Performance comparison of least squares, iterative and global L1 Norm minimization and exhaustive search methods for outlier detection in leveling networks

Abstract

[EN] Different approaches have been proposed to determine the possible outliers existing in a dataset. The most widely used consists in the application of the data snooping test over the least squares adjustment results. This strategy is very likely to succeed for the case of zero or one outliers but, contrary to what is often assumed, the same is not valid for the multiple outlier case, even in its iterative application scheme. Robust estimation, computed by iteratively reweighted least squares or a global optimization method, is other alternative approach which often produces good results in the presence of outliers, as is the case of exhaustive search methods that explore elimination of every possible set of observations. General statements, having universal validity, about the best way to compute a geodetic network with multiple outliers are impossible to be given due to the many different factors involved (type of network, number and size of possible errors, available computational force, etc.). However, we see in this paper that some conclusions can be drawn for the case of a leveling network, which has a certain geometrical simplicity compared with planimetric or three-dimensional networks though a usually high number of unknowns and relatively low redundancy. Among other results, we experience the occasional failure in the iterative application of the data snooping test, the relatively successful results obtained by both methods computing the robust estimator, which perform equivalently in this case, and the successful application of the exhaustive search method, for different cases that become increasingly intractable as the number of outliers approaches half the number of degrees of freedom of the network.