Uncertainty assessment in geodetic network adjustment by combining GUM and Monte-Carlo-simulations

Niemeier, Wolfgang; Tengen, Dieter

doi:10.1515/jag-2016-0017

Cited by 20 publications

(12 citation statements)

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“…The uncertainty results [12] of 3D points obtained by measurement with laser triangulation is linked with the uncertainty of the inputs. According to GUM (Guides to the expression of Uncertainty in Measurement) [13], uncertainty is determined by the non-negative parameter, which represents the dispersion of a value for a measurement and its precision parameter.…”

Section: Monte Carlo Methodsmentioning

confidence: 99%

A Study on the Uncertainty of a Laser Triangulator Considering System Covariances

Puerto¹,

Estala²,

Mendikute³

2020

Sensors

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A laser triangulation system, which is composed of a camera and a laser, calculates distances between objects intersected by the laser plane. Even though there are commercial triangulation systems, developing a new system allows the design to be adapted to the needs, in addition to allowing dimensions or processing times to be optimized; however the disadvantage is that the real accuracy is not known. The aim of the research is to identify and discuss the relevance of the most significant error sources in laser triangulator systems, predicting their error contribution to the final joint measurement accuracy. Two main phases are considered in this study, namely the calibration and measurement processes. The main error sources are identified and characterized throughout both phases, and a synthetic error propagation methodology is proposed to study the measurement accuracy. As a novelty in uncertainty analysis, the present approach encompasses the covariances of correlated system variables, characterizing both phases for a laser triangulator. An experimental methodology is adopted to evaluate the measurement accuracy in a laser triangulator, comparing it with the values obtained with the synthetic error propagation methodology. The relevance of each error source is discussed, as well as the accuracy of the error propagation. A linearity value of 40 µm and maximum error of 0.6 mm are observed for a 100 mm measuring range, with the camera calibration phase being the main error contributor.

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Section: Monte Carlo Methodsmentioning

confidence: 99%

A Study on the Uncertainty of a Laser Triangulator Considering System Covariances

Puerto¹,

Estala²,

Mendikute³

2020

Sensors

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“…Bulletin of Geodetic Sciences, 24(2): 152-170, Apr-Jun, 2018 example, Ryan and Lachapelle (2001) used simulations to obtain the minimal detectable bias polygon for the case of two outliers; Lehmann and Scheffler (2011) used MCS method to solve the problem how to determine the optimal levels of Type I error probabilities for global and local tests in DS; Lehmann (2012) used MCS method to improve the critical values of the test statistics; Niemeier and Tengen (2017) extended the classical concept of geodetic network adjustment by combining the uncertainty modeling and MCS.…”

Section: Preliminary Conceptsmentioning

confidence: 99%

Design of Geodetic Networks Based on Outlier Identificationcriteria: An Example Applied to the Leveling Network

2018

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Abstract:We present a numerical simulation method for designing geodetic networks. The quality criterion considered is based on the power of the test of data snooping testing procedure. This criterion expresses the probability of the data snooping to identify correctly an outlier. In general, the power of the test is defined theoretically. However, with the advent of the fast computers and large data storage systems, it can be estimated using numerical simulation. Here, the number of experiments in which the data snooping procedure identifies the outlier correctly is counted using Monte Carlos simulations. If the network configuration does not meet the reliability criterion at some part, then it can be improved by adding required observation to the surveying plan. The method does not use real observations. Thus, it depends on the geometrical configuration of the network; the uncertainty of the observations; and the size of outlier. The proposed method is demonstrated by practical application of one simulated leveling network. Results showed the needs of five additional observations between adjacent stations. The addition of these new observations improved the internal reliability of approximately 18%. Therefore, the final designed network must be able to identify and resist against the undetectable outliers -according to the probability levels.Keywords: Reliability, Outlier, Numerical Simulation, Monte Carlo, Design of geodetic networks. Resumo:Nós apresentamos um método de simulação numérica para planejamento de redes geodésicas. O critério de qualidade considerado é baseado no poder do teste do procedimento estatístico data snooping. Esse critério expressa a probabilidade do procedimento data snooping de identificar corretamente um outlier. Em geral, o valor do poder do teste é sempre desconhecido na prática (definido na teoria). Porém, com o advento de computadores mais rápidos e sistemas de armazenamento de dados de maior capacidade, o poder do teste pode ser estimado por meio de simulações numéricas. O número de experimentos que o procedimento data snooping identifica corretamente um outlier é quantificado por meio do método Monte Carlo de simulação. Se a configuração inicial da rede não atender o critério de confiabilidade, então uma nova observação é adicionada no projeto da rede. O método não faz uso de observações reais coletadas em campo, dependendo apenas da configuração geométrica da rede, das incertezas das observações e da magnitude dos outliers. A eficiência do método é verificada por meio de um exemplo numérico de uma rede de nivelamento geométrico simulada. Os resultados mostraram a necessidade de cinco observações adicionais entre os pontos adjacentes. A adição destas novas observações melhorou a confiabilidade interna da rede de aproximadamente 18%. Portanto, a rede é projetada de modo que seja capaz de identificar outliers e ainda resistir a outilers não identificados nas observações -de acordo com os níveis de probabilidade.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Matsuoka

Rofatto

Klein

et al. 2019

Geoplanning: Journal of Geomatics and Planning

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Today with the fast and powerful computers, large data storage systems and modern softwares, the probabilities distribution and efficiency of statistical testing algorithms can be estimated using computerized simulation. Here, we use Monte Carlo simulation (MCS) to investigate the power of the test and error probabilities of the Baarda’s iterative data snooping procedure as test statistic for outlier identification in the Gauss-Markov model. The MCS discards the use of the observation vector of Gauss-Markov model. In fact, to perform the analysis, the only needs are the Jacobian matrix; the uncertainty of the observations; and the magnitude intervals of the outliers. The random errors (or residuals) are generated artificially from the normal statistical distribution, while the size of outliers is randomly selected using standard uniform distribution. Results for simulated closed leveling network reveal that data snooping can locate an outlier in the order of magnitude 5σ with high success rate. The lower the magnitude of the outliers, the lower is the efficiency of data snooping in the simulated network. In general, considering the network simulated, the data snooping procedure was more efficient for α=0.01 (1%) with 82.8% success rate.

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Uncertainty assessment in geodetic network adjustment by combining GUM and Monte-Carlo-simulations

Cited by 20 publications

References 10 publications

A Study on the Uncertainty of a Laser Triangulator Considering System Covariances

A Study on the Uncertainty of a Laser Triangulator Considering System Covariances

Design of Geodetic Networks Based on Outlier Identificationcriteria: An Example Applied to the Leveling Network

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

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