Journal of Geodesy最新文献

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Numerical modeling and analysis of GNSS carrier-phase diffraction error in occlusion environments 遮挡环境下GNSS载波相位衍射误差的数值模拟与分析
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-04-25 DOI: 10.1007/s00190-025-01956-4
Ruijie Xi, Luming Han, Qusen Chen, Weiping Jiang, Xiaolin Meng, Xiangdong An, Wei Xuan
{"title":"Numerical modeling and analysis of GNSS carrier-phase diffraction error in occlusion environments","authors":"Ruijie Xi, Luming Han, Qusen Chen, Weiping Jiang, Xiaolin Meng, Xiangdong An, Wei Xuan","doi":"10.1007/s00190-025-01956-4","DOIUrl":"https://doi.org/10.1007/s00190-025-01956-4","url":null,"abstract":"<p>In urban canyons or natural valleys, diffraction effect occurs when the signal of Global Navigation Satellite Systems (GNSS) transmits to the edge of obstructions, such as buildings, trees, and slopes, resulting in large diffraction error, which is one of the important error sources in carrier-phase-based precise positioning. However, the theoretical formula derivation and numerical modeling of the diffraction error have been rarely studied. In this study, we derived the theoretical formula of the diffraction error based on the geometrical structure of the signal propagation path in satellite-obstruction-antenna geometry. Then, the diffraction error extraction and modeling method were proposed to study the time-varying characteristics of diffraction error and verify the validity of the theoretical formula of the diffraction error. Based on the GNSS data collected in occlusion environment, a designed experiment was carried out. The results show that the diffraction error generally increases or decreases monotonically, and mostly the amplitude of it could be larger than 50 mm and even reach 200 mm. The time-varying characteristics of diffraction error can be precisely simulated with the vertical and horizontal diffraction formulas developed, and the diffraction error model established could be applied in sidereal filtering method to correct the diffraction error. From the experiment, the fixed rate of ambiguity resolution can be improved from 76.8 to 98.87%, and the positioning reliability is improved from 80 to over 98% with the diffraction correction. The results of this paper provided theoretical basis and experience for the processing of GNSS diffraction error and show the significance in applications of high-precision positioning.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"3 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875897","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}
引用次数: 0
Spectral gravity forward modelling of 3D variable densities using an arbitrary integration radius with application to lunar topographic masses 基于任意积分半径的三维变密度光谱重力正演模拟及其在月球地形质量中的应用
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-04-23 DOI: 10.1007/s00190-025-01951-9
Blažej Bucha
{"title":"Spectral gravity forward modelling of 3D variable densities using an arbitrary integration radius with application to lunar topographic masses","authors":"Blažej Bucha","doi":"10.1007/s00190-025-01951-9","DOIUrl":"https://doi.org/10.1007/s00190-025-01951-9","url":null,"abstract":"<p>Spectral gravity forward modelling delivers gravitational fields of mass distributions by evaluating Newton’s integral in the spectral domain. We generalize its spherical harmonic variant to 3D variable densities and to any integration radius. The former is achieved by expressing the density function as an infinite-degree polynomial in the radial direction with polynomial coefficients varying laterally as a bounded function. The latter generalization builds on Molodensky’s truncation coefficients and allows to evaluate gravitational contribution of masses found up to and beyond some integration radius. In a numerical study, we forward-model lunar topographic masses by first assuming constant and then 3D variable density. Our validation with respect to GRAIL-based models shows that the 3D density model yields superior gravitational field compared to the constant density model. Thanks to the efficiency of FFT-based spherical harmonic transforms, the new technique can be employed in high-resolution modelling of topographic potentials. A numerical implementation is made available through CHarm, which is a C/Python library for high-degree spherical harmonic transforms accessible at https://github.com/blazej-bucha/charm.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"42 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143866929","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}
