Fitting a Precise Levelling Network to Control Points Using a Modified Robust Huber’s Mean Error Function

Abstract

The purpose of this research was to fit a high-accuracy levelling network to points of the vertical national control network, the control points of which are unstable because of vertical terrain movements caused by underground mining. For this reason, the robust M-estimation is used to reduce a negative impact of control points with gross errors on the estimated parameters. Because it has been found that the classical nonlinear Huber mean error function does not lead to any reasonable solutions, a new error function, a linear modification of Huber’s function, is introduced here. Using this function, a consistent solution of the robust adjustment and correct values of the estimated parameters can be achieved. To validate the results, other robust weight functions proposed by other authors are implemented as well. The results obtained in the particular variants are very close to those obtained using the proposed linear modification of Huber’s function. Moreover, the authors propose an adjustment strategy that is based on the combination of classical and robust adjustment, which can be applied to identify unstable control points in a levelling network.