The L1-norm estimation is a resistant estimation method and therefore used for the detection of gross errors in geodetic measurement data. Alternatively, other Lp-norms have been suggested in literature for resistant parameter estimation. A common numerical solution method for Lp-norm estimation is the method of iteratively reweighted least squares. Procedural manners for a successful application of this method are considered. A modification of the method is given, which reduces the number of iterations significantly. By means of a simulation the applicability of the mentioned methods and the success of different Lp-norms in the detection of gross errors are tested. It shows that solving the L1-norm numerically may be unsuccessful and that instead a resistant Lp-norm is to be recommended, which is comparably successful in the detection of gross errors and can successfully be solved numerically by the presented modification of iteratively reweighted least squares.
© 2013 by Walter de Gruyter GmbH & Co.