引用次数: 0
A new method for determining geoid gradient components from SWOT wide-swath data for marine gravity field 利用海洋重力场SWOT宽幅数据确定大地水准面梯度分量的新方法
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-04-12 DOI: 10.1007/s00190-025-01950-w
Daocheng Yu, Xiaoli Deng, Ole Baltazar Andersen, Huizhong Zhu, Jia Luo
{"title":"A new method for determining geoid gradient components from SWOT wide-swath data for marine gravity field","authors":"Daocheng Yu, Xiaoli Deng, Ole Baltazar Andersen, Huizhong Zhu, Jia Luo","doi":"10.1007/s00190-025-01950-w","DOIUrl":"https://doi.org/10.1007/s00190-025-01950-w","url":null,"abstract":"<p>The Surface Water and Ocean Topography (SWOT) altimeter mission provides a significant opportunity to improve the accuracy of geoid gradients (GGs) and marine gravity fields. This paper presents a new method, namely LSA3, to determine the north and east (<span>(xi )</span> and <span>(eta )</span>) components of GGs from simulated and real SWOT data in the northern South China Sea. To fully use SWOT’s fine-scale sea surface height (SSH) measurements, LSA3 first determines GGs in SWOT along-, cross- and oblique-track directions and constructs a grid for each gradient. Least-squares adjustment (LSA), accounting for correlations of the GGs in three directions, is then employed to point-wisely estimate <span>(xi )</span> and <span>(eta )</span> components at grid points. The accuracy of estimated <span>(xi )</span> and <span>(eta )</span> components is assessed using those computed by numerical differentiations. For comparison, GG components are also estimated using least-squares collocation (LSC) and weighted LSA (WLSA) methods with empirically determined data window sizes and without accounting for correlations. Simulated results show that LSA3-estimated GG components achieve the root-mean-square deviation (RMSD) values of 0.43 and 0.47 microrad for <span>(xi )</span> and <span>(eta )</span>, respectively, outperforming LSC (0.82 and 0.86 microrad) and WLSA (0.49 and 0.54 microrad). The results from the real SWOT data indicate that LSA3 is comparable to LSC with a mean RMSD of 1.88 mgal for marine gravity anomalies when compared to shipborne gravity data, but LSA3 is more computationally efficient than LSC. Compared to the Sandwell V32.1 gravity field, SWOT improves gravity accuracy by an average of 12.0%, with a maximum improvement of 44.3% for a single ship trajectory.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"43 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143822915","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}
引用次数: 0
Theory for the ambiguity function method: probability model and global solution 模糊函数方法的理论:概率模型和全局解
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-04-04 DOI: 10.1007/s00190-025-01945-7
P. J. G. Teunissen, L. Massarweh
{"title":"Theory for the ambiguity function method: probability model and global solution","authors":"P. J. G. Teunissen, L. Massarweh","doi":"10.1007/s00190-025-01945-7","DOIUrl":"https://doi.org/10.1007/s00190-025-01945-7","url":null,"abstract":"<p>In this contribution, we introduce some new theory for the classical GNSS ambiguity function (AF) method. We provide the probability model by means of which the AF-estimator becomes a maximum likelihood estimator, and we provide a globally convergent algorithm for computing the AF-estimate. The algorithm is constructed from combining the branch-and-bound principle, with a special convex relaxation of the multimodal ambiguity function, to which the projected-gradient-descent method is applied to obtain the required bounds. We also provide a systematic comparison between the AF-principle and that of integer least-squares (ILS). From this comparison, the conclusion is reached that the two principles are fundamentally different, although there are identified circumstances under which one can expect AF- and ILS-solutions to behave similarly.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"26 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143775698","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}
引用次数: 0
Depth modernization by integrating mean sea surface model, ocean tide model, and precise ship positioning 通过综合平均海面模型、海潮模型和精确船舶定位实现深度现代化
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-03-24 DOI: 10.1007/s00190-025-01949-3
