scenarios, precise ERP is not available for satellites. With the 180-day prediction ERP, the orbit 3D errors and URE due to the gradually increased UT1-UTC error can be elevated to 14.62 and 2.91 m during our AOD experiments. Result analysis shows if OCS can upload latest prediction ERP at a frequency of once a week, the 180-day distributed AOD is expected to consistently produce real-time orbits preferable to broadcast ephemeris derived by the traditional region L-band tracking network.

To take the sphericity of the Earth into account, tesseroids are often utilized as grid elements in large-scale gravitational forward modeling. However, such elements in a latitude–longitude mesh suffer from degenerating into poorly shaped triangles near poles. Moreover, tesseroids have limited flexibility in describing laterally variable density distributions with irregular boundaries and also face difficulties in achieving completely equivalent division over a spherical surface that may be desired in a gravity inversion. We develop a new method based on triangular spherical prisms (TSPs) for 3D gravitational modeling in spherical coordinates. A TSP is defined by two spherical surfaces of triangular shape, with one of which being the radial projection of the other. Due to the spherical triangular shapes of the upper and lower surfaces, TSPs enjoy more advantages over tesseroids in describing mass density with different lateral resolutions. In addition, such an element also allows subdivisions with nearly equal weights in spherical coordinates. To calculate the gravitational effects of a TSP, we assume the density in each element to be polynomial along radial direction so as to accommodate a complex density environment. Then, we solve the Newton’s volume integral using a mixed Gaussian quadrature method, in which the surface integral over the spherical triangle is calculated using a triangle-based Gaussian quadrature rule via a radial projection that transforms the spherical triangles into linear ones. A 2D adaptive discretization strategy and an extension technique are also combined to improve the accuracy at observation points near the mass sources. The numerical experiments based on spherical shell models show that the proposed method achieves good accuracy from near surface to a satellite height in the case of TSPs with various dimensions and density variations. In comparison with the classical tesseroid-based method, the proposed algorithm enjoys better accuracy and much higher flexibility for density models with laterally irregular shapes. It shows that to achieve the same accuracy, the number of elements required by the proposed method is much less than that of the tesseroid-based method, which substantially speeds up the calculation by more than 2 orders. The application to the tessellated LITHO1.0 model further demonstrates its capability and practicability in realistic situations. The new method offers an attractive tool for gravity forward and inverse problems where the irregular grids are involved.

As its contribution to the latest release of the International Terrestrial Reference Frame, ITRF2020, the International GNSS Service (IGS) provided a 27-year-long series of daily “repro3” terrestrial frame solutions obtained by combining reprocessed solutions from ten Analysis Centers. This contribution represents an improvement over the previous contribution to ITRF2014, not only by the inclusion of more stations with longer and more complete position time series, but also by a general reduction in random and systematic errors. The IGS contribution to ITRF2020 also provided, for the first time, an independent estimate of the terrestrial scale based on the calibration of the Galileo satellite antennas. Despite the various observed improvements, the repro3 station position time series remain affected by a variety of random and systematic errors. This includes spurious periodic variations in several frequency bands, originating mostly from orbit and tide modeling errors, on top of a combination of white and flicker noise, whose origins remain to be precisely understood. These various components should carefully be accounted for when modeling GNSS station position time series and interpreting them in terms of Earth’s surface deformation. The Galileo-based scale of the repro3 solutions is found to be significantly offset (by (+)4.3 mm at epoch 2015.0) and drifting (by (+)0.11 mm/year) from the SLR/VLBI-based scale of ITRF2020. The reasons for this offset and drift remain to be uncovered.

Satellite product combination has been a major effort for the International GNSS Service Analysis Center Coordinator to improve the robustness of orbits, clocks and biases over original AC-specific contributions. While the orbit and clock combinations have been well documented, combining phase biases is more of a challenge since they have to be aligned with the clocks precisely to preserve the exactitude of integer ambiguities in precise point positioning (PPP). In the case of dual-frequency signals, frequency-specific phase biases are first translated into an ionosphere-free form to agree with the IGS satellite clocks, and they can then be integrated as integer clocks to facilitate a joint combination. However, regarding multi-frequency phase biases, forming their ionosphere-free counterparts would be cumbersome as they are linearly dependent. We therefore propose a concept of “frequency-specific integer clock” where all third-frequency phase biases are integrated individually with satellite clocks to enable an efficient frequency-wise combination. The resultant combined product will ensure all-frequency PPP ambiguity resolution over any frequency choices and observable combinations. Our combination test based on the GPS/Galileo satellite products from four IGS-ACs in 2020 showed that the mean phase clock/bias consistencies among ACs for all third-frequency signals (i.e., GPS L5, Galileo E6 and E5b) were as high as 10 ps, and the ambiguity fixing rates were all around 95%. Both quantities reached the same levels as those for the baseline frequencies (i.e., GPS L1/L2 and Galileo E1/E5a). The combined products outperformed AC-specific products since outlier contributions were excluded in the combination.

