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

Document Type: Original Article

Author

Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan, Iran

Abstract

L1 norm adjustment is a powerful technique to detect gross errors in geodetic observations. This paper
investigates 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 rank
deficient linear(ized) system of equations. Then, an alternative technique is explained based on the least
squares residuals. The results are tested on both linear and non-linear functional models, which confirm the
efficiency of both formulations. The results also indicate that the L1 norm minimization, compared to the
weighted 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 norm
minimization method.

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Main Subjects


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