Cheinway Hwang, Chung-Yen Kuo, Hsuan-Chang Shih, Wen-Hsuan Huang, Wen-Hau Lan
{"title":"Depth modernization by integrating mean sea surface model, ocean tide model, and precise ship positioning","authors":"Cheinway Hwang, Chung-Yen Kuo, Hsuan-Chang Shih, Wen-Hsuan Huang, Wen-Hau Lan","doi":"10.1007/s00190-025-01949-3","DOIUrl":"https://doi.org/10.1007/s00190-025-01949-3","url":null,"abstract":"<p>This paper presents a study on depth modernization, paralleling height modernization for land elevations. Depth modernization integrates mean sea surface (MSS) models, ocean tide models, and precise ship positioning to achieve accurate seafloor depth measurements. Conventional methods rely on tidal corrections and chart datum from temporary tide gauges, which can be challenging in regions with complex tidal patterns and inconsistent chart datums. For depth modernization, we developed (1) a hybrid MSS model using satellite altimeter data, tide gauge records, and a regional geoid model, and (2) a hydrodynamic-driven ocean model with 26 tidal constituents to determine separations between the hybrid MSS and five tidal surfaces, resulting in five ellipsoid-based surfaces analogous to a geoid model for height modernization. Precise ship positioning is demonstrated using GNSS data collected by the Legend research ship in the Pacific Ocean east of Taiwan and the Canadian spatial reference system precise point positioning toolbox. We used measurements in the Taiwan Strait to show how modern depth is implemented. Comparisons of depths in four regions from the conventional and modern methods show small (a few cm) to moderate (a few dm) differences with some variability depending on the region and equipment. Discontinuities in depths from the conventional method are analyzed. Depth modernization has significantly benefited rapid and accurate bathymetric mapping for electronic navigation charts. Future work in MSS and ocean tide models and the availability of PPP tools for depth modernization are discussed. For mapping agencies worldwide, depth modernization should be prioritized alongside height modernization to ensure rapid and accurate depth data provision.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"2 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143678150","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}
引用次数: 0
Translated spherical harmonics for semi-global gravitational field modeling: examples for Martian moon Phobos and asteroid 433 Eros 半全球引力场建模的平移球面谐波:火星卫星火卫一和小行星爱神的例子
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-03-12 DOI: 10.1007/s00190-025-01944-8
Xuanyu Hu
{"title":"Translated spherical harmonics for semi-global gravitational field modeling: examples for Martian moon Phobos and asteroid 433 Eros","authors":"Xuanyu Hu","doi":"10.1007/s00190-025-01944-8","DOIUrl":"https://doi.org/10.1007/s00190-025-01944-8","url":null,"abstract":"<p>The gravitational field of a planetary body is most often modeled by an exterior spherical harmonic series, which is uniformly convergent outside the smallest mass-enclosing sphere centered at the origin of the coordinate system, known as the Brillouin sphere. The model can become unstable inside the spherical boundary. Rarely deliberated or emphasized is an obvious fact that the radius of the Brillouin sphere, which is the maximum radius coordinate of the body, changes with the origin. The sphere can thus be adjusted to fit a certain convex portion of irregular body shape via an appropriate coordinate translation, thereby maximizing the region of model stability above the body. We demonstrate that it is, while perhaps counterintuitive, rational to displace the coordinate origin from the center of figure, or even off the body entirely. We review concisely the theory and a method of spherical harmonic translation. We consider some textbook examples that illuminate the physical meaning and the practical advantage of the transformation, the discussion of which, as it turns out, is not so easily encountered. We provide seminormalized as well as fully normalized version of the algorithms, which are compact and easy to work with for low-degree applications. At little cost, the proposed approach enables the spherical harmonics to be comparable with the far more complicated ellipsoidal harmonics in performance in the case of two small objects, Phobos and 433 Eros.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"5 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143607920","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}
