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Licensed Unlicensed Requires Authentication Published by De Gruyter March 22, 2013

On resistant Lp-Norm Estimation by means of iteratively reweighted least Squares

Christian Marx

Abstract

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.

Published Online: 2013-03-22
Published in Print: 2013-03

© 2013 by Walter de Gruyter GmbH & Co.