Utilisation of Fast Fourier Transform and Least-squares Modification of Stokes formula to compile a gravimetric geoid model over Khartoum State: Sudan

Abdalla, Ahmed; Green, Christopher M.

doi:10.1007/s12517-015-2117-8

Cited by 8 publications

(4 citation statements)

References 39 publications

(30 reference statements)

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“…The KTH method has been utilised in the computation of gravimetric geoid models in several regions and countries, including Sudan [17], Malaysia [18], Poland [19], Uganda [20], Bosnia and Herzegovina [21], and Latvia [22]. These countries are among the prominent users of the KTH method in this field.…”

Section: Introductionmentioning

confidence: 99%

Evaluating the Impact of the Recent Combined and Satellite-Only Global Geopotential Model on the Gravimetric Geoid Model

Azmin,

Pa’suya,

Din

et al. 2024

IOP Conf. Ser.: Earth Environ. Sci.

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Geoid represents Earth’s surface, ocean, and gravitational field, which influence the elevations, shape, and mass distribution of the geopotential surface, a hypothetical surface that is perpendicular to the direction of gravity at every point. This geopotential surface serves as a reference for measuring elevations and is used as a fundamental reference surface for geodetic and surveying purposes. In this study, the Least Squares Modification of Stokes Formula (LSMS) with Additive Corrections (AC), also known as the KTH method, is used to generate a new gravimetric geoid model for Peninsular Malaysia. The KTH method was developed at the Royal Institute of Technology (KTH) in Stockholm-Sweden. The dataset used is the most recent global digital elevation model, Shuttle Radar Topography Mission (SRTM) 1 Arc-Second Global, generated by the National Aeronautics and Space Administration (NASA) and the National Imagery and Mapping Agency (NIMA). In addition to this elevation data, the dataset includes the Global Geopotential Model (GGM), which is composed of the XGM2016, XGM2019e, Tongji_GGMG2021S, and Tongji-Grace02k models. Furthermore, it incorporates sets of regional gravity data, including terrestrial gravity, airborne gravity, and marine gravity anomalies, all of which are derived from the Technical University of Denmark (DTU 21). The actual 45 Global Navigation Satellite System (GNSS)-levelling points data have been compared to the gravimetric geoid model developed in this study and the geoid acquired from Department of Survey and Mapping Malaysia (DSMM). According to the statistical results, NXGM2019e provides better accuracy, with the Root Mean Square Error (RMSE) geoid model errors of ±0.033 m, compared to the deviations in free-air anomalies, XGM2019e, which has the minimum RMSE of 10.291 mGal. Meanwhile, Tongji-GMMG2021S has the maximum RMSE of 14.792 mGal. The geoid is derived from the XGM2019e model and has maximum and minimum values of 0.032 m and 0.147 m, respectively, with mean residuals of 0.089 m. In conclusion, the XGM2019e has the potential to determine a precise local geoid model for Peninsular Malaysia

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Section: Introductionmentioning

confidence: 99%

Evaluating the Impact of the Recent Combined and Satellite-Only Global Geopotential Model on the Gravimetric Geoid Model

Azmin,

Pa’suya,

Din

et al. 2024

IOP Conf. Ser.: Earth Environ. Sci.

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“…Abbak selected the mountainous area of central Turkey as the experimental area with sparse terrestrial gravity data and a single GPS leveling route; the results showed that the KTH method was significantly better than the RCR method [22]. Abdalla conducted the same experiment in the Khartoum state of Sudan with the blank boundary of the area filled by EGM2008; the final results were produced at the decimeter level [31], which may be attributed to the poor accuracy of the original EGM2008 model in the area.…”

Section: Introductionmentioning

confidence: 99%

Performance Comparison of Geoid Refinement between XGM2016 and EGM2008 Based on the KTH and RCR Methods: Jilin Province, China

