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

Abstract

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.

Outlier=gross Error? Do Only Gross Errors Cause Outliers in Geodetic Networks? Addressing These and Other Questions

“…Nevertheless, there is a continuous research on outliers in geodetic networks. Among others, in addition to those papers already mentioned in this article, we can also cite: (Klein, Matsuoka and Souza 2011), (Baselga 2011), (Hekimoglu, Erdogan and Tunalioglu 2012), (Klein et al 2012), (Hekimoglu and Erdogan 2013), (Klein, Matsuoka and Monico 2013), (Erdogan 2014), (Guo 2015), (Klein, Matsuoka and Guzatto 2015), (Zhao and Gui 2017), (Rofatto, Matsuoka and Klein 2017), (Teunissen 2018) and (Rofatto, Matsuoka and Klein 2018).…”

Monte Carlo Simulation for Outlier Identification Studies in Geodetic Network: An Example in A Levelling Network Using Iterative Data Snooping

“…MCS methods are used whenever the functional relationships are analytically not tractable, as is the case for Iterative Data Snooping procedure (Rüdiger Lehmann, 2012b). The MCS has already been applied in outlier detection (Lehmann & Scheffler, 2011;Klein et al, 2012;Klein et al, 2015;Erdogan, 2014;Niemeier & Tengen, 2017) The studies presented in this paper are a continuation of the first experiments presented by Rofatto et al (2017). However, unlike Rofatto et al, (2017), here in this paper we evaluate the proposed method in a geodetic network with uncorrelated observations and also we analyze the power of the test of Iterative Data Snooping procedure when outliers of magnitude equal to the MDB (Minimal Detectable Bias) are inserted into the geodetic network.…”

The efficiency of different outlier detection approaches in geodetic networks: case study for Pobednik statue

“…The principle of the robust-M-estimation application is based on the iterative Least squares (LS) adjustment respecting the condition about gradual changes of the weights of individual observations (Třasák and Štroner, 2014). The LS is very sensitive to deviations from the model assumptions (Hampel et al, 1986) and it extends the effects of outliers to residuals of all observations (Hekimoglu et al, 2011(Hekimoglu et al, , 2014Hekimoglu and Erdogan, 2012;Erdogan, 2014). LS play an essential role in all methods of detecting outliers mentioned above.…”

“…MSR is given as the number of successes divided by the number of experiments (Hekimoglu andKoch, 1999, 2000). MSR is used for the efficiency measurements of outlier detection methods (Hekimoglu and Erenoglu, 2007;Erenoglu and Hekimoglu, 2010;Hekimoglu et al, 2011Hekimoglu et al, , 2014Erdogan, 2014) and methods of deformation analysis (Hekimoglu, Erdogan and Butterworth, 2010;Nowel, 2016;Sušić et al, 2017).…”