Modelling local GPS/levelling geoid undulations using artificial neural networks

Kavzoğlu, Taşkın; Saka, M. H.

doi:10.1007/s00190-004-0420-3

Cited by 64 publications

(47 citation statements)

References 19 publications

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“…This work, however, does not attempt to estimate α, but D matrix with a priori noise. The choice of the covariance model is arbitrary in some sense, but it is based on the frequent applications of Gauss-Markov third order model (GM3) in the literature in geoid (Kavzoglu and Saka, 2005) or gravity interpolation (Moreaux, 2008)…”

Section: Trend Removal Lsc and Loo Validationmentioning

confidence: 99%

A priori noise and regularization in least squares collocation of gravity anomalies

Jarmołowski¹

2013

Geodesy and Cartography

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Abstract:The paper describes the estimation of covariance parameters in least squares collocation (LSC) by the cross-validation (CV) technique called leave-one-out (LOO). Two parameters of Gauss-Markov third order model (GM3) are estimated together with a priori noise standard deviation, which contributes signifi cantly to the covariance matrix composed of the signal and noise. Numerical tests are performed using large set of Bouguer gravity anomalies located in the central part of the U.S. Around 103 000 gravity stations are available in the selected area. This dataset, together with regular grids generated from EGM2008 geopotential model, give an opportunity to work with various spatial resolutions of the data and heterogeneous variances of the signal and noise. This plays a crucial role in the numerical investigations, because the spatial resolution of the gravity data determines the number of gravity details that we may observe and model. This establishes a relation between the spatial resolution of the data and the resolution of the gravity fi eld model. This relation is inspected in the article and compared to the regularization problem occurring frequently in data modeling.

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Section: Trend Removal Lsc and Loo Validationmentioning

confidence: 99%

A priori noise and regularization in least squares collocation of gravity anomalies

Jarmołowski¹

2013

Geodesy and Cartography

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“…Some authors have been using Artificial Neural Networks (ANN) to obtain geoid undulations (Maia and Segatine 2003, Kavzoglu and Saka 2005, Veronez et al 2011. With the results, this type of interpolator has been found to have great potential in modeling offsets.…”

Section: Gnss Positioning and Geoid Model Integrationmentioning

confidence: 99%

“…Goldani (2006) has presented a geoid model developed only with benchmark data tracked by GNSS for the State of Paraná, the GEOIDERAAP, where RMS obtained was ± 0.10 m, evidencing the model improvement over the national geoid when using this type of data in the model. The State of São Paulo has been the subject of several studies to improve the geoid through alternative methods with integration of GNSS leveling (Maia and Segatine 2003, Kavzoglu and Saka 2005, Veronez et al 2011). …”

Section: Hybrid Geoid Modelsmentioning

confidence: 99%

Hybrid Geoid Model: Theory and Application in Brazil

Arana¹,

Camargo²,

Guimarães

2017

An. Acad. Bras. Ciênc.

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Determination of the ellipsoidal height by Global Navigation Satellite Systems (GNSS) is becoming better known and used for purposes of leveling with the aid of geoid models. However, the disadvantage of this method is the quality of the geoid models, which degrade heights and limit the application of the method. In order to provide better quality in transforming height using GNSS leveling, this research aims to develop a hybridization methodology of gravimetric geoid models EGM08, MAPGEO2015 and GEOIDSP2014 for the State of São Paulo, providing more consistent models with GNSS technology. Radial Basis Function (RBF) neural networks were used to obtain the corrector surface, based on differences between geoid model undulations and the undulations obtained by GNSS tracking in benchmarks. The experiments showed that the most suitable interpolation for correction modeling is the linear RBF. Checkpoints indicate that the geoid hybrid models feature root mean square deviation ± 0.107, ± 0.104 and ± 0.098 m, respectively. The results shows an improvement of 30 to 40% in consistencies compared with the gravimetric geoids, providing users with better quality in transformation of geometric to orthometric heights.

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“…The selection of the covariance model is partially based on the frequent use of GM3 model in the literature for geoid (Kavzoglu and Saka 2005) or gravity interpolation (Moreaux 2008). The use of this and other planar models is very popular in local gravity modeling by LSC and in the analyses of the covariance parameters (Camacho et al 1997;Kotsakis 2007).…”

Section: Assigning Noise By Restricted Maximum Likelihood (Reml)mentioning

confidence: 99%

Least squares collocation with uncorrelated heterogeneous noise estimated by restricted maximum likelihood

Jarmołowski

2015

J Geod

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The article describes the estimation of a priori error associated with heterogeneous, non-correlated noise within one dataset. The errors are estimated by restricted maximum likelihood (REML). The solution is composed of a cross-validation technique named leave-one-out (LOO) and REML estimation of a priori noise for different groups obtained by LOO. A numerical test is the main part of this case study and it presents two options. In the first one, the whole data is split into two subsets using LOO, by finding potentially outlying data. Then a priori errors are estimated in groups for the better and worse subset, where the latter includes the mentioned outlying data. The second option was to select data from the neighborhood of each point and estimate two a priori errors by REML, one for the selected point and one for the surrounding group of data. Both ideas have been validated with the use of LOO performed only in points of the better subset from the first kind of test. The use of homogeneous noise in the two example sets leads to LOO standard deviations equal 1.83 and 1.54 mGal, respectively. The group estimation generates only small improvement at the level of 0.1 mGal, which can also be reached after the removal of worse points. The pointwise REML solution, however, provides LOO standard deviations that are at least 20 % smaller than statistics from the homogeneous noise application.

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Modelling local GPS/levelling geoid undulations using artificial neural networks

Cited by 64 publications

References 19 publications

A priori noise and regularization in least squares collocation of gravity anomalies

A priori noise and regularization in least squares collocation of gravity anomalies

Hybrid Geoid Model: Theory and Application in Brazil

Least squares collocation with uncorrelated heterogeneous noise estimated by restricted maximum likelihood

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