Wang

et al. 2020

Remote Sensing

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The selection of an appropriate global gravity field model and refinement method can effectively improve the accuracy of the refined regional geoid model in a certain research area. We analyzed the accuracy of Experimental Geopotential Model (XGM2016) based on the GPS-leveling data and the modification parameters of the global mean square errors in the KTH geoid refinement in Jilin Province, China. The regional geoid was refined based on Earth Gravitational Model (EGM2008) and XGM2016 using both the Helmert condensation method with an RCR procedure and the KTH method. A comparison of the original two gravity field models to the GPS-leveling benchmarks showed that the accuracies of XGM2016 and EGM2008 in the plain area of Jilin Province are similar with a standard deviation (STD) of 5.8 cm, whereas the accuracy of EGM2008 in the high mountainous area is 1.4 cm better than that of XGM2016, which may be attributed to its low resolution. The modification parameters between the two gravity field models showed that the coefficient error of XGM2016 model was lower than that of EGM2008 for the same degree of expansion. The different modification limits and integral radii may produce a centimeter level difference in global mean square error, while the influence of the truncation error caused by the integral was at the millimeter level. The terrestrial gravity data error accounted for the majority of the global mean square error. The optimal least squares modification obtained the minimum global mean square error, and the global mean square error calculated based on XGM2016 model was reduced by about 1~3 cm compared with EGM2008. The refined geoid based on the two gravity field models indicated that both KTH and RCR method can effectively improve the STD of the geoid model from about six to three centimeters. The refined accuracy of EGM2008 model using RCR and KTH methods is slightly better than that of XGM2016 model in the plain and high mountain areas after seven-parameter fitting. EGM2008 based on the KTH method was the most precise at ± 2.0 cm in the plain area and ± 2.4 cm in the mountainous area. Generally, for the refined geoid based on the two Earth gravity models, KTH produced results similar to RCR in the plain area, and had relatively better performance for the mountainous area where terrestrial gravity data is sparse and unevenly distributed.

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“…The Fast Fourier Transform (FFT) [8] which computes the DFT of an n-size signal in O(n log n) time greatly simplifies the complexity of DFT and gets a wide range of applications. In [9], [10] and [11], [12] are implementations of the discrete Fourier transform (DFT). Fourier transform hypotheses of central importance in a vast range of applications in engineering, applied mathematics, and physical science.…”

Section: Introductionmentioning

confidence: 99%

Towards an Improvement of Fourier Transform

Aznag¹,

Datsi²,

Oirrak³

et al. 2020

IJACSA

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With the development of information technology and the coming period of large data, the image signals play an increasingly more significant role in our life because of the phenomenal development of system correspondence innovation, and the comparing high proficiency image handling strategies are requested earnestly. The Fourier transform is an important image processing tool, which is used in a wide range of applications, such as image filtering, image analysis, image compression and image reconstruction. It 's the simplest among the other transformation method used in mathematics. The real time consumption is lesser due to this method. It has a vast use in image processing, particularly object 2D, 3D and other representation. This paper proposes a new Fourier transform which is called Non Uniform Fourier Transform (NUFT). The proposed descriptor takes into consideration the change of point index. Also, an application is made on 2D set of points and a real image. The main advantages of the proposed transform are invariance under change of index point and robustness to noise. Also, the extraction of invariant under rotation and affinity is immediate because the linearity is assured. The proposed descriptor is tested on MPEG 7 database and compared with the normal Fourier transform to shows its efficiency. The experimental results prove the effectiveness of the proposed descriptor.

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Utilisation of Fast Fourier Transform and Least-squares Modification of Stokes formula to compile a gravimetric geoid model over Khartoum State: Sudan

Cited by 8 publications

References 39 publications

Evaluating the Impact of the Recent Combined and Satellite-Only Global Geopotential Model on the Gravimetric Geoid Model

Evaluating the Impact of the Recent Combined and Satellite-Only Global Geopotential Model on the Gravimetric Geoid Model

Performance Comparison of Geoid Refinement between XGM2016 and EGM2008 Based on the KTH and RCR Methods: Jilin Province, China

Towards an Improvement of Fourier Transform

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