<i>L</i>₁Norm Minimization in GPS Networks

Abstract

The least squares method is a statistical tool for the estimation of unknown parameters. All the results which are derived from the method of least squares are deteriorated when outliers are present in the observation data. Therefore, outliers have to be detected and eliminated by using statistical tests or robust methods. For this purpose, L 1 norm minimization, which is a robust method, can be used in geodetic networks. In this paper, the formulation of L 1 norm minimization for correlated observations is presented. The method is applied to a simulated GPS network. The performances of the least squares method and L 1 norm minimization are compared in the cases of observations with or without outliers. Our example shows that L 1 norm minimization is a more successful method than the least squares method for outlier detection and the obtained coordinates are more reasonable and reliable than those from the least squares when some observations are burdened with blunders.