Journal of Geodesy最新文献

{"title":"Multi-objective optimization of inter-satellite links assignment for GNSS based on constrained non-dominated sorting genetic algorithm","authors":"Xiaoying Gong, Mengyao Chai, Shixiang Cai, Shilong Zhang, Dingfa Huang","doi":"10.1007/s00190-026-02093-2","DOIUrl":"https://doi.org/10.1007/s00190-026-02093-2","url":null,"abstract":"Global Navigation Satellite System (GNSS) satellites are capable of ranging and communicating with one another through Inter-Satellite Links (ISLs), thereby enhancing system autonomy. ISL assignment can be formulated as a complex Constrained Multi-objective Optimization Problem (CMOP). It is critical to GNSS performance but is heavily constrained by compact satellite platforms and point-to-point link types. Prior research has predominantly focused on meeting communication and ranging requirements, often neglecting the load-balancing requirement within the system. To address these challenges, we propose the Constrained ISL-dependent NSGA-II (C-ISL-NSGA-II) method. This algorithm incorporates a novel Constrained Single-Link Rebuilding (CSLR) mutation operator and simultaneously optimizes ranging, communication, and load-balancing performance. Using the BeiDou constellation as a case study, we demonstrate that the CSLR mutation operator outperforms traditional Exchange Mutation (EM) and Displacement Mutation (DM) operators. It achieves faster convergence and superior solution quality across all three objectives. Additionally, we analyze the effects of crossover and mutation rates, finding that a configuration with a high mutation rate and a low crossover rate yields the best Pareto-set approximation for the BeiDou-3 constellation. An empirical parametric study indicates that employing 900 generations with a population of 100 individuals achieves a favorable trade-off among convergence speed, diversity, and computational cost. Compared with randomly generated initial solutions, the mean values of WAPDOP, SDDTD, and WAVWNL in the obtained Pareto-optimal solutions are reduced by 63%, 72%, and 78%, respectively. Finally, by expanding the problem to incorporate a third load-balancing objective, we observe a significant reduction in total link loads and inter-satellite load disparities, albeit at the expense of a slight decrease in ranging accuracy.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"2 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552215","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":"Spherical harmonic expansions for the gravitational field of a tesseroid with radially variable density","authors":"Jinbo Li, Heping Sun","doi":"10.1007/s00190-026-02061-w","DOIUrl":"https://doi.org/10.1007/s00190-026-02061-w","url":null,"abstract":"We derive spherical harmonic coefficients for the external gravitational potential generated by a tesseroid with radially variable density. The Newtonian volume integrals required to compute the coefficients are decomposed into 2D surface integrals and 1D radial integrals. Analytical expressions are derived for the radial integrals corresponding to polynomial, exponential, and parabolic density functions, while an adaptive Gauss–Legendre quadrature is used to numerically evaluate the radial integrals for general smooth density distributions. Simplified expressions for the surface integrals are further obtained of special geometries, including spherical zonal bands, spherical sectors, and spherical shells. The derived formulas extend the tesseroid-based spectral technique for gravimetric forward modeling beyond the common assumption of constant density within each tesseroid. Benchmark tests indicate that our approach is reliable and offers a favorable trade-off of accuracy and efficiency. No pronounced polar-singularity and polar-region problems are observed, whereas a near-zone problem appears as evaluation points approach the source. This behavior is primarily attributed to truncation errors and can be mitigated by increasing the truncated harmonic degree, leading to good agreement with a spatial-domain double exponential quadrature method. Finally, we compute the gravitational field of global marine sediments with 3D variable density and provide the resulting potential coefficients model to support related geodetic and geophysical applications.