Monitoring the time-variable geopotential identifies the mass redistribution across the Earth and reveals, e.g., climate change and availability of water resources. The features of interest are characterized by spatial and temporal scales accessible only through space missions. Among the most important gravity missions are GRACE (2002–2017), its successor GRACE-FO (since 2018), and GOCE (2009–2013), which all sense the Earth’s gravity field via the geopotential derivatives. We investigate the geopotential estimation through frequency comparisons between orbiting clocks by means of the Doppler-canceling technique, describing the clocks’ behavior in the Earth’s gravitational field via Einstein’s general relativity. The novelty of this approach lies in measuring gravity by sensing the geopotential itself. The proof of principle for the measurement is achieved through an innovative mission scenario: for the first time, the observations are collected by a probing clock in LEO. We show gravity solutions obtained by simulating an estimation problem via our proposed architecture. The results suggest that we can conceivably retrieve the geopotential coefficients with accuracy comparable to the GRACE measurement concept by employing clocks with stabilities of order ({10}^{-18}). Presently, terrestrial clocks can routinely attain fractional frequency stabilities of ({10}^{-18}), whereas spaceborne clocks are still at the ({10}^{-15}) level. While our findings are promising, further analysis is needed to obtain more realistic indications on the feasibility of an actual mission, whose realization will be possible when clock technology reaches the required performance. The goal is for the technique investigated in this study to become a future staple for gravity field estimation.

This paper introduces a novel method for solving the resection problem in two and three dimensions based on conformal geometric algebra (CGA). Advantage is taken because of the characteristics of CGA, which enables the representation of points, lines, planes, and volumes in a unified mathematical framework and offers a more intuitive and geometric understanding of the problem, in contrast to existing purely algebraic methods. Several numerical examples are presented to demonstrate the efficacy of the proposed method and to compare its validity with established techniques in the field. Numerical simulations indicate that our vector geometric algebra implementation is faster than the best-known algorithms to date, suggesting that the proposed GA-based methods can provide a more efficient and comprehensible solution to the two- and three-dimensional resection problem, paving the way for further applications and advances in geodesy research. Furthermore, the method’s emphasis on graphical and geometric representation makes it particularly suitable for educational purposes, allowing the reader to grasp the concepts and principles of resection more effectively. The proposed method has potential applications in a wide range of other fields, including surveying, robotics, computer vision, or navigation.

The goal for the next generation of terrestrial reference frames (TRF) is to achieve a 1-mm- and 0.1-mm/yr-accurate frame realization through the combination of reference station solutions by multi-technique geodetic observatories. A potentially significant source of error in TRF realizations is the inter-system ties between the instruments at multi-technique stations, usually independently determined through ground-based local surveying. The quality of local tie surveys is varied and inconsistent, largely due to differences in measurement techniques, surveying instruments, site conditions/geometries, and processing methods. The Global Geodetic Observing System (GGOS) has tried to address these problems by issuing guidelines for the construction and layout of future multi-technique observatories, promoting uniformity and quality while minimizing existing problems with local surveying that are exacerbated over longer baseline distances. However, not every observatory is going to be able to completely satisfy these guidelines, and in this work, a successful endeavor to satisfy the accuracy goals while exceeding the GGOS baseline guideline is detailed for the McDonald Geodetic Observatory (MGO) in the Davis Mountains of Texas, USA. MGO consists of a VLBI Geodetic Observing System (VGOS), infrastructure in place for a Space Geodesy Satellite Laser Ranging (SGSLR) telescope, and several Global Navigation Satellite Systems (GNSS) stations spanning a 900 m baseline and a 120 m elevation change. The results of the local ties between the GNSS stations across the near-kilometer baseline, as measured from their antenna reference points, show sub-mm precision and 1 mm accuracy validated through repeatability across several surveys conducted in 2021as well as 1 mm consistency with the monthly averaged daily solutions of the GNSS-based positioning. In this paper, we report these results as well as the framework of the surveys with sufficient detail and rigor in order to give confidence to the quality claims and to present the novel design and techniques employed in the procedure, processing, and error-budget analysis, which were determined through iterative research methods across repeated survey campaigns.