Aplicação das normas L1 e L∞ em redes altimétricas: identificação de outliers e construção do modelo estocástico

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.