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"32 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552128","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 improved picosecond-level laser time transfer for China’s space station","authors":"Renfang Geng, Zhibo Wu, Yong Huang, Kai Tang, Haifeng Zhang, Wendong Meng, Zhien Cheng, Yanming Guo, Shuaihe Gao, Wenbin Wang, Xinyuan Mao, Tong Liu, Zhibao Wang, Xiao Wang, Zhongping Zhang","doi":"10.1007/s00190-026-02095-0","DOIUrl":"https://doi.org/10.1007/s00190-026-02095-0","url":null,"abstract":"The development of techniques for the comparison of remote clocks plays an important role in metrology and fundamental science. Recent progress in the domain of ground-based and space-based atomic clocks requires important improvements in existing time and frequency transfer links. Here, we propose a satellite-based improved laser time transfer (ILTT) scheme based on existing satellite laser ranging (SLR) technique, which has been deployed on the Mengtian Laboratory Module of China’s Space Station (CSS). The ILTT payload comprises a single-photon avalanche diode (SPAD), a multi-level optimized optical system, an event timer, and a laser retroreflector array (LRA). A repetition rate of 10 kHz is adopted to improve normal-point precision. Laboratory experiments demonstrate that the time deviation (TDEV) of the entire ILTT system was better than 1 ps at 1 s and 0.6 ps at 100,000 s. In addition, we introduce a relativistic laser time transfer model and evaluate the impact of relativistic frequency shift terms on time transfer stability, meeting the requirements of the high-precision time–frequency rack (HTFR) mission aboard the CSS. In the on-orbit experiments, we have achieved state-of-the-art satellite-to-ground time synchronization with a precision of 2–5 ps at 1 s and a TDEV of 0.7 ps at 50 s. This approach is also sufficient for future time transfer links to geosynchronous and cislunar orbits.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"34 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552214","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":"Celestial pole offsets prediction with multiple data sources: a data-driven approach","authors":"Marcin Ligas, Maciej Michalczak, Santiago Belda, Jose M. Ferrándiz, Maria Karbon, Sadegh Modiri","doi":"10.1007/s00190-026-02092-3","DOIUrl":"https://doi.org/10.1007/s00190-026-02092-3","url":null,"abstract":"This paper presents a hybrid prediction approach based on Dynamic Mode Decomposition principle and designed to improve 30-day forecasts of the celestial pole offset (CPO), expressed through its components dX and dY. We assess the method in an experimental framework referenced to the IERS EOP 14 C04 and IERS EOP 20 C04 series. The procedure also incorporates the JPL dX, dY time series as an auxiliary input, used as a supplementary source of information during prediction. To ensure consistency with the IERS CPO values, predictions generated from the JPL series are systematically transformed using total least squares (orthogonal) regression, explicitly accounting for measurement uncertainties in both datasets. In parallel, the IERS CPO series is preprocessed with a penalized least-squares smoother (Whittaker smoother); the resulting smoothed series is then treated as an additional information source within the prediction routine. A key feature of this workflow is that it avoids relying on external data to bridge latency gaps in the final IERS product. Instead, gap handling is performed internally as part of the prediction process, making the method well suited to real-time applications. The experimental setup therefore mirrors operational conditions by combining prediction with simultaneous gap filling. We benchmark the approach against results from the 2nd Earth Orientation Parameters Prediction Comparison Campaign (EOPPCC) and also evaluate its long-term performance in a 10-year experiment using two IERS reference series (EOP 14 C04 and EOP 20 C04). In this long-term test, the best-performing variants for dX (EOP 14 C04) achieve an average mean absolute error (MAE) of 61.5 µas at day 10 and 64.2 µas at day 30; for EOP 20 C04, the corresponding values are 68.9 µas and 72.1 µas. For dY, the averaged MAE with EOP 14 C04 is 66.1 µas at day 10 and 71.8 µas at day 30, while for EOP 20 C04 it is 74.4 µas and 78.0 µas, respectively. In the 2nd EOPPCC comparison, the top variants yield MAE ranges of 40–55 µas for dX and 50–80 µas for dY across the full 30-day forecast horizon.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"120 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612847","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":"Enhancing real-time LEO kinematic precise orbit determination during ionospheric disturbances by optimizing stochastic model and cycle-slip detection","authors":"Yehao Zhao, Keke Zhang, Xingxing Li, Wei Zhang","doi":"10.1007/s00190-026-02090-5","DOIUrl":"https://doi.org/10.1007/s00190-026-02090-5","url":null,"abstract":"Real-time kinematic precise orbit determination (KPOD) is inherently a precise point positioning (PPP)-based method for estimating the precise position of low Earth orbit (LEO) satellites, which relies solely on the onboard global navigation satellite system (GNSS) observations without considering the dynamic model. The high precision and continuous tracking capability of GNSS enable excellent KPOD of LEO satellites. However, the performance of KPOD is severely degraded during ionospheric disturbances, as the geometry-free (GF) cycle-slip detection becomes less reliable and the standard observation stochastic model proves inadequate for characterizing scintillation signals. To address these challenges, two new metrics, the acceleration of total electron content (AOT) and the AOT index (AOTI) are defined in this study. AOT represents the second-order time derivative of the total electron content (TEC), while AOTI is the standard deviation of AOT. AOT and AOTI are proposed to address the unreliable cycle-slip detection and the inadequate stochastic model, respectively, during ionospheric disturbances. By eliminating the first-order variation of TEC, AOT-based GF cycle-slip detection method can prevent the over-detection of spurious cycle slips without increasing the detection threshold. When AOT remains constant over a short interval (e.g., 10 s), AOTI serves as a proportional proxy for phase observation noise, permitting its real-time, on-the-fly estimation. The implementation of AOT and AOTI yields a significant improvement in real-time KPOD of the Swarm-A satellite. During ionospheric disturbances over the last five years, the average improvements in the root mean square (RMS) values computed from orbit errors below the 95th percentile are 21.4% (A), 17.2% (C), 31.6% (R), and 26.1% (3D). Corresponding improvements in the 95th percentile values are 29.7% (A), 22.4% (C), 42.4% (R), and 37.0% (3D). It validates the efficacy of AOT and AOTI as robust metrics for enhancing GNSS-based KPOD of LEO satellites during ionospheric disturbances. Besides, a more substantial reduction in the 95th percentile value compared to the RMS value indicates that the method specifically targets and mitigates the larger orbit errors.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"1 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552129","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":"The development of the unified Baltic Sea Chart Datum 2000 (BSCD2000) height transformation grid: an unprecedented example of height system unification based on state-of-the-art marine geoid modelling","authors":"Joachim Schwabe, Sander Varbla, Jonas Ågren, Hergeir Teitsson, Artu Ellmann, Gunter Liebsch, René Forsberg, Gabriel Strykowski, Mirjam Bilker-Koivula, Ivars Liepiņš, Eimuntas Paršeliūnas, Kristian Keller, Ove Christian Dahl Omang, Olav Vestøl, Jānis Kaminskis, Monika Wilde-Piórko, Małgorzata Szelachowska, Krzysztof Pyrchla, Jarosław Somla, Patrick Westfeld, Thomas Hammarklint, Per-Anders Olsson, Christoph Förste, E. Sinem Ince","doi":"10.1007/s00190-026-02096-z","DOIUrl":"https://doi.org/10.1007/s00190-026-02096-z","url":null,"abstract":"The shallow Baltic Sea is a vital waterway with dense shipping traffic, requiring accurate and reliable nautical charts for safe navigation. Until recently, different realisations of the mean sea level were used in the paper charts of each country, sometimes even between harbours. This created obstacles for the digitalisation of ship navigation, including electronic nautical charts combined with satellite-based positioning. To resolve this, the Baltic Sea Hydrographic Commission decided in 2013 to introduce the Baltic Sea Chart Datum 2000 (BSCD2000) as a common height/depth reference system for the maritime sector in the Baltic Sea. The new reference level for all depth and water level information is strictly the quasigeoid, which is practically identical to the geoid at sea. The BSCD2000 is defined in accordance with the European reference systems: the European Terrestrial Reference System 1989 (ETRS89) for ellipsoidal coordinates and the European Vertical Reference System (EVRS) for physical heights. This enables the practical implementation of the zero level through a seamless height transformation grid with standard uncertainties of approximately 1–2 cm, which is harmonised with national coordinates, heights, and height reference surfaces. To the authors’ knowledge, this level of harmonisation is unprecedented in the maritime sector and exemplifies the value of the unification of height systems in geodesy. The paper outlines the foundations of the BSCD2000 and the approach to construct the BSCD2000 height transformation grid. While the computation of the gravimetric marine quasigeoid model is based on well-established methods, special focus is placed on practical harmonisation across national borders and along the coastline. To this end, a novel fitting and blending scheme based on distance maps was developed. Finally, comparison of the new gravimetric marine quasigeoid solution with a preliminary geometric marine geoid model based on SWOT altimetry data and hydrodynamic modelling confirmed good agreement within a few centimetres in most areas of the Baltic Sea.