Comparison of local geoid height surfaces, in the province of Trabzon

Karaaslan, Özge; Kayıkçı, Emine Tanır; Aşik, Yusuf

doi:10.1007/s12517-016-2470-2

Cited by 7 publications

(6 citation statements)

References 13 publications

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“…The weighting function is assigned to the data using the weighting power (k). This value is chosen by the user (i.e., k = 1, 2, 3, 4, or 5) (Karaaslan et al, 2016). More descriptive information can be found in the article by Yanalak and Baykal (2003).…”

Section: Inverse Distance To a Powermentioning

confidence: 99%

“…where ℎ is the ellipsoidal height, is the orthometric height, and is the geoid undulation or geoid height. The geoid undulation determined by the GNSS/leveling technique can also be used as data in the determination of the geoid via various estimation techniques such as the interpolation, least-squares collocation (LSC) and geophysical gravity data inversion (GGI) methods (Kotsakis and Sideris, 1999;Tscherning et al, 2001;Erol et al, 2008;Trojanowicz, 2012Trojanowicz, , 2015Doganalp and Selvi, 2015;Doganalp, 2016;Karaaslan et al, 2016;Tusat and Mikailsoy, 2018;Trojanowicz et al, 2020). Several soft-computing methods have been applied as alternative techniques to produce accurate results in the prediction of geoid undulation, including the artificial neural network (ANN), least square support vector machines (LS-SVM), and adaptive neuro-fuzzy inference systems (ANFIS).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Inverse Distance To a Powermentioning

confidence: 99%

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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“…As a result of the study, they have proposed using radial basis functions instead of polynomials for the stripping project. Karaaslan et al 6 have applied weighted average interpolation, polynomial surface regression, and multi‐quadratic interpolation methods for a local geoid determination. In particular, they have stated that one of the important factors affecting the selection of the appropriate interpolation model is the number of points chosen as homogeneously as possible.…”

Section: Introductionmentioning

confidence: 99%

Application of a metaheuristic gradient‐based optimizer algorithm integrated into artificial neural network model in a local geoid modeling with global navigation satellite systems/leveling measurements

Konakoǧlu

Aydemı̇r

Onay

2022

Concurrency and Computation

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In the present article, the efficiency of a new hybrid learning method, named artificial neural network with gradient‐based optimizer algorithm (ANN‐GBO), is investigated to determine a local geoid. The outcomes of the assessed method are compared with classical ANN (without GBO), some metaheuristic‐based ANN models and other study results (interpolation methods). Four commonly used performance metrics, root mean square error (RMSE), mean absolute error (MAE), mean absolute relative error (MARE) and coefficient of determination (R2$$ {R}^2 $$) have been used to assess the applied methods. Assessment of predictions revealed that ANN‐GBO yielded the best results (RMSE: 10.51 cm, MAE: 8.26 cm, MARE: 0.27 cm, and R2$$ {R}^2 $$: 0.9622). The outcomes of the work clearly show that the ANN‐GBO approach has the lowest prediction error compared with ANN. It can be said that the GBO algorithm enhances the ANN capability in local geoid modeling. It may be recommended to optimize the weights of the ANN with GBO for high prediction accuracy. This research can be extended to other regions.

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“…They also commented that if the number of reference points had been increased, the results might have been better. Karaaslan et al (2016) created a local geoid model in Trabzon Province using geometric methods. Polynomial surfaces were created using MQ and weighted average (WA) interpolation methods.…”

Section: Introductionmentioning

confidence: 99%

Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study

Konakoǧlu

Akar

2022

Earth sci. res. j.

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The present work aimed to develop a prediction model to estimate geoid undulation and to compare its efficiency with other methods including radial basis function neural network (RBFNN), generalized regression neural network (GRNN), multiple linear regression (MLR) and, ten different interpolation methods. In this study, the k-fold cross-validation method was used to evaluate the model and its behavior on the independent dataset. With this validation method, each of a k number of groups has the chance to be divided into training and testing data. The performances of the methods were evaluated in terms of the root mean square error (RMSE) mean absolute error (MAE), Nash–Sutcliffe efficiency coefficient (NSE), and correlation coefficient (R2) and using graphical indicators. The evaluation of the performance of the datasets obtained using cross-validation was done in two ways. If we accept the method having the minimum error result as the most appropriate method, the natural neighbor (NN) method in the DS#5 dataset gave better results than the other methods (RMSE=0.14173 m, MAE=0.09729 m, NSE=0.98986, and R2=0.99011. On the other hand, it has been observed that, the GRNN method exhibited the best performance, on average, with RMSE=0.18539 m, MAE=0.13676 m, NSE=0.98229, and R2=0.98249.

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Comparison of local geoid height surfaces, in the province of Trabzon

Cited by 7 publications

References 13 publications

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

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

Application of a metaheuristic gradient‐based optimizer algorithm integrated into artificial neural network model in a local geoid modeling with global navigation satellite systems/leveling measurements

Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study

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