Zhao Li, Ran Lu, Weiping Jiang, Danan Dong, Jintao Lei, Yang Lu, Xin Ding, Kaichun Yang, Hua Chen, Qusen Chen
{"title":"A refined full-spectrum temperature-induced subsurface thermal expansion model and its contribution to the vertical displacement of global GNSS reference stations","authors":"Zhao Li, Ran Lu, Weiping Jiang, Danan Dong, Jintao Lei, Yang Lu, Xin Ding, Kaichun Yang, Hua Chen, Qusen Chen","doi":"10.1007/s00190-024-01834-5","DOIUrl":"https://doi.org/10.1007/s00190-024-01834-5","url":null,"abstract":"<p>The thermal expansion effects of GNSS stations are influenced by not only temperature variations, but also bedrock depths and types. Unfortunately, the current studies treat the subsurface GNSS monument and their nearby bedrock as a whole, without taking into account the inconsistencies among bedrock depths and types, while the existing full-spectrum finite element method (FEM) cannot be easily extended to consider the bedrock information. To solve this problem, we propose a refined full-spectrum temperature-induced subsurface thermal expansion model (FSH<sub>BDT</sub>) that considers both seasonal and non-seasonal temperature variations as well as bedrock information based on the half-space harmonic model. Results show that the full-spectrum half-space harmonic model (FSH), which considers only seasonal and non-seasonal temperature variations, can obtain comparable results to the FEM and even outperform the FEM for inland stations. In addition, the depth and type of bedrock have significant effects on the annual amplitude and phase of thermal expansion-induced vertical displacement. In particular, we find that the station displacement increases by more than 1 mm and the annual phase delays by up to 10° for high-latitude and deeper bedrock stations when bedrock depths are taken into account. The FSH<sub>BDT</sub> improves the correlation coefficient between GNSS height and mass load displacements by up to 42.3% compared to the FEM and explains up to 8.2% of the nonlinear variation in the GNSS height time series. Our work confirms the advantage of rigorous subsurface thermal expansion modeling to correct the nonlinear variations of global GNSS stations, which might provide a potential opportunity to improve the terrestrial reference frame toward the goal of 1 mm accuracy.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"84 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140538351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"RANSAC-based instantaneous real-time kinematic positioning with GNSS triple-frequency signals in urban areas","authors":"","doi":"10.1007/s00190-024-01833-6","DOIUrl":"https://doi.org/10.1007/s00190-024-01833-6","url":null,"abstract":"<h3>Abstract</h3> <p>The demand for high-precision positioning has risen substantially in modern urban settings. In that regard, Global Navigation Satellite Systems (GNSS) offer several advantages such as global coverage, real-time capability, high accuracy, ease of use, and cost-effectiveness. The accuracy of GNSS-based positioning, however, suffers in urban environments due to signal blockage, reflection, and diffraction, which makes it difficult to fix ambiguities correctly within a real-time kinematic (RTK). To address this issue, this paper applies random sample consensus (RANSAC) to develop a novel single-epoch triple-frequency RTK positioning method. In our proposed method, the ambiguities of the extra-wide-lane, wide-lane, and original frequencies are resolved sequentially. RANSAC then detects and excludes incorrectly fixed ambiguities. To validate the effectiveness of the proposed method, two static experiments (cases 1 and 2) and one dynamic experiment (case 3) were conducted in representative urban areas. The findings demonstrate that the proposed method outperforms all comparative methods in positional availability, with comparable positional accuracy in terms of root-mean-square errors (RMSEs). In cases 1, 2, and 3, the proposed method achieves 3D RMSEs of 2.74, 4.29, and 20.35 cm, and the positional availabilities of 100%, 75.0%, and 73.1%, using a 10-degree mask angle (and a carrier-to-noise ratio (<em>C</em>/<em>N</em><sub>0</sub>) threshold 35 dB-Hz). The corresponding RMSEs (positional availabilities) of comparative methods are from 1.51 to 4.04 cm (75.7 to 96.3%) in case 1, 4.19 to 7.78 cm (34.5 to 49.9%) in case 2, and 23.52 to 37.54 cm (15.4 to 33.9%) in case 3, respectively. Compared to these methods, the proposed method shows improvements of positional availabilities between 3.7 and 24.3 percentage points in case 1, between 25.1 and 40.5 percentage points in case 2, and between 39.2 and 57.7 percentage points in case 3.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"13 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140533967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global, spatially explicit modelling of zenith wet delay with XGBoost","authors":"","doi":"10.1007/s00190-024-01829-2","DOIUrl":"https://doi.org/10.1007/s00190-024-01829-2","url":null,"abstract":"<h3>Abstract</h3> <p>Radio signals transmitted by Global Navigation Satellite System (GNSS) satellites experience tropospheric delays. While the hydrostatic part, referred to as zenith hydrostatic delay (ZHD) when mapped to the zenith direction, can be analytically modelled with sufficient accuracy, the wet part, referred to as zenith wet delay (ZWD), is much more difficult to determine and needs to be estimated. Thus, there exist several ZWD models which are used for various applications such as positioning and climate research. In this study, we present a data-driven, global model of the spatial ZWD field, based on the Extreme Gradient Boosting (XGBoost). The model takes the geographical location, the time, and a number of meteorological variables (in particular, specific humidity at several pressure levels) as input, and can predict ZWD anywhere on Earth as long as the input features are available. It was trained on ZWDs at 10718 GNSS stations and tested on ZWDs at 2684 GNSS stations for the year 2019. Across all test stations and all observations, the trained model achieved a mean absolute error of 6.1 mm, respectively, a root mean squared error of 8.1 mm. Comparisons of the XGBoost-based ZWD predictions with independently computed ZWDs and baseline models underline the good performance of the proposed model. Moreover, we analysed regional and monthly models, as well as the seasonal behaviour of the ZWD predictions in different climate zones, and found that the global model exhibits a high predictive skill in all regions and across all months of the year.