引用次数: 0
Enhanced multi-GNSS precise point positioning based on ERA5 precipitation water vapor information 基于ERA5降水水汽信息的增强多gnss精确点定位
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-03-11 DOI: 10.1007/s00190-025-01948-4
Xiongwei Ma, Xinzhe Wang, Yibin Yao, Hang Zhu, Bao Zhang, Ruitao Chu, Qi Zhang, Yangmin Feng
{"title":"Enhanced multi-GNSS precise point positioning based on ERA5 precipitation water vapor information","authors":"Xiongwei Ma, Xinzhe Wang, Yibin Yao, Hang Zhu, Bao Zhang, Ruitao Chu, Qi Zhang, Yangmin Feng","doi":"10.1007/s00190-025-01948-4","DOIUrl":"https://doi.org/10.1007/s00190-025-01948-4","url":null,"abstract":"<p>For a rapid retrieval of zenith wet delay (ZWD) and multi-global navigation satellite system (GNSS) precise point positioning (PPP) enhancement, a lightweight ZWD retrieval model was constructed by combining ground-based GNSS observations and precipitable water vapor (PWV) data provided by the European Center for Medium-Range Weather Forecasts Reanalysis (ERA5). The proposed model can rapidly produce ZWD without relying on the meteorological profile parameters. The proposed ZWD retrieval model achieved an RMSE and STD of 1.74 cm, with a correlation coefficient of 0.98. The enhanced performance of PWV-generated ZWD in GNSS PPP was tested in this study. The results showed that the ZWD constraint in GNSS PPP mainly affects the convergence time of the standard PPP solution, with the most significant effect in the U-direction. The PPP convergence time can be shortened by a maximum of 43%, with an average reduction of 24% for the eight sites over the four seasons. In the PPP-ambiguity resolution solution, the time to first fix (TTFF) was shorter for all sites with ZWD enhancement than for those without ZWD enhancement. The TTFF of the eight sites was significantly shortened in all four seasons, with an average improvement of 31%. The ZWD retrieval method based on the ERA5 PWV proposed in this study can quickly generate ZWD with high accuracy and resolution over a large area and significantly enhance GNSS PPP. The methodology proposed in this study is valuable for utilizing multi-source PWV-generated ZWD services for GNSS PPP enhancement.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"20 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143599100","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}
引用次数: 0
Handling temporal correlated noise in large-scale global GNSS processing 大规模全球GNSS处理中时间相关噪声的处理
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-03-10 DOI: 10.1007/s00190-025-01946-6
Patrick Dumitraschkewitz, Torsten Mayer-Gürr
{"title":"Handling temporal correlated noise in large-scale global GNSS processing","authors":"Patrick Dumitraschkewitz, Torsten Mayer-Gürr","doi":"10.1007/s00190-025-01946-6","DOIUrl":"https://doi.org/10.1007/s00190-025-01946-6","url":null,"abstract":"<p>Global Navigation Satellite System (GNSS) products are an integral part of a wide range of scientific and commercial applications. The creation of such products requires processing software capable of solving a combined station position and GNSS satellite orbit estimation by least squares adjustment, also known as global GNSS processing. Such processing is routinely performed by the International GNSS Service (IGS) and its Analysis Centers. For the IGS Reprocessing Campaign 3 (repro3), Graz University of Technology (TUG) participated as an AC using the raw observation approach, which uses all measurements as observed by the receivers. However, a common feature of almost all global multi-GNSS processing strategies is the use of diagonal covariance matrices as stochastic models for simplicity. This implies that any spatial or temporal correlations are ignored. However, numerous studies have shown that GNSS processing is indeed affected by spatial and temporal correlations. For global GNSS processing, research on stochastic modeling and its challenges is rather scarce. In this work, a detailed insight into the problems of stochastic modeling in global GNSS processing using the raw observation approach is given along with a detailed overview of the intended TUG approach. An analysis of the impact of temporal correlation modeling on the resulting GNSS products and GNSS frame estimation is also given.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"192 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143589940","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}