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"1 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612846","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 discrete contraction conjecture for estimating gravity fields on irregular closed surfaces","authors":"Crichton Ogle, Michael Bevis, Dena Asta, Dean Ogle, Jim Fowler","doi":"10.1007/s00190-026-02074-5","DOIUrl":"https://doi.org/10.1007/s00190-026-02074-5","url":null,"abstract":"We construct an estimator for gravitational potential on an irregular closed surface as a finite spherical polynomial, based on a finite number of sample observations. This estimator is a natural discrete adaptation of an approximation for gravitational potential suggested by Sanso and Sideris. We consider the following discrete analogue of their conjecture: that the error in our estimator is a contraction operator, implying that the estimation process can be iterated to approximate gravitational potential to arbitrarily levels of accuracy. We then offer evidence for the conjecture through a series of numerical simulations and conclude with a simulation using a model of the Earth’s topography and real-world data.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"16 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148409144","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":"TropDS: downscaling to enhance tropospheric delay grid precision in space geodesy","authors":"Junsheng Ding, Wu Chen, Junping Chen, Jungang Wang, Yize Zhang","doi":"10.1007/s00190-026-02086-1","DOIUrl":"https://doi.org/10.1007/s00190-026-02086-1","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"40 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148409145","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 hybrid genetic algorithm for calculating the relaxation time constants of stochastic post-seismic GPS coordinate time series","authors":"Chang Xu, Yan Cui, Xiaoxing He","doi":"10.1007/s00190-026-02087-0","DOIUrl":"https://doi.org/10.1007/s00190-026-02087-0","url":null,"abstract":"Modeling post-seismic deformation (PSD) of Global Positioning System (GPS) station trajectory models invokes logarithmic or/and exponential decay functions with pre-assigned relaxation time constants (RTCs). We propose a hybrid optimization method combining genetic algorithms and interior-point techniques to determine station-specific RTCs. Two criteria (root mean square (RMS) misfit and the Akaike Information Criterion (AIC), a posterior measure of log-likelihood) are used to gauge the goodness of fit. Validation was performed on synthetic data and eight daily GPS coordinate time series subject to the 2011 Tohoku-Oki earthquake in Japan. We find that the temporally correlated noise, optimization strategy and the tradeoffs among sub-models of station trajectory jointly govern the identification of decay function form and the accuracy of inferred RTCs. The double logarithmic model can fit the post-seismic data well and exhibits more uniform RTCs, making it more practical for PSD modeling. Significant trajectory misfit is evident during the initial weeks to months after the earthquake, with millimeter-level discrepancies observed between the RMS and AIC criteria. Incorrect RTC assignments further exacerbate these discrepancies and introduce biases into PSD modeling and co-seismic offset estimation, risking misleading post-seismic predictions.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"1 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355546","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":"Extended zenith delay prediction for SLR based on quasi-hydrostatic approximations","authors":"Yuanchen Fu, Keke Zhang, Xingxing Li, Yuxin Zheng, Wei Zhang, Yingzhe Li","doi":"10.1007/s00190-026-02076-3","DOIUrl":"https://doi.org/10.1007/s00190-026-02076-3","url":null,"abstract":"Tropospheric delay is the crucial modeling error in satellite laser ranging (SLR). The current tropospheric model for SLR neglects the Coriolis term, implicitly assuming vanishing horizontal winds. Here, we extend the Coriolis term based on quasi-hydrostatic approximations and validate the model with 3 years of ray-tracing and SLR-derived geodetic parameters. Omitting the Coriolis term induces a mean bias of –0.3 mm in zenith hydrostatic delay, which is non-negligible when considering the 1 mm accuracy requirement for the ITRF. The proposed model removes this bias. For the geodetic parameter, the proposed model shifts the terrestrial scale by + 0.07 ppb, eliminating 46.7% of the SLR–Very Long Baseline Interferometry (VLBI) scale discrepancy. The incorporation of time-varying wind further reduces the annual amplitude of the Z-geocenter coordinate by 0.3 mm, corresponding to a 7.3% decrease. Because tropospheric mismodeling directly impacts the fundamental geophysical parameters, we recommend adopting the extended tropospheric model for routine SLR analysis and provide site-specific wind parameters for the ILRS network.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"74 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355548","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}