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"46 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140533963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Assessment of length-of-day and universal time predictions based on the results of the Second Earth Orientation Parameters Prediction Comparison Campaign","authors":"","doi":"10.1007/s00190-024-01824-7","DOIUrl":"https://doi.org/10.1007/s00190-024-01824-7","url":null,"abstract":"<h3>Abstract</h3> <p>Predicting Earth Orientation Parameters (EOP) is crucial for precise positioning and navigation both on the Earth’s surface and in space. In recent years, many approaches have been developed to forecast EOP, incorporating observed EOP as well as information on the effective angular momentum (EAM) derived from numerical models of the atmosphere, oceans, and land-surface dynamics. The Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) aimed to comprehensively evaluate EOP forecasts from many international participants and identify the most promising prediction methodologies. This paper presents the validation results of predictions for universal time and length-of-day variations submitted during the 2nd EOP PCC, providing an assessment of their accuracy and reliability. We conduct a detailed evaluation of all valid forecasts using the IERS 14 C04 solution provided by the International Earth Rotation and Reference Systems Service (IERS) as a reference and mean absolute error as the quality measure. Our analysis demonstrates that approaches based on machine learning or the combination of least squares and autoregression, with the use of EAM information as an additional input, provide the highest prediction accuracy for both investigated parameters. Utilizing precise EAM data and forecasts emerges as a pivotal factor in enhancing forecasting accuracy. Although several methods show some potential to outperform the IERS forecasts, the current standard predictions disseminated by IERS are highly reliable and can be fully recommended for operational purposes.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"158 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140182838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Factor graph-based PPP-RTK for accurate and robust positioning in urban environments","authors":"Xin Li, Xingxing Li, Xuanbin Wang, Hanyu Chang, Yuxuan Tan, Zhiheng Shen","doi":"10.1007/s00190-024-01828-3","DOIUrl":"https://doi.org/10.1007/s00190-024-01828-3","url":null,"abstract":"<p>The PPP-RTK system, which is capable of providing a centimeter-level real-time positioning service for an unlimited number of users, is becoming a promising tool in mass-market applications such as smartphones, the Internet of Things (IoT), and the automotive industry. The extended Kalman filter (EKF) is the conventional method for parameter estimation in the existing PPP-RTK system. Recently, an alternative method known as factor graph optimization (FGO), which fully leverages the time correlation among current and historical measurements, has the potential to further improve the accuracy and robustness of PPP-RTK solutions. In this contribution, a factor graph optimization-based PPP-RTK framework is developed, where raw pseudorange, phase measurements, precise atmospheric corrections, and time-differenced carrier-phase (TDCP) measurements serve as factors in FGO estimators. The continuously tracked phase ambiguities are estimated as the time-invariant state node and propagated by marginalization while ambiguity resolution is conducted independently between epochs. A second optimization process with the utilization of ambiguity-resolved solutions and time-differenced carrier-phase (TDCP) measurements is conducted to further improve the reliability of positioning results. The effectiveness of the proposed method is evaluated by vehicular tests in urban environments. Results indicate that the FGO method could improve the performance of ambiguity resolution by reducing the ambiguity search space and increasing the ratio values, leading to a significant accuracy improvement of 55% in an open-sky environment compared to the traditional EKF-based method. Furthermore, in GNSS signal partly block scenes, the FGO-based PPP-RTK is capable of obtaining more robust and accurate positioning solutions with fewer outliers compared to the EKF method.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"9 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140145942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correcting flawed orbits with significant along-track offset in LOLA data to remove apparent noise in DEM","authors":"","doi":"10.1007/s00190-024-01827-4","DOIUrl":"https://doi.org/10.1007/s00190-024-01827-4","url":null,"abstract":"<h3>Abstract</h3> <p>The lunar orbiter laser altimeter (LOLA) onboard the lunar reconnaissance orbiter has performed high-precision, full-coverage, and high-density laser ranging observations for the entire lunar surface since its launch. Statistics have shown that LOLA has collected 6.94 billion effective altimeter data up to June 2022. Most of the typical orbits in the LOLA dataset have a high quality and exhibit horizontal offsets of almost 7 m and radial offsets of almost 0.5 m. However, there is still a category of orbits in the dataset that will cause apparent noise in the constructed DEM, which is attributed to the orbits with large or anomalous errors. We call such orbits as flawed orbits in this paper. The flawed orbits can be identified and screened by the elevation discrepancy at the crossovers of the orbits. The results show that the flawed orbits are caused by significant along-track errors, which also result in the radial error of up to several kilometers. Moreover, most of the flawed orbits are concentrated in several consecutive time intervals. A correction method is then proposed to correct the flawed orbits in the local region. The position of the flawed orbits is reconstructed using the feature points matching of the DEMs before and after they are removed. Some experimental analyzes show that the apparent terrain artifacts have been eliminated and more identifiable terrain details are reappeared. Identifying and correcting these flawed orbits with significant along-track offsets paves the way for improving the quality of the LOLA data and reconstructing the topography of the Moon.