On the use of two L1 norm minimization methods in geodetic networks

L1 norm adjustment is a powerful technique to detect gross errors in geodetic observations. This paperinvestigates the results of two formulations that provide the L1 norm adjustment of a linear functional model.The usual method for implementation of the L1 norm adjustment leads to solving a linear programming (LP)problem. The formulation of the L1 norm minimization is presented based on the LP problem for a rankdeficient linear(ized) system of equations. Then, an alternative technique is explained based on the leastsquares residuals. The results are tested on both linear and nonlinear functional models, which confirm theefficiency of both formulations. The results also indicate that the L1 norm minimization, compared to theweighted least squares method, is a robust technique for the detection of blunders in geodetic observations.Finally, this contribution presents a data snooping procedure to the residuals obtained by the L1 normminimization method.