Resumo: Nesse artigo, aplicações da minimização da norma L1 (ML1) e da norma L∞ (ML∞) na estimação de redes altimétricas foram investigadas. Redes de nivelamento simuladas pela Técnica de Monte Carlo e dados reais da rede brasileira de nivelamento foram empregados nos experimentos. Na identificação de outliers pela ML1, foi verificado que o ajustamento com pesos unitários apresentou condições vantajosas em relação ao modelo estocástico usual dos pesos proporcionais ao inverso do comprimento das linhas de nivelamento. O Classificador VL1, que estipula um Valor de Corte para os resíduos do ajustamento pela ML1 a partir do qual a respectiva observação passa a ser classificada como outlier, foi proposto. A taxa de sucesso dele na identificação de outliers foi superior à do procedimento data snooping iterativo em cenários de geometria da rede deficiente. Já a aplicação da ML∞ investigada é posterior ao tratamento de outliers. Um modelo estocástico alternativo para ajustamento da rede pelo MMQ que aproveitou a característica de minimização do máximo resíduo absoluto da rede no ajustamento pela ML∞ foi analisado. Além dessa minimização, o ajustamento da rede pelo MMQ com o modelo alternativo gerou, na significativa maioria dos casos, resíduos e precisão desses e dos parâmetros estimados mais homogêneos, com menor desvio padrão, que aqueles com o modelo estocástico usual. Todos os resultados são especialmente relevantes para o caso de redes altimétricas.

Abstract In this paper, applications of L1 norm minimization (ML1) and of L∞ norm minimization (ML∞) in the estimation of leveling networks were investigated. Leveling networks simulated by the Monte Carlo technique and real data from the Brazilian leveling network were employed in the experiments. In the identification of outliers by ML1, it was verified that the adjustment with unit weights presented advantageous conditions in relation to the usual stochastic model of weights of observations as proportional to the inverse of the length of the leveling lines. The Classificador VL1, which stipulates a cut-off value for the residuals of the adjustment by ML1 from which the respective observation is classified as outlier, was proposed. Its success rate in identifying outliers was higher than that of the iterative data snooping procedure in poor network geometry scenarios. The application investigated for ML∞ is after the treatment of outliers. An alternative stochastic model for network adjustment by Least Squares (LS) that took advantage of the characteristic of minimization of the maximum absolute residual of the network in the adjustment by ML∞ was analyzed. In addition to this minimization, the adjustment of the network by LS with the proposed model generated, in most cases, residuals and precision of these and of the estimated parameters more homogeneous, with lower standard deviation, than those with the usual stochastic model. All results are especially relevant for the case of altimetric networks.

Abstract This article has theoretically discussed some points regarding outliers caused by errors in geodetic observations (see consideration made). Comments have also been made on the usual 3σ-rule to identify outliers and its common approachs in the simulation of outliers in geodetic networks. Three simulated experiments have been conducted to verify the elements discussed. In the first one, with the simulation of random errors, we have verified that it can have a magnitude large enough to generate outliers. In the second one, in scenarios of leveling network simulated by Monte Carlo methods, observations containing gross errors with a lower magnitude than their respective σ tended to not be identified as outliers by the iterative data snooping procedure. This has also occurred in the third experiment, in which gross errors of magnitude 3.1σ had their value masked by the random error of the respective observation. From the conceptual discussion presented, we have concluded that gross error and outlier are not synonyms, and neither is one a particular case of the other. From the obtained results, we have concluded that there are inconsistencies in how outliers have been simulated in geodetic networks, which indicates the need to continue with investigations.