Using a least squares support vector machine to estimate a local geometric geoid model

Kao, Szu-Pyng; Chen, Chao-Nan; Huang, Haiyang; Shen, Yu‐Ting

doi:10.1590/s1982-21702014000200025

Cited by 13 publications

(3 citation statements)

References 12 publications

(12 reference statements)

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“…Для обчислення регіональної моделі геометричного геоїда здебільшого використовують штучну нейронну мережу [Kao, 2014] та розклад у ряд за степеневими функціями Eteje et al, 2018 IJASRE, 4 (8), 206-214. Haines G. V. (1985).…”

Section: основні розрахункиunclassified

Construction of STHA-model of geometric geoid on the Lviv region area

Zablotskyi¹,

Dzhuman²

2021

MAGSI

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Nowadays there is a need to modernize the high system of Ukraine, which requires its integration in the European Vertical Reference System EVRS. In this regard there is also a need to build a regional model of the geoid on the territory of our country, which would be well consistent with the model of the European geoid EGG2015. To obtain the optimal model, it is necessary to use both gravimetric and geometric data. In this case, the model is called gravimetric-geometric. This approach is used both when building a model of the European geoid and when building geoid models on the territory of different European countries. Aim. The purpose of this work is to build a regional geometric STHA-model of the geoid on the Lviv region area and assess its accuracy. In the future it is planned to build a gravimetric STHA-model of the geoid in the same area and compare the results. Methods. To build a geometric STHA-model of the geoid on the Lviv region area, the heights of the geometric geoid, obtained from GNSS-observations at the points of SGN of I, II and III classes, were used. RMS error of determination of geodetic heights , obtained from GNSS leveling in static mode, did not exceed 15 mm. 205 values of the calculated heights of the geoid were used to build the geoid model. 8 values were not involved in the construction of the model, because they were used for an independent assessment of model accuracy. Results. The regional model of geoid within the “Remove–Compute–Restore” procedure with introduction of regularization parameter is obteined. RMS error of the obtained model, calculated on the basis of the data used in its construction, is 12 mm, and on other independent data is 25 mm. Scientific novelty and practical significance. For the first time STHA-functions were tested to build a regional geoid model. The geometric model of the geoid on the Lviv region are is calculated and the accuracy of the obtained model is estimated on the basis of dependent and independent data. The RMS error of the obtained model was about 2 cm, which corresponds to the accuracy of GNSS-measurements. The obtained model can be used as a transformation field on the Lviv region area.

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Section: основні розрахункиunclassified

Construction of STHA-model of geometric geoid on the Lviv region area

Zablotskyi¹,

Dzhuman²

2021

MAGSI

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“…Based on the results of this research, the MLPNN model was found to be more accurate than the other methods tested. Another soft-computing method is represented by the least square support vector machine (LS-SVM), which is the least squares formulation of the support vector machine (SVM) and has been applied to detect a geoid model (Zaletnyik et al, 2008;Kao et al, 2014;Kaloop et al, 2018). In addition to ANN and LS-SVM methods, the ANFIS approach has also been used by geodesy researchers in geoid modeling (Akyilmaz et al, 2008;Yilmaz, 2010;Yılmaz and Arslan, 2013).…”

Section: Introductionmentioning

confidence: 99%

Geoid undulation prediction using Gaussian Processes Regression: A case study in a local region in Turkey

Konakoǧlu¹

2021

Acta Geodynamica Et Geomaterialia

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In order to convert ellipsoidal heights obtained by the Global Navigation Satellite System (GNSS) to orthometric heights, it is necessary to know the distance between the ellipsoidal and geoid surface, called the geoid undulation. The geoid undulation can be predicted using emerging mathematics tools and algorithms. The objective of this study was to develop a model for predicting the geoid undulation using Gaussian Process Regression (GPR), one of the soft machine learning algorithms having different covariance functions. This method was then compared with the radial basis function neural network (RBFNN), generalized regression neural network (GRNN), and the interpolation method of inverse distance to a power (IDP) with the power of 1, 2, 3, 4, and 5. First, 70 % of GNSS/leveling data (422 points) were used in the training phase. The remaining 185 points were used as testing data to check the effectiveness of the constructed model. In the GPR modeling, ten covariance functions (Materniso d= 1, 3, 5; Maternard d= 1, 3, 5; SEiso; SEard; RQiso; and RQard) were tested for prediction on this dataset. The GPR based on the Materniso (d = 1) covariance function model was introduced as an effective method for predicting geoid undulation and provided the best results (RMSE = 8.32 cm, MAE = 5.51 cm, R 2 = 0.98968) when compared with the other developed GPR models. In addition, the statistical findings showed that the accuracy of all the GPR models was also better in predicting geoid undulation than the RBFNN, GRNN, and IDP with the power of 1, 2, 3, 4, and 5.

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“…Numerous studies have investigated the development of suitable local geoid undulation models by applying various fitting methods to measurements of ellipsoidal height h and leveling orthometric height H obtained using global positioning systems (GPSs) (Odera et al, 2014;Abdalla et al, 2011;Abdalla and Fairhead, 2011;Akcin and Celik, 2013;Abdalla, 2009;Featherstone et al, 2004;Kao et al, 2014 ;Kao, 2006;Kotsakis and Sideris, 1999;Kao and Bethel, 1992(a); Kao and Bethel, 1992(b) ;Ning, 2015;Lin, 2007;Tranes et al, 2007;Kiamehr, 2006;Ustun and Demirel, 2006;You, 2006;Yang and Chen, 1999). The geoid of each position in a location can be calculated to determine H for each position.…”

Section: Introductionmentioning

confidence: 99%

Using Particle Swarm Optimization to Establish a Local Geometric Geoid Model

et al. 2017

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Abstract:There exist a number of methods for approximating the local geoid surface and studies carried out to determine a local geoid. In this study, performance of geoid by PSO method in modeling local geoid was presented and analyzed. The ellipsoidal heights (h), derived from GPS observations, and known orthometric heights from first-order bench marks were first used to create local geometric geoid model, then the PSO method was used to convert ellipsoidal heights into orthometric heights (H). The resulting values were used to compare between the spirit leveling and GPS methods. The adopted PSO method can improve the fitting of local geometric geoid by quadratic surface fitting method, which agrees with the known orthometric heights within ±1.02cmthe Cartography produced: General Map, Partial Maps, Profile, Cross Sections and others. Keywords: Particle swarm optimization (PSO); Quadratic surface fitting; Ellipsoidal height; Orthometric height. Resumo:Existe uma série de métodos para aproximar a superfície do geoide local bem como vários estudos conduzidos para determinar um geoide local. Neste estudo, apresentou-se e analisou-se o desempenho do geoide pelo método de otimização por exame de partículas (PSO, do inglês Particle Swarm Optimization) na modelagem do geoide local. As altitudes elipsoidais (h), derivada de observações GPS, e altitudes ortométricas de referências de nível de primeira ordem foram usados para criar um modelo do geoide geométrica local, na sequencia usou-se o método PSO para converter altitudes elipsoidais em altitudes ortométricas (H

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Using a least squares support vector machine to estimate a local geometric geoid model

Cited by 13 publications

References 12 publications

Construction of STHA-model of geometric geoid on the Lviv region area

Construction of STHA-model of geometric geoid on the Lviv region area

Geoid undulation prediction using Gaussian Processes Regression: A case study in a local region in Turkey

Using Particle Swarm Optimization to Establish a Local Geometric Geoid Model

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