引用次数: 0
Optimized gravity field retrieval for the MAGIC mission concept using background model uncertainty information 利用背景模型不确定性信息优化MAGIC任务概念重力场检索
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-03-10 DOI: 10.1007/s00190-024-01931-5
Josefine Wilms, Markus Hauk, Natalia Panafidina, Michael Murböck, Karl Hans Neumayer, Christoph Dahle, Frank Flechtner
{"title":"Optimized gravity field retrieval for the MAGIC mission concept using background model uncertainty information","authors":"Josefine Wilms, Markus Hauk, Natalia Panafidina, Michael Murböck, Karl Hans Neumayer, Christoph Dahle, Frank Flechtner","doi":"10.1007/s00190-024-01931-5","DOIUrl":"https://doi.org/10.1007/s00190-024-01931-5","url":null,"abstract":"<p>Errors in ocean tide and non-tidal atmospheric and oceanic models are among the largest error sources in gravity field recovery from space. We co-estimate corrections to these background models subject to uncertainty constraints during the adjustment procedure of gravity field spherical harmonic coefficients. Simulations are performed for the Mass-Change and Geoscience International Constellation to evaluate the effect of such a constrained procedure on monthly gravity field retrievals for the planned ESA-NASA double-pair mission. The influence of co-estimating background model corrections subject to known uncertainty information is evaluated separately for both types of background models and is then combined and used to retrieve monthly gravity fields over one year. Retrieval errors are compared to those obtained with the standard recovery procedure, which neglects these corrections. It is shown that gravity field retrieval errors are reduced by up to 36%. In addition, the one-year simulation is used to estimate residual corrections for eight major tidal constituents in order to improve ocean tide background modelling. Adding these residual corrections to the applied a priori ocean tide model shows that ocean tide errors are decreased by up to 27%.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"212 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143582881","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}
引用次数: 0
Stochastic modelling of polyhedral gravity signal variations. Part I: First-order derivatives of gravitational potential 多面体重力信号变化的随机建模。第一部分:引力势的一阶导数
IF 4.4 2区 地球科学
Journal of Geodesy Pub Date : 2025-03-10 DOI: 10.1007/s00190-025-01937-7
Georgia Gavriilidou, Dimitrios Tsoulis
{"title":"Stochastic modelling of polyhedral gravity signal variations. Part I: First-order derivatives of gravitational potential","authors":"Georgia Gavriilidou, Dimitrios Tsoulis","doi":"10.1007/s00190-025-01937-7","DOIUrl":"https://doi.org/10.1007/s00190-025-01937-7","url":null,"abstract":"<p>The stochastic modelling of a finite mass distribution can provide a new perspective on the dynamic evaluation of time variable gravity fields. The algorithm for estimating variations of spherical harmonic coefficients implied by corresponding shape changes is implemented for the first-order derivatives of the gravitational potential. The described algorithm uses the spherical harmonic synthesis formula expressed in Cartesian coordinates that includes the derived Legendre functions (DLFs). Here, we expand the estimation process by implementing also the traditional spherical harmonic synthesis formula of normalized associated Legendre functions (ALFs) expressed in spherical coordinates. The variations obtained by applying the two approaches are compared with gravity signal differences induced by the modelled shape changes using the line integral analytical approach. The numerical comparisons refer to three asteroid shape models of Eros, Didymos and Dimorphos. The first-order derivative values provided by the DLF expressions and their variations using ALF are closer to the analytical method’s results. The highest calculated differences refer to Δ<i>V</i><sub><i>z</i></sub> with their mean value reaching 37% with respect to the other components obtained by all methods. Finally, the respective harmonic series converge to a fixed numerical value at a maximum expansion degree equal to 15 near Brillouin sphere and 5 as the distance of the computation point increases.</p>","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"1 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143583070","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}
引用次数: 0
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