Outlier Detection in Partial Errors-in-Variables Model

Abstract

Abstract:The weighed total least square (WTLS) estimate is very sensitive to the outliers in the partial EIV model. A new procedure for detecting outliers based on the data-snooping is presented in this paper. Firstly, a two-step iterated method of computing the WTLS estimates for the partial EIV model based on the standard LS theory is proposed. Secondly, the corresponding w-test statistics are constructed to detect outliers while the observations and coefficient matrix are contaminated with outliers, and a specific algorithm for detecting outliers is suggested. When the variance factor is unknown, it may be estimated by the least median squares (LMS) method. At last, the simulated data and real data about two-dimensional affine transformation are analyzed. The numerical results show that the new test procedure is able to judge that the outliers locate in x component, y component or both components in coordinates while the observations and coefficient matrix are contaminated with outliers. Keywords: Partial EIV model; Two-step iterated method; Weighted total least-squares; Outlier detection; Data-snooping; Two-dimensional affine transformation Resumo:O estimador dos Mínimos Quadrados Total é muito sensível à presença de outliers no modelo de observações de erro. Neste trabalho apresenta-se um novo modelo para detecção de outliers baseado na técnica data-snooping. Primeiro, é proposto um método iterativo para determinar o estimador dos Mínimos Quadrados Total na teoria dos Mínimos Quadrados. Em seguida, o teste estatatístico w é construído para detectar outliers enquanto as observações e a matriz de coeficientes são contaminadas com a presença de outliers, sendo sugerido um algoritmo específico para detecção de outliers.

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).…”

Performing 3d Similarity Transformation With Large Rotation Angles Using Constrained Multivariate Total Least Squares

“…Zeng et al (2015) derived the WTLS algorithm with inequality constraints. Zhao and Gui (2017) studied the outlier detection for PEIV model. Because different observation types usually lead to a model with heterogenous observations, variance component estimation for the EIV model was also derived (Xu et al 2014;Wang and Xu 2016).…”