Robust M-Estimation in Analysis of Control Network Deformations: Classical and New Method

Abstract

Robust M-estimation is very useful in the geometric deformation analysis of geodetic control networks, especially in the analysis of single-point displacements in these networks. In fact, a robust M-estimation allows one to identify the datum that resists individual displaced points. This paper describes and tests two competing methods for displacement analysis based on robust M-estimation. Both methods accept relative and absolute control networks. The first method is the classical robust method, in which the displacement vector is determined from differences in adjusted coordinates. The second method is a new and alternative robust method, in which the displacement vector is determined from differences in unadjusted observations. The proposed method was conventionally called Generalized Robust Estimation of Deformation from Observation Differences. Classical and proposed robust methods were tested on the basis of the simulated two-epoch observations of the absolute control network of the Montsalvens Dam in Switzerland (which is well known in the literature) and on the basis of Monte Carlo simulations. The test results showed that the proposed robust method, in some cases, might be more efficacious than the classical robust method, especially when low values of displacements that slightly exceed measurement errors are expected. Moreover, this paper showed that the proposed robust method might also be more broadly applied than the classical robust method.