Effect of heteroscedasticity and heterogeneousness on outlier detection for geodetic networks

Hekimoğlu, Şerif; Erenoǧlu, Ramazan Cüneyt

doi:10.1007/s00190-006-0095-z

Cited by 41 publications

(34 citation statements)

References 19 publications

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“…In addition, for each sample was contaminated by one and two outliers 100 times. Thus, 10 000 contaminated samples were obtained for one outlier and two outliers separately (HEKIMOGLU and ERENOGLU, 2007;ERENOGLU and HEKIMOGLU, 2010;HEKIMOGLU et al, 2011;HEKIMOGLU and ERDOGAN, 2013).…”

Section: Classical Approachmentioning

confidence: 99%

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An Outlier Detection Method in Geodetic Networks Based on the Original Observations

Erdoğan¹

2014

Bol. Ciênc. Geod.

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The observations in geodetic networks are measured repetitively and in the network adjustment step, the mean values of these original observations are used. The mean operator is a kind of Least Square Estimation (LSE). LSE provides optimal results when random errors are normally distributed. If one of the original repetitive observations has outlier, the magnitude of this outlier will decrease because the mean value of these original observations is used in the network adjustment and outlier detection. In this case, the reliability of the outlier detection methods decreases, too. Since the original repetitive observations are independent, they can be used in the adjustment model instead of the estimating mean value of them. In this study, to show the effects of the estimating mean value of the original repetitive observations, a leveling network that contains both outward run and backward run observations were simulated. Tests for outlier, Huber and Danish methods were applied to two different cases. First, the mean values of the original observations (outward run and return run) were used; and then all original observations were considered in the outlier detection. The reliabilities of the methods were measured by Mean Succes Rate. According to the obtained results, the second case has more reliable results than first case. Keywords: Outlier Detection; Original Observations; Tests for Outlier; Robust Method; Reliability.Erdogan, B.Bol. Ciênc. Geod., sec. Artigos, Curitiba, v. 20, n o 3, p.578-589, jul-set, 2014.5 7 9 RESUMO As observações nas redes geodésicas são medidas repetitivamente, e na fase de ajustamento, os valores médios destas observações originais são usados. O operador "média", é um tipo de estimador de mínimos quadrados (LSE). O LSE oferece resultados ótimos quando os erros aleatórios são normalmente distribuídos. Se uma das observações repetitivas originais tem outlier, a magnitude deste outlier diminui porque o valor médio das observações originais é usado no ajustamento da rede e consequentemente, na detecção de outlier a confiabilidade do método também diminui. Uma vez que as observações repetitivas originais são independentes, elas próprias podem ser usadas no método de ajustamento ao invés do valor médio estimado. Neste estudo, para mostrar os efeitos do valor médio estimado das observações repetitivas originais, uma rede de nivelamento que contém ambas as observações de ida e volta dos percursos foi simulada com outliers. Para testar a detecção dos mesmos, os métodos Huber e Danish foram aplicados em dois casos diferentes. Primeiramente, os valores médios das observações originais (de ida e de volta) foram usados, e então todas as observações originais foram consideradas na detecção dos outliers. A confiabilidade dos métodos foi medida pela razão de sucesso médio. De acordo com os resultados calculados o segundo caso teve resultados mais confiáveis do que o primeiro.

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Section: Classical Approachmentioning

confidence: 99%

“…reliability) of the robust methods (XU 2005;YOUCAI 1995). The MSR has been used in regression analysis (HEKIMOGLU and KOCH 1999;HEKIMOGLU and KOCH 2000;HEKIMOGLU and BERBER 2003;HEKIMOGLU 2005) also in geodetic networks (HEKIMOGLU and ERENOGLU 2007;ERENOGLU and HEKIMOGLU 2010;HEKIMOGLU et al 2011;HEKIMOGLU and ERDOGAN 2013).…”

Section: Introductionmentioning

confidence: 99%

An Outlier Detection Method in Geodetic Networks Based on the Original Observations

Erdoğan¹

2014

Bol. Ciênc. Geod.

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“…To this end one from the basic strain parameters ( , , ) determines the additional ones (Talich, 2007): model efficiency. A more detailed explanation of MRS can be found in the literature (Hekimoglu and Koch, 1999;Hekimoglu and Erenoglu, 2007;Erenoglu and Hekimoglu, 2010;Nowel, 2016a). …”

Section: Resultsmentioning

confidence: 99%

Geometric deformation analysis in free geodetic networks: case study for Fruska Gora in Serbia

Sušić¹

2017

Acta Geodynamica Et Geomaterialia

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“…Another problem is that the robust procedures or methods are not always efficient, and their robustness, effectiveness or success depend on many factors (see, e.g. Hekimoglu and Erenoglu, 2007;Prószyński, 2010). Thus, it may happen that gross errors still influence results of analyses, regardless of methods applied.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity of robust estimators applied in strategy for testing stability of reference points. EIF approach

Duchnowski¹

2011

Geodesy and Cartography

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Abstract:In deformation analyses, it is important to find a stable reference frame and therefore the stability of the possible reference points must be controlled. There are several methods to test such stability. The paper's objective is to examine one of such methods, namely the method based on application of R-estimation, for its sensitivity to gross errors. The method in question applies three robust estimators, however, it is not robust itself. The robustness of the method depends on the number of unstable points (the fewer unstable points there are, the more robust is the proposed method). Such property makes it important to know how the estimates applied and the strategy itself respond to a gross error. The empirical influence functions (EIF) can provide necessary information and help to understand the response of the strategy for a gross error. The paper presents examples of EIFs of the estimates, their application in the strategy and describes how important and useful is such knowledge in practice.

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Effect of heteroscedasticity and heterogeneousness on outlier detection for geodetic networks

Cited by 41 publications

References 19 publications

An Outlier Detection Method in Geodetic Networks Based on the Original Observations

An Outlier Detection Method in Geodetic Networks Based on the Original Observations

Geometric deformation analysis in free geodetic networks: case study for Fruska Gora in Serbia

Sensitivity of robust estimators applied in strategy for testing stability of reference points. EIF approach

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