Journal of Geodesy最新文献

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.

The truncation coefficient is widely utilized in non-global coverage computations of geophysics and geodesy and is always altitude dependent. As the two commonly used calculation methods for truncation coefficients, i.e., the spectral form and the recursive formula, both suffer from decreasing precision caused by high-altitude, leading to slow convergence for the former and numerical instability recursion for the latter. The asymptotic expansion mathematically converges with increasing degree and can precisely compensate for the shortcomings of the two methods. This study introduces asymptotic expansion to accurately compute the truncation coefficient for the spectral gravity forward modeling to a high degree. The evaluation at the whole altitudes and whole integral radii indicates that the proposed method has the following advantages: (i) The calculation precision increases with increasing degree and is altitude independent; (ii) the accurate calculation can be supported by a double-precision format; and (iii) the calculation can be conducted nearly without extra time cost with increasing degree. Generally, asymptotic expansion is used to calculate the high degree truncation coefficients, while the truncation coefficients at low degrees can be calculated using spectral form or recursive formulas in multiprecision format as a supplement; and the available range of asymptotic expansion is provided in the appendix.

Accurate positioning using the Global Positioning System relies on accurate modeling of tropospheric delay. Estimated tropospheric delay must vary sufficiently to capture true variations; otherwise, systematic errors propagate into estimated positions, particularly the vertical. However, if the allowed delay variation is too large, the propagation of data noise into all parameters is amplified, reducing precision. Here we investigate the optimal choice of tropospheric constraints applied in the GipsyX software, which are specified by values of random walk process noise. We use the variability of 5-min estimated positions as a proxy for tropospheric error. Given that weighted mean 5-min positions closely replicate 24-h solutions, our ultimate goal is to improve 24-h positions and other daily products, such as precise orbit parameters. The commonly adopted default constraint for the zenith wet delay (ZWD) is 3 mm/√(hr) for 5-min data intervals. Using this constraint, we observe spurious wave-like patterns of 5-min vertical displacement estimates with amplitudes ~ 100 mm coincident with Winter Storm Ezekiel of November 27, 2019, across the central/eastern USA. Loosening the constraint suppresses the spurious waves and reduces 5-min vertical displacement variability while improving water vapor estimates. Further improvement can be achieved when optimizing constraints regionally, or for each station. Globally, results are typically optimized in the range of 6–12 mm/√(hr). Generally, we at least recommend loosening the constraint from the current default of 3 mm/√(hr) to 6 mm/√(hr) for ZWD every 300 s. Constraint values must be scaled by √(x/300) for alternative data intervals of x seconds.

Differential code bias (DCB) is widely used to achieve consistency between global navigation satellite system (GNSS) observations at different frequencies. Since a strong correlation exists between satellite DCBs at different frequencies and the satellite clock offset, the DCB products need to be aligned with the corresponding clock products. This paper proposes a satellite’s DCB conversion model between different clock products released by the International GNSS Service (IGS) via the uncombined method. First, a one-step uncombined approach with a simplified ionospheric processing model is proposed for multi-frequency DCB estimation. In the second step, a linear function model is applied to represent the relationship between the initial satellite clock bias and the DCB estimates at different frequencies. To test the proposed model, BeiDou global system (BDS-3) multi-frequency data collected from 60 multi-GNSS experiment stations and precise clock products released by four IGS analysis centers are used to estimate the DCB. The DCB estimates are compared to the DCB products released by the Chinese Academy of Sciences (CAS) and the Deutsches Zentrum für Luft-und Raumfahrt (DLR). The average root-mean-square (RMS) values of the differences between the DCB estimates and the two DCB products are 0.61 ns and 0.52 ns, which are significantly larger than the corresponding monthly standard deviations. This indicates that systematic bias exists between the DCB estimates and the two DCB products. Additionally, systematic biases are also observed in the DCB estimation when different clock products are used, with the maximum value reaching 4 ns. In order to study the propagation of parameter errors between the DCB estimates and the clock products, regression analysis is conducted to determine the linear model coefficients of the DCB conversion model. The results show that the model coefficients for the four frequency pairs C2I-C6I, C2I-C1X, C2I-C5X and C2I-C7Z are 0.394, 0.237, 0.238, and 0.238, respectively. Kinematic precision point positioning is conducted for model verification. During the first 6-h period, the average three-dimensional RMS of the positioning errors is 13.5 cm when the DCB estimates are corrected by the conversion model, which is improved by 32.5%, 14.6%, and 11.3% compared with the usage of the CAS and DLR products and those without model conversion, respectively.

Very-long-baseline interferometry (VLBI) networks have historically lacked enough antennas to densify the southern hemisphere adequately. This situation not only impacts directly the realization of the Celestial Reference System but also the determination of the Earth Orientation Parameters (EOP). In the last years, a significant step in the modernization of the VLBI infrastructure has been taken with the VLBI Global Observing System (VGOS). However, the distribution of VGOS antennas is still far from being homogeneous. In this work, we used the software VieSched++ for VLBI scheduling to simulate nine new VGOS arrays. These networks, which are more dense in the southern hemisphere and focus on South America, were planned considering existing geodetic sites where a VGOS antenna could be added and new sites where the installation is feasible. We compared the statistical performance of the proposed networks with that of a simulated standard VGOS network and the actual VGOS performance for the last 2 years. A more uniform station distribution does not seem to be associated with better repeatabilities for station coordinates, but the results for EOP and source coordinates improve as expected.