{"title":"Determination of the time-variable geopotential by means of orbiting clocks","authors":"Simone Giuliani, Byron D. Tapley, John C. Ries","doi":"10.1007/s00190-024-01868-9","DOIUrl":"https://doi.org/10.1007/s00190-024-01868-9","url":null,"abstract":"<p>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 <span>({10}^{-18})</span>. Presently, terrestrial clocks can routinely attain fractional frequency stabilities of <span>({10}^{-18})</span>, whereas spaceborne clocks are still at the <span>({10}^{-15})</span> 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.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"26 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141264820","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}
Jorge Ventura, Fernando Martinez, Francisco Manzano-Agugliaro, Aleš Návrat, Jaroslav Hrdina, Ahmad H. Eid, Francisco G. Montoya
{"title":"A novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensions","authors":"Jorge Ventura, Fernando Martinez, Francisco Manzano-Agugliaro, Aleš Návrat, Jaroslav Hrdina, Ahmad H. Eid, Francisco G. Montoya","doi":"10.1007/s00190-024-01854-1","DOIUrl":"https://doi.org/10.1007/s00190-024-01854-1","url":null,"abstract":"<p>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.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"26 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141159641","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}
Jullian Rivera, Srinivas Bettadpur, John Griffin, Zhigui Kang, John Ries
{"title":"Measuring 1-mm-accurate local survey ties over kilometer baselines at McDonald Geodetic Observatory","authors":"Jullian Rivera, Srinivas Bettadpur, John Griffin, Zhigui Kang, John Ries","doi":"10.1007/s00190-024-01853-2","DOIUrl":"https://doi.org/10.1007/s00190-024-01853-2","url":null,"abstract":"<p>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.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"44 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141156707","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}
Léo Martire, Thomas F. Runge, Xing Meng, Siddharth Krishnamoorthy, Panagiotis Vergados, Anthony J. Mannucci, Olga P. Verkhoglyadova, Attila Komjáthy, Angelyn W. Moore, Robert F. Meyer, Byron A. Ijima, Donald W. Green
{"title":"The JPL-GIM algorithm and products: multi-GNSS high-rate global mapping of total electron content","authors":"Léo Martire, Thomas F. Runge, Xing Meng, Siddharth Krishnamoorthy, Panagiotis Vergados, Anthony J. Mannucci, Olga P. Verkhoglyadova, Attila Komjáthy, Angelyn W. Moore, Robert F. Meyer, Byron A. Ijima, Donald W. Green","doi":"10.1007/s00190-024-01860-3","DOIUrl":"https://doi.org/10.1007/s00190-024-01860-3","url":null,"abstract":"<p>The Jet Propulsion Laboratory (JPL) develops JPL-GIM, a software for generating global ionospheric maps (GIMs) of total electron content (TEC) using measurements from multiple Global Navigation Satellite System (GNSS) constellations. Within this overview paper, we delve into the current state and the most recent enhancements of JPL-GIM. An adaptable Kalman filter provides maps with user-defined temporal and spatial resolutions, while concurrently delivering essential covariance data for uncertainty assessment. Furthermore, multiple shell models offer a versatile framework to balance accuracy and computational efficiency. We present the five operational JPL GIM products (JPLG, JPRG, JPLI, JPLD, JPRT), highlighting JPLG and JPRG, our products routinely delivered to the International GNSS Service (IGS), and introduce a new near-real-time product (JPRT). As an added demonstration of JPL-GIM’s capabilities, we present a very-high-resolution (2-minute, multi-GNSS, 1000-station) configuration to showcase JPL-GIM’s ability to resolve long-lasting effects of the 2022 Hunga Tonga-Hunga Ha’apai eruption. Validations using independent datasets confirm the accurate reproduction of ionospheric variations across all latitudinal bands.