Chebyshev norm adjustment: what to expect? case study in a leveling network

Resumo

This work drew attention to the Chebyshev norm minimization, a method of adjustment of observations still little explored in the geodetic literature. Chebyshev norm minimization refers to the minimization of the maximum weighted absolute residual of adjusted observations. In addition to contributions to the formulation of Chebyshev norm adjustment by linear programming, numerical examples of its application in a leveling network were presented and compared with the respective Least Squares adjustments in this work. We verified that residuals analysis of Chebyshev norm adjustment is even less effective than of Least Squares for outlier identification. We also highlighted other characteristics of the method that had never been explored in geodetic literature before. In special, Chebyshev norm adjustment presented lower maximum absolute residual, and more homogeneous absolute residuals than LS when applied with the usual distance-dependent stochastic model. More experiments should be conducted in future work to confirm these tendencies. We also analyzed the adjustment by Chebyshev norm minimization with unit weights, which generates the minimum maximum absolute residual for a network. As some characteristics of Chebyshev norm adjustment seen promising, other suggestions for future work were also made.