An Introduction to Least-Squares Collocation

Ruffhead, A. C.

doi:10.1179/sre.1987.29.224.85

Cited by 13 publications

(5 citation statements)

References 2 publications

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“…Least Square Collocation is most commonly used in geodesy for geoid determination, interpolation, and spherical harmonic coefficients [10]. Collocation is useful for predicting and filtering gravity anomalies from reduced gravity observations; the term "reduced" here refers to removing normal gravity [11]. The method used to calculate the geoid in Sudan is the remove-compute-restore (RCR) methodology.…”

Section: Methodsmentioning

confidence: 99%

Determination of a new gravimetric geoid modelling for Sudan using the least-squares collocation technique

Osman

Anjasmara

2023

IOP Conf. Ser.: Earth Environ. Sci.

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The main purpose of this study is to compute a new gravimetric geoid model for Sudan by using the least-square collocation technique (LSC method) and applying the remove-compute-restore (RCR) technique. The computation of the model contains different datasets which are the gravity contribution of the model GO_CONS_GCF_2_TIM_R6e degree/order 300, BGI free-air gravity dataset in Sudan, GPS/levelling data, and high-resolution topographic information from ASTER digital elevation model. The “residual gravity anomalies” were run through the GEOCOL program using the GRAVSOFT software package, and the effects were restored to calculate the quasi-geoid surface (height anomalies). The gravimetric geoid was computed by adding the (N − 𝜁 h ) separation term to the quasi-geoid and was fitted to the GPS and levelling data provided by Sudan. The accuracy of our gravimetric geoid model SDN-LSC-G22 of the area of Sudan and some areas of bordering countries has been investigated by using geoid undulations computed from GPS and levelling data and by investigating the differences between the geoids of the GGM models which are EGM2008 and SGG-UGM-2. Our gravimetric geoid model (SDN-LSC-G22) has indicated an accuracy of 17.4 cm, in terms of a standard deviation compared with 66 GPS and Leveling data distributed in the area of Khartoum (most of these points are control points and benchmarks). Also, we evaluated our gravimetric geoid model by using 19 points distributed in the area of Sudan, and they indicated a standard deviation of 51.3 cm. The overall accuracy of SDN-LSC-G22 compared with the geoid undulation of all GPS and levelling has indicated an STD of 34.1 cm. The model SDN-LSC-G22 has shown better accuracy and significant differences compared with the GGM models EGM2008 and SGG-UGM-2 in terms of the differences with the available GPS and levelling data which have shown ~17 cm differences using (Abdalla, 2009) GPS and levelling data. It has demonstrated STD of ~17 cm differences by using 66 GPS and levelling data. Therefore, the model SDN-LSC-G22 provided better improvements and reliable geoid heights over Sudan compared to EGM2008 and SGG-UGM-2 gravity field models.

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Section: Methodsmentioning

confidence: 99%

Determination of a new gravimetric geoid modelling for Sudan using the least-squares collocation technique

Osman

Anjasmara

2023

IOP Conf. Ser.: Earth Environ. Sci.

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“…Tanto a CMQ quanto a krigagem são consideradas difíceis em vista da manifestação usual das etapas relacionadas aos mínimos quadrados. Ruffhead (RUFFHEAD, 1987) cita a dificuldade em separar a etapa que gera as funções e o seu posterior ajustamento, embora essa técnica já tenha sido utilizada desde 1976 (RAMPAL, 1976), por exemplo, na Fotogrametria. Os autores ainda discretizam o tratamento de parte das observáveis (como ruído ou como efeito sistemático), escolhido pelo operador.…”

Section: Histórico E Estado Da Arteunclassified

Revisitando o variograma e covariância

Pereira,

Moraes,

Timm

2024

Rev. Bras. Cartogr.

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Este trabalho revisa as funções covariância empírica (CE) e o variograma (VAR), associadas a Colocação por Mínimos Quadrados (CMQ) e a Krigagem, respectivamente. O texto almeja facilitar o aprendizado da técnica aos interessados e chamar a atenção para questões específicas relacionadas às projeções cartográficas. A CMQ e a krigagem são técnicas adotadas nas geociências para análise, predição e interpolação/extrapolação de dados. A sua aplicação adequada pode ser entendida em duas etapas principais: 1) a criação de mais de uma função, CE ou VAR, dependendo do modo como ela foi construída, e 2) o ajustamento dessa função, usualmente adotando o Método dos Mínimos Quadrados (MMQ) para fazer a predição. Este trabalho está concentrado nas funções CE e VAR de modo a recuperar suas definições mais originais com exemplos confeccionados pelos autores. Como aplicação, apresenta diferenças construtivas das CE e VAR geradas partir de coordenadas curvilíneas dos Sistemas Geodésicos de Referência e coordenadas dos Sistemas Projetivos. A exposição dos coeficientes ajustados pelo MMQ torna evidente as diferentes respostas. Por último, sugere cuidados importantes na utilização destas funções a partir de sistemas projetivos.

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“…The flat-spots effect can be reduced by splitting the function into a trend model and a signal (analogous to the noise-free version of least-squares collocation; see Ruffhead (1987)). If a suitable trend model is identified, its parameters can be obtained by least-squares optimisation.…”

Section: Inverse Distance To a Powermentioning

confidence: 99%

Enhancement of inverse-distance-weighting 2D interpolation using accelerated decline

Ruffhead

2023

Reports on Geodesy and Geoinformatics

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Two-dimensional interpolation – or surface fitting – is an approximation tool with applications in geodetic datum transformations, terrain modelling and geoid determination. It can also be applied to many other forms of geographic point data, including rainfall, chemical concentrations and noise levels. The problem of fitting of a smooth continuous interpolant to a bivariate function is particularly difficult if the dataset of control points is scattered irregularly. A typical approach is a weighted sum of data values where the sum of the weights is always unity. Weighting by inverse distance to a power is one approach, although a power greater than 1 is needed to ensure smooth results. One advantage over other methods is that data values can be incorporated into the interpolated surface. One disadvantage is the influence of distant points. A simple cut-off limit on distance would affect continuity. This study proposes a transition range of accelerated decline by means of an adjoining polynomial. This preserves smoothness and continuity in the interpolating surface. Case studies indicate accuracy advantages over standard versions of inverse-distance weighting.

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An Introduction to Least-Squares Collocation

Cited by 13 publications

References 2 publications

Determination of a new gravimetric geoid modelling for Sudan using the least-squares collocation technique

Determination of a new gravimetric geoid modelling for Sudan using the least-squares collocation technique

Revisitando o variograma e covariância

Enhancement of inverse-distance-weighting 2D interpolation using accelerated decline

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