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"65 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141096680","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":"On the optimality of DIA-estimators: theory and applications","authors":"P. J. G. Teunissen","doi":"10.1007/s00190-024-01859-w","DOIUrl":"https://doi.org/10.1007/s00190-024-01859-w","url":null,"abstract":"<p>In this contribution, we introduce, in analogy to penalized ambiguity resolution, the concept of penalized misclosure space partitioning, with the goal of directing the performance of the DIA-estimator towards its application-dependent tolerable risk objectives. We assign penalty functions to each of the decision regions in misclosure space and use the distribution of the misclosure vector to determine the optimal partitioning by minimizing the mean penalty. As each minimum mean penalty partitioning depends on the given penalty functions, different choices can be made, in dependence of the application. For the DIA-estimator, we introduce a special set of penalty functions that penalize its unwanted outcomes. It is shown how this set allows one to construct the optimal DIA-estimator, being the estimator that within its class has the largest probability of lying inside a user specified tolerance region. Further elaboration shows how these penalty functions are driven by the influential biases of the different hypotheses and how they can be used operationally. Hereby the option is included of extending the misclosure partitioning with an additional undecided region to accommodate situations when it will be hard to discriminate between some of the hypotheses or when identification is unconvincing. By extending the analogy with integer ambiguity resolution to that of integer-equivariant ambiguity resolution, we also introduce the maximum probability estimator within the similar larger class.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"23 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141079196","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}
Adam Cegla, Witold Rohm, Gregor Moeller, Paweł Hordyniec, Estera Trzcina, Natalia Hanna
{"title":"GNSS signal ray-tracing algorithm for the simulation of satellite-to-satellite excess phase in the neutral atmosphere","authors":"Adam Cegla, Witold Rohm, Gregor Moeller, Paweł Hordyniec, Estera Trzcina, Natalia Hanna","doi":"10.1007/s00190-024-01847-0","DOIUrl":"https://doi.org/10.1007/s00190-024-01847-0","url":null,"abstract":"<p>Traditionally, GNSS space-based and ground-based estimates of tropospheric conditions are performed separately. It leads to limitations in the horizontal (e.g., a single space-based radio occultation profile covers a 300 km slice of the troposphere) and vertical resolution (e.g., ground-based estimates of troposphere conditions have spacing equal to stations’ distribution) of the tropospheric products. The first stage to achieve an integrated model is to create an effective 3D ray-tracing algorithm for the satellite-to-satellite (radio occultation) path reconstruction. We verify the consistency of the simulated data with the RO observations from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-1) Data Analysis and Archive Center (CDAAC) in terms of excess phase and bending angle. The results show that our solution provides an effective RO excess phase, with a relative error varying from 35% at the height of 25–30 km (1.0–1.5 m) to 0.5% at heights 5–10 km (0.1–1 m) and 14 to 2% at heights below 5 km (2–14 m). The bending angle retrieval on simulated data attained for high-resolution ray-tracing, bias lower than 2% with respect to the observed bending angle. The optimal solution takes about 1 s for one transmitter–receiver pair with a tangent point below 5 km altitude. The high-resolution processing solution takes 3 times longer.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"40 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141079179","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":"Gravity field modeling in mountainous areas based on band-limited SRBFs","authors":"Zhiwei Ma","doi":"10.1007/s00190-024-01852-3","DOIUrl":"https://doi.org/10.1007/s00190-024-01852-3","url":null,"abstract":"<p>In this study, a novel two-scale spherical radial basis function (SRBF) modeling method is proposed for regional gravity field determination. First, satellite-only global gravity field models (GGMs) are combined with airborne gravity data at medium-frequency bands, and a series of combined gravity field models based on band-limited SRBFs are established for the mountainous areas of California and Oregon. The combined gravity field models are then compared with the airborne-only gravity field models. The results show that the combined models exhibit standard deviation (STD) values of 0.106–0.120 m in terms of geoid height differences w.r.t. the global positioning system (GPS)/leveling data, while the corresponding airborne-only models yield STD values of 0.126–0.131 m. The STD values of the combined models are reduced by 0.9–2.0 cm, which implies a potential benefit for the medium-frequency gravity field modeling