Journal of Geodesy最新文献

Global Navigation Satellite Systems (GNSS) applications require computation of the geometric range between the satellite vehicle at the time-of-signal transmission and the receiver antenna location at the time-of-signal reception. This computation requires attention to the frames of reference due to the rotation of the Earth-Centered Earth-Fixed (ECEF) frame during the time-of-signal propagation. Three range computation approaches are commonplace and will be discussed herein. The first is the Global Positioning System Interface Control Document recommendation to rotate the ECEF frames to a common reference time. The other two are forms of the Sagnac correction. The Sagnac derivations already in the literature are either limited to stationary receivers or lack the connection between the Earth-centered inertial (ECI) and ECEF frames. Neither form of the Sagnac correction exactly reproduces the geometric range. They are approximations. The literature does not currently contain an analysis of the error involved in using either form of the Sagnac correction. This article makes two contributions: (1) it presents derivations for both forms of the Sagnac correction that are valid for moving receivers and that maintain the connection between the ECI and ECEF frames; and (2) it analyzes the error of the Sagnac correction for orbits of different radius. The analysis shows that Sagnac corrections introduce range errors less than (7.57times 10^{-4}) meters for GNSS satellites at medium Earth orbit.

The geoid and quasi-geoid serve as the reference surfaces of the orthometric and normal height systems, respectively. In order to improve the accuracy of the (quasi-) geoid determined by the Stokes integral with use of the Remove-Compute-Restore (RCR) technique, various modification methods for the spherical Stokes’ kernels, including the spheroidal, cosine-, power-, and Molodensky-modified kernels, are studied in this paper. In addition to the traditional Molodensky-modified Stokes’ kernel, a more effective Molodensky-modified Stokes’ kernel is put forward. A general formula for spectral decomposition of the Stokes integral in the RCR mode is derived, followed by the spectral analysis to reveal the transfer principles of gravity data when using different Stokes’ kernels. The spheroidal and modified Stokes integrals can cause spectral leakage phenomenon, and a method to eliminate spectral leakage is presented based on spectral analysis. The research indicates the low truncation degree of the spheroidal Stokes’ kernel and the low modification degrees of the modified Stokes’ kernel affect the accuracy of the (quasi-) geoid significantly. Quantitative methods for estimating the empirical values of the parameters of the low-degree spheroidal and modified Stokes’ kernels are proposed and the effectiveness of the methods is validated through numerical tests.

As an important data source for monitoring the behavior and variations of the ionosphere, the accuracy of current real-time global ionospheric maps (RT-GIMs) in low-latitude regions and oceanic regions is usually poor, and the accuracy during geomagnetic storms is not ideal. Therefore, the ionospheric vertical total electron content (VTEC) short-term forecast results were integrated into the global ionospheric real-time modeling process to improve the accuracy of RT-GIMs. Firstly, the preliminary RT-GIMs were established by constructing a virtual grid and determining the number of ionospheric pierce points in the grid. Then, different strategies were used to determine the virtual VTEC observations and filled the preliminary RT-GIMs. Finally, the filled RT-GIMs were modeled using spherical harmonic expansion and generated the final RT-GIMs, XRTG. On this basis, three ways were selected to evaluate the accuracy of XRTG. The GPS dSTEC (differential slant total electron content) assessment results showed that the performance of XRTG was the closest to that of Centre for Orbit Determination in Europe’s final GIMs (CODG), and it outperformed other RT-GIMs during geomagnetic storm periods and low-latitude regions. Compared with Universitat Politècnica de Catalunya’s RT-GIMs (UADG) with better performance in other RT-GIMs, the maximum decrease in root mean square error (RMSE) of XRTG during the geomagnetic storm period exceeds 25%, and the maximum decrease in the overall average RMSE of the 20 stations in low latitudes exceeds 27%. The Jason-3 VTEC assessment results showed that the accuracy of XRTG was closer to that of UADG and CODG, and the performance of XRTG and UADG in the range of 22° N–22° S was significantly better than that of other RT-GIMs. The consistency between XRTG and Universitat Politècnica de Catalunya’s rapid GIMs, Chinese Academy of Sciences’ final GIMs, and CODG was good, and the VTEC deviations from each post-processing GIMs were mainly concentrated in the range of ± 5 TECU.

