{"title":"Simulation of errors related to the VLBI transmitter on Genesis and their impact on the terrestrial reference frame","authors":"Helene Wolf, Lisa Kern, Johannes Böhm","doi":"10.1007/s00190-026-02120-2","DOIUrl":"https://doi.org/10.1007/s00190-026-02120-2","url":null,"abstract":"Mission Genesis of the European Space Agency has been approved for launch in 2028. Its primary goal is the enhancement of the terrestrial reference frame by establishing a space tie on the Genesis satellite between all space geodetic techniques used for the determination of the frame. The satellite will be equipped with a dedicated Very Long Baseline Interferometry (VLBI) transmitter for geodesy. In this work, simulation studies with a global 20-station VLBI network are carried out to assess the impact of errors related to the VLBI transmitter on the terrestrial reference frame, more precisely on station coordinates derived from VLBI observations to Genesis. Our findings indicate that the calibration of the position of the VLBI transmitter on Genesis is critical for the success of the mission. Errors in the position at the one-centimeter-level will cause station coordinate errors of several millimeters. In particular, the tangential and cross-track components do have a significant influence. The precision of the VLBI group delays, however, is not as critical. Simulating white noise for the group delays of 40 ps does still yield station coordinate accuracies at the millimeter level, if estimated in a global solution from weekly 24-h sessions over five years. Considering the investigated aspects, the simulations confirm that the VLBI-related goals of Genesis can be achieved, if stringent requirements with the VLBI transmitter are fulfilled.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"56 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149221447","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}
Zitong Zhu,Vitali Müller,Changqing Wang,Yihao Yan,Heng Yin,Jiangjun Ran,Haoming Yan
{"title":"Impact of range scale factor and baseline biases on gravity field estimation: analysis and validation with GRACE follow-on data and simulations","authors":"Zitong Zhu,Vitali Müller,Changqing Wang,Yihao Yan,Heng Yin,Jiangjun Ran,Haoming Yan","doi":"10.1007/s00190-026-02123-z","DOIUrl":"https://doi.org/10.1007/s00190-026-02123-z","url":null,"abstract":"Abstract GRACE/GRACE-FO missions recover gravity field from orbits observed by GPS and variations in inter-satellite distances obtained by the inter-satellite ranging systems. Compared to GRACE, GRACE-FO is also equipped with a laser ranging interferometer (LRI), a more precise inter-satellite ranging technology and the preferred choice for future gravity missions. While the majority of studies predominantly focus on stochastic errors, this research highlights the critical role of non-stochastic biases, specifically the range scale factor for the K-Band ranging (KBR) and LRI data, and baseline biases in GPS observations, i.e., offsets over the ~200 km separation. The effects of range scale factor and baseline biases on the gravity field spherical harmonic coefficients (SHCs) are evaluated through simplified bias models (SBM). We demonstrate that baseline biases exert an influence on the SHCs in a manner analogous to that of the range scale factor. At low SH degrees (2–8), range scale factor and baseline biases impact SHCs approximately proportional to the static gravity field coefficients. The SBM agrees well with error-free simulations, but deviations appear at higher degrees (8–60) when background model errors are included and scale biases are below 1 ppm. Additionally, the effectiveness of the SBM is validated using real GRACE-FO data. A strong correspondence was observed between the scale factor corrections and the C 20 relative errors, which provides a practical basis for error budgeting in future missions. These findings indicate the significant impact of scale factors and baseline biases on gravity missions, which can be effectively evaluated using the SBM presented here.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"1 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209733","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}
Georgia Gavriilidou,Dimitrios Tsoulis,Georgios Vergos,Elisavet Maria Mamagiannou,Thomas Papanikolaou,Dimitrios Natsiopoulos
{"title":"Precise topographic modelling in the frame of a cm-level IHRF realization","authors":"Georgia Gavriilidou,Dimitrios Tsoulis,Georgios Vergos,Elisavet Maria Mamagiannou,Thomas Papanikolaou,Dimitrios Natsiopoulos","doi":"10.1007/s00190-026-02118-w","DOIUrl":"https://doi.org/10.1007/s00190-026-02118-w","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"13 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209736","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":"An evaluation of global ionosphere maps for the ionospheric correction of C-band InSAR data","authors":"Xue Li,Cunren Liang,Jiafeng Li,Kejie Chen","doi":"10.1007/s00190-026-02084-3","DOIUrl":"https://doi.org/10.1007/s00190-026-02084-3","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"12 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209737","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":"Gravitational field of a homogeneous spherical longitudinal sector","authors":"Xiao-Le Deng,Nico Sneeuw","doi":"10.1007/s00190-026-02110-4","DOIUrl":"https://doi.org/10.1007/s00190-026-02110-4","url":null,"abstract":"Abstract When investigating the gravitational field (e.g., gravitational potential, gravitational vector, gravitational gradient tensor, and gravitational curvature) in the spherical coordinate system, there are currently three benchmarks: a spherical shell, a spherical zonal band, and a spherical prism. To obtain simple analytical formulas similar to those of a spherical shell and to reduce computation time with respect to a spherical zonal band, we introduce a spherical longitudinal sector as a new benchmark. It is defined geometrically as the part of a spherical shell confined between two meridians. Alternatively, one can consider the spherical longitudinal sector to be a spherical prism without latitude