by combining GGM and airborne gravity data. Second, after removing the low-frequency and medium-frequency gravity field signals as well as the residual terrain model signals from gravity data, a second SRBF modeling process is implemented using multisource residual gravity data. Subsequently, a high-resolution two-scale SRBF gravity field model is constructed for the mountainous areas of California and Oregon. The results indicate that the STD of geoid height differences for the two-scale SRBF model w.r.t. the GPS/leveling data is 0.098 m, with reductions of 3.0–6.2 cm compared to the models based on the single-scale SRBF modeling method. These findings indicate the effectiveness of the two-scale SRBF modeling method for refining the regional gravity field model in complex areas.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"49 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141069270","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":"Bias-constrained integer least squares estimation: distributional properties and applications in GNSS ambiguity resolution","authors":"A. Khodabandeh, P. J. G. Teunissen","doi":"10.1007/s00190-024-01851-4","DOIUrl":"https://doi.org/10.1007/s00190-024-01851-4","url":null,"abstract":"<p>To accommodate the presence of bounded biases in mixed-integer models, Khodabandeh (2022) extended integer estimation theory by introducing a new admissible integer estimator. The estimator follows the principle of integer least squares estimation and is computed via the integer search method of BEAT. In this contribution, we present the probability distributions of a class of estimators to which the proposed bias-constrained integer least squares estimation belongs. Some important interferometric measuring systems, whose estimation problems can be covered by BEAT, are identified. To show the proposed estimator at work, we apply BEAT to the problem of GLONASS single-differenced (SD) ambiguity resolution. Numerical results of several short-baseline datasets are presented to illustrate why one can achieve more accurate positioning solutions when considering between-receiver SD ambiguity resolution for the cases where carrier phase data are captured on frequency-varying signals with bounded SD receiver phase delays.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"34 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140919636","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}
Alex Conrad, Penina Axelrad, Shailen Desai, Bruce Haines
{"title":"Sentinel-6 Michael Freilich precise orbit determination using PODRIX and TriG receiver measurements","authors":"Alex Conrad, Penina Axelrad, Shailen Desai, Bruce Haines","doi":"10.1007/s00190-024-01842-5","DOIUrl":"https://doi.org/10.1007/s00190-024-01842-5","url":null,"abstract":"<p>The Sentinel-6 Michael Freilich altimetry mission flies two GNSS receivers: a primary multi-GNSS (GPS plus Galileo) PODRIX receiver and a GPS-only TriG receiver. Each of these receivers is independently capable of supporting the precise orbit determination (POD) requirement for < 1.5 cm radial rms error. In this study, we characterize the performance of single-receiver solutions and evaluate the benefits of a combined TriG and PODRIX orbit solution. The availability of both sets of receiver observations revealed a 10 mm in-track difference between orbit solutions derived independently from TriG and PODRIX tracking data. Based on satellite laser ranging (SLR) residuals, this bias has been isolated to an apparent inconsistency between the estimated TriG receiver clock and observation time-tags of approximately 1.3 <span>(mu hbox {s})</span>, which is equivalent to a common range error of roughly 400 m in the TriG observations. After applying this calibration, the TriG and PODRIX displayed similar performance in terms of orbit overlap precision. PODRIX-Galileo observations showed lower code and phase tracking residual rms values compared to the GPS observations. Overall, processing the calibrated TriG and PODRIX observations separately results in highly accurate orbit solutions with radial orbit accuracies better than 1 cm rms as indicated by one-way SLR residual rms of 7.2 mm or better for each solution. Orbit solution accuracy is slightly improved by processing both TriG and PODRIX observations together, resulting in one-way SLR residual rms of 7.0 mm.\u0000</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"33 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140907413","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}