The power function of (F-) distribution is the complementary cumulative distribution function of the non-central (F-) distribution. It is used to evaluate the power of the test based on the (F) or ({chi }^{2}-) distributed statistics. This paper revisits its computation and solution for the non-centrality parameter in geodetic studies and shows that the power function related to these studies can be computed efficiently and with minimal effort. To facilitate this, we introduce a novel standalone algorithm that consistently computes the power of the test, even for large non-centrality parameters (e.g., (>{10}^{5})) and for ({chi }^{2})-distribution. The solution of the power function for the non-centrality parameter is typically obtained using standard root finding algorithms, such as the bisection or Newton–Raphson methods. However, they may encounter convergence problems, particularly when the non-centrality parameter increases. We demonstrate that a solution can be readily obtained from a logarithmic form of the power function, ensuring convergence and removing the requirement for a precisely defined initial value. Furthermore, we utilize a few geometric relationships during the iteration to expedite the solution process. As a result, we propose a novel solution algorithm that is highly precise, stable, and at least four times faster than standard algorithms, even for the solution interval of (<{0, 10}^{6}>). This efficient solution is published online as a web-based application for geodetic detectability studies in addition to the given MATLAB and Python codes.

The complete set of five Earth Orientation Parameters (EOP) can only be estimated accurately using geodetic Very Long Baseline Interferometry (VLBI). Their precision and accuracy depends on network geometry and station-dependent properties. Atmospheric turbulence poses one of the largest error sources for geodetic VLBI, impacting the precision of EOP. Thus, it becomes imperative to consider this factor while choosing the optimal locations for geodetic VLBI. The magnitude of tropospheric turbulence is approximated through the refractive index structure constant, (C_textrm{n}^textrm{2}). In this study, we simulate the optimal locations for geodetic VLBI in India, considering individual tropospheric turbulence parameters per telescope location. The study identifies 14 potential VLBI stations, co-located with GPS stations and homogeneously distributed all over India, and computes the (C_textrm{n}) values from zenith wet delay variances over 24 h obtained from GPS data. These locations are simulated in addition to three different reference networks, which show the current and future VLBI Global Observing System (VGOS) networks. Multiple schedules have been generated and simulated for each configuration using VieSched++, and the precision of EOP is compared when constant and station-specific tropospheric turbulence parameters are used. The study shows that, for the investigated networks, southern stations are optimal for polar motion and celestial pole offsets estimation, whereas an eastern station is optimal for UT1−UTC estimation. Furthermore, the study highlights that for reference networks with fewer stations, utilizing station-specific (C_textrm{n}) values significantly influences the determination of optimal locations. It further demonstrates how station-specific (C_textrm{n}) values impact the positioning of VGOS telescopes in each network for each EOP differently. The findings show that higher (C_textrm{n}) values generally lead to a degradation in EOP precision. Geometrically, a station might be at a good location, but if the (C_textrm{n}) value is too high, that location is not favorable.

A bridge may displace due to various loadings (e.g., thermal (Xia et al. in Struct Control Health Monit 28(7):e2738, 2013), winds (Owen et al. in J Wind Eng Ind Aerodyn 206:104389, 2020), and vehicles (Xu et al. in J Struct Eng 133(1):3–11, 2007)) acting upon the bridge. Identifying the contributions of individual loading factors to the measured bridge displacements is important for understanding the structural health conditions of the bridge. There is however no effective method to quantify the contributions when multiple loadings act simultaneously on a bridge. We propose a new data-driven method, termed random forest (RF)-assisted variational mode decomposition (RF-AVMD), for more effective identification of dominant loading factors and for quantifying the contributions of individual loading factors to the measured bridge displacements. The proposed method is applicable to studying the displacements of any bridge structures and allows for the first time to separate the contributions of individual loadings. The effectiveness of the proposed method is validated using data from Tsing Ma Bridge (TMB), a large suspension bridge in Hong Kong recorded during two consecutive strong typhoons. The results reveal that the transverse displacements of TMB mid-span were controlled by the crosswinds, the longitudinal displacements were dominated by the temperature and winds along the bridge centerline, and the vertical displacements were mainly due to the winds along the bridge centerline, temperature, and traffic flows. Displacement time series that responded to each loading factor was derived. The proposed method provides important new insights into the impacts of individual loadings on the displacements of long-span bridges.