restrictions, i.e., extending from pole to pole. Based on the relationship with a spherical prism, we derive analytical expressions for the gravitational potential, gravitational vector, gravitational gradient tensor, and gravitational curvature of a homogeneous spherical longitudinal sector when the computation point is on the polar axis. The effectiveness of this proposed benchmark of a spherical longitudinal sector discretized into spherical prisms has been validated through numerical experiments. Numerical results indicate that, compared to a spherical zonal band discretized into spherical prisms, a spherical longitudinal sector improves computational efficiency by a factor of 2, corresponding to a 50% reduction in computation time when the longitudinal and colatitudinal grid sizes are identical. A spherical longitudinal sector computes roughly 360/ n times faster than a spherical shell, where n is the longitudinal grid size in degree. The analytical expressions for the gravitational field of a homogeneous spherical longitudinal sector can be an additional benchmark for the gravity forward modeling in geodesy, geophysics, and planetary sciences.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"25 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209735","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}
David Schunck, Lucia McCallum, Jamie McCallum, Tiege McCarthy
{"title":"Comprehensive VLBI observations of Galileo satellites with the AuScope array","authors":"David Schunck, Lucia McCallum, Jamie McCallum, Tiege McCarthy","doi":"10.1007/s00190-026-02124-y","DOIUrl":"https://doi.org/10.1007/s00190-026-02124-y","url":null,"abstract":"Interest in the topic of geodetic co-location in space and space ties has recently intensified within the geodetic community, particularly following the approval of the European Space Agency’s Genesis mission. From the perspective of very long baseline interferometry (VLBI), observations of Earth-orbiting satellites are not standard practice yet. To enable VLBI support for future co-location satellite missions, such observations must be integrated into the VLBI processing chain. In this study, we present comprehensive VLBI observations of Galileo navigation satellites conducted with the Australian AuScope VLBI array. Using the 12-m antennas in Hobart, Katherine, and Yarragadee equipped with VLBI Global Observing System instrumentation, Galileo E1 and E6 signals were observed in test experiments and a series of four full-scale 24-h observing sessions. We present the estimation of VLBI station coordinates from observations to navigation satellites, thereby demonstrating, for the first time, inter-technique ties between the VLBI and global navigation satellite system (GNSS) frame. We describe the processing strategy, including correlation, fringe fitting, precision assessment, and satellite tracking approach. Delay observables achieve precisions of a few picoseconds in the E1 band and several tens of picoseconds in the E6 band for 1-s integration times. However, unmodelled signals on the order of several hundred picoseconds are found in the residual delays. Estimated station coordinates agree with a priori values at the metre level, while baseline lengths agree at the sub-metre level. These results demonstrate the feasibility of large-scale VLBI observations to GNSS satellites and provide critical groundwork for future co-location satellite missions such as Genesis.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"94 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149130453","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":"Sequential integral inversion in regional gravity field modelling","authors":"Mehdi Eshagh","doi":"10.1007/s00190-026-02102-4","DOIUrl":"https://doi.org/10.1007/s00190-026-02102-4","url":null,"abstract":"Abstract Two sequential strategies for the integral inversion of multi-platform gravimetric observations are presented for regional gravity field modelling. In contrast to conventional batch solutions, the proposed approaches enable the progressive combination of large, heterogeneous and ill-conditioned systems while preserving full stochastic information. In the first, a priori background information and its variance–covariance matrix (VCM) are incorporated in a formulation conceptually analogous to data assimilation, allowing the sequential update of the solution and its precision measures. In the second, multiple ill-conditioned systems derived from discretised integral equations are combined sequentially without external background information. For both approaches, rigorous models are derived for the sequential propagation and combination of observations, VCMs, a posteriori variances and regularisation-induced biases within a Tikhonov regularisation framework. The methods are applied to the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient data over Central Europe during August–September 2013. A total of 94,540 observations are divided into ten subsets and processed sequentially to recover gravity anomalies at sea level. The results are compared with a conventional batch inversion. When reliable background information is available, the first algorithm yields stable and consistent solutions. The second algorithm produces results largely equivalent to the batch solution, with differences generally below 1 mGal in standard deviation. The proposed formulation provides a computationally feasible and fully stochastic alternative to batch integral inversion for large gravimetric data sets and enables the consistent integration of multi-platform observations in regional gravity field modelling.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"9 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149091360","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":"Numerical computation of the gravitational field of a geodetic tesseroid","authors":"Toshio Fukushima","doi":"10.1007/s00190-026-02105-1","DOIUrl":"https://doi.org/10.1007/s00190-026-02105-1","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"1 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149091361","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}