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"41 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140139511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A complete closed-form method for transformation from Cartesian to geodetic coordinates","authors":"","doi":"10.1007/s00190-024-01821-w","DOIUrl":"https://doi.org/10.1007/s00190-024-01821-w","url":null,"abstract":"<h3>Abstract</h3> <p>By introducing the auxiliary variable with respect to the reduced latitude, a new closed-form method for transforming Cartesian to geodetic coordinates has been proposed based on the solution of a special constructed unary quartic equation. The algorithm comes with rigorous and concise procedure of root-finding. Moreover, through theoretical analysis, different approaches with respective pros and cons to determine the geodetic latitude and height have been explored. Besides fast computation, numerical experiments covering the magnitude of the geodetic height from <span> <span>(- 6.33 times 10^{6} {text{m}})</span> </span> to <span> <span>(10^{10} {text{m}})</span> </span> have also shown that the new method can be operational with high precision at almost any point including the region near or at the pole, the equator and the center of the reference ellipsoid. Considering the accuracy, efficiency and adaptability simultaneously, it is prospective to be applied into computation and inspection on critical occasions in comparison to existing methods.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"502 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140043228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling trends and periodic components in geodetic time series: a unified approach","authors":"","doi":"10.1007/s00190-024-01826-5","DOIUrl":"https://doi.org/10.1007/s00190-024-01826-5","url":null,"abstract":"<h3>Abstract</h3> <p>Geodetic time series are usually modeled with a deterministic approach that includes trend, annual, and semiannual periodic components having constant amplitude and phase-lag. Although simple, this approach neglects the time-variability or stochasticity of trend and seasonal components, and can potentially lead to inadequate interpretations, such as an overestimation of global navigation satellite system (GNSS) station velocity uncertainties, up to masking important geophysical phenomena. In this contribution, we generalize previous methods for determining trends and seasonal components and address the challenge of their time-variability by proposing a novel linear additive model, according to which (i) the trend is allowed to evolve over time, (ii) the seasonality is represented by a fractional sinusoidal waveform process (fSWp), accounting for possible non-stationary cyclical long-memory, and (iii) an additional serially correlated noise captures the short term variability. The model has a state space representation, opening the way for the evaluation of the likelihood and signal extraction with the support of the Kalman filter (KF) and the associated smoothing algorithm. Suitable enhancements of the basic methodology enable handling data gaps, outliers, and offsets. We demonstrate the advantage of our method with respect to the benchmark deterministic approach using both observed and simulated time series and provide a fair comparison with the Hector software. To that end, various geodetic time series are considered which illustrate the ability to capture the time-varying stochastic seasonal signals with the fSWp.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"66 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140024895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Triangulation of the Earth’s surface and its application to the geodetic velocity field modelling","authors":"Sandi Berk","doi":"10.1007/s00190-023-01817-y","DOIUrl":"https://doi.org/10.1007/s00190-023-01817-y","url":null,"abstract":"<p>The Earth’s crust is exposed by tectonic processes and is not static over time. Modelling of the Earth’s surface velocities is of utmost importance for research in geodesy, geophysics, structural geology, and other geosciences. It may support positioning, navigation, seismic risk, and volcano notification services, for example. Space geodetic techniques can be used to provide high-quality velocities in a network of geodetic sites. Velocity field modelling should, however, expand the velocities from a discrete set of points to any location in-between. This paper presents four new methods for the Earth’s surface velocity interpolation. Contrary to the widely used approach dividing the velocity field to the horizontal and vertical components, a full 3D interpolation approach is proposed based on the Delaunay triangulation and the n-simplex interpolation. The use of a combination of all three components is advantageous for\u0000geophysical interpretation. The proposed interpolation approach is entirely local but enables global modelling, which does not suffer from map projection distortions and singularities at the poles. Various global and regional position/velocity datasets are used to evaluate the performance of the proposed velocity interpolation methods. The latter provide practically the same results when applied to regional velocity field modelling. However, the so-called continuous piecewise quasi-radial 3D velocity field interpolation method is recommended for its favourable properties. It introduces an ellipsoidal Earth model, appropriately considers vertical/up and horizontal velocity components, tends to radial symmetry, and provides continuity for the interpolated velocity components as well as for the estimated uncertainties.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"2014 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139938795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}