Currently, the least-square estimation method is the mainstream method for recovering spherical harmonic coefficients from area mean values over equiangular blocks. Since the least-square estimation method involves matrix inversion, it requires great computation power when the maximum degree to be solved is large. In comparison, numerical quadrature methods are faster. Recent numerical quadrature methods designed for spherical harmonic analysis of area mean values over blocks delineated by equiangular and Gaussian grids are both fast and exact for band-limited data. However, for band-limited area mean values over an equiangular grid that has (N) blocks along the colatitude direction and (2N) blocks along the longitude direction, the maximum degree that can be recovered by using current exact numerical quadrature methods is no larger than (N/2-1). In this study, by using Lagrange’s method for polynomial interpolation, recently proposed numerical quadrature methods that employ the recurrence relations for the integrals of the associated Legendre’s functions are modified into two new methods. By using these methods, the maximum degree of recovered spherical harmonic coefficients is (N-1). The results show that these newly proposed methods are comparable in computation speed with the current numerical quadrature methods and are comparable in accuracy with the least-square estimation method for both band-limited and aliased data. Moreover, solving linear systems is not necessary for these two new methods. The error characteristics of these two new methods are quite different from those of methods that employ least-square methods. The spherical harmonic coefficients recovered using these new methods can effectively supplement those recovered using least-square methods.

Benefited from the advantage of high precision, wide area and low cost, the time transfer method based on precise point positioning (PPP) has become a popular technique for the remote clock comparisons. Although the time reference to which satellite clocks are referred can be eliminated by the difference between stations, the effect of satellite clock biases on the estimation of receiver clock offset is always ignored for PPP time transfer. Considering the PPP technique is extended from the all-in-view (AV) by the full use of precise carrier phase observables, a method to evaluate the effects of satellite clock biases on AV and PPP time transfer is proposed first. Then, the GPS, Galileo and BDS-3 time transfer results with different international GNSS Service (IGS) precise products are compared to verify the negative effects of satellite clock biases on AV and PPP time transfer. In our experiment, precise orbit and clock products provided by GFZ (German Research Centre for Geosciences), ESA (European Space Agency) and COD (Center for Orbit Determination in Europe) are used to obtain the clock comparison results of nine time links, including three short baselines, three medium baselines and three long baselines. The results show that the effects of satellite clock biases on AV and PPP time transfer are related to the magnitude of satellite clock biases and the baseline distance between stations. After removing the satellites with larger satellite clock biases, we assess the negative effects of satellite clock biases on AV and PPP time transfer for GPS, Galileo and BDS-3, respectively. By using GFZ, COD and ESA precise products for AV time transfer, the inconsistency of GPS and Galileo time transfer results caused by satellite clock biases is below 0.2 ns for long baseline. Due to the larger satellite clock biases for BDS-3, the inconsistency of BDS-3 AV time transfer results caused by satellite clock biases could reach 0.3 ns for medium baseline and even reach 0.9 ns for long baseline. For GPS and Galileo PPP time transfer, the inconsistency of time transfer results is below 0.05 ns for long baseline. However, the inconsistency of BDS-3 PPP time transfer results can only achieve 0.11 ns for medium baseline and 0.3 ns for long baseline. Thus, it is concluded that the satellite clock biases of BDS-3 precise satellite clock products need refining to improve the performance of BDS-3 PPP time transfer.

Combining the Liouville equations for polar motion (PM) with forecasted geophysical effective angular momentum (EAM) functions can significantly improve the accuracy of Earth's PM predictions. These predictions rely on deconvolution and convolution methods. Deconvolution derives the geodetic EAM function from the PM observations, while convolution uses both the geodetic and geophysical EAM functions to reproduce and predict the PM values. However, there are limitations in existing numerical realisations of deconvolution and convolution that must be addressed. These limitations include low-frequency biases, high-frequency errors, and edge errors, which can negatively impact the accuracy of PM prediction. To overcome these concerns, we develop the Convolution Least Squares (Conv-LS) scheme through a multi-perspective analysis in the frequency domain, PM domain, and EAM domain. By comparing representative approaches for reproducing three different PM series (IERS C01, IERS C04, and IGS) with varying sampling intervals (18.25 days, daily, and 6 h), we demonstrate that the Conv-LS scheme can effectively eliminate the usually present spurious signals and also integrate high-accuracy deconvolution algorithms to reduce reproduced errors further. Compared to the traditional approacsh (using a low-accuracy discrete PM equation for deconvolution and numerical integration for convolution), our new approach (utilising a high-accuracy deconvolution algorithm along with the Conv-LS scheme for convolution) reduces the standard deviations of the residuals' x-component by 31.0%, 60.1%, and 13.7% for C01, C04, and IGS PM series, respectively, while also reducing the y-component by 17.3%, 47.0%, and 14.0%, respectively. These results highlight the superiority of the Conv-LS scheme, leading us to recommend it for practical applications.