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

Abstract

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.

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

“…This hypothesis test-based approach is called the mean-shift model [20]. The mean-shift model has been widely employed in a variety of applications, such as structural deformation analyses, sensor data processing, the integrity monitoring of GNSS (Global Navigation Satellite System) models and the design and quality control of geodetic networks (see, e.g., [1,3,6,8,12,[19][20][21][22]45,51,[57][58][59][60][61]). The alternative to the mean-shift model is variance inflation.…”

“…In this experiment, we considered two closed levelling networks: one with a low correlation between residuals and another one with a high correlation. For the low correlation case, we used the network given by Rofatto et al [60], whereas for the high correlation, we chose the network from Knight et al [43]. Figures 2a,b show the configuration of these networks, respectively.…”

“…Thus, it is possible to guarantee a high outlier identification rate. This kind of analysis can be performed, for instance, during the design stage of a geodetic network (see, e.g., [60]). Figure 10 gives only the overall rate of P WE .…”

“…Levelling geodetic networks: (a) Levelling network adapted from[60] with a low correlation between w-test statistics; (b) Levelling network adapted from[43] with a high correlation between w-test statistics.…”

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

“…Mean-shift model has been widely employed in a variety of applications, such as structural deformation analyses, sensor data processing, the integrity monitoring of GNSS (Global Navigation Satellite System) models and the design and quality control of geodetic networks (see e.g. [1,3,6,8,12,[19][20][21][22]36,43,[49][50][51][52][53]).…”