Deformation Analysis by Statistical Methods

Abstract

The monitoring of deformations is a very important task in engineering surveying. The object to be investigated is represented by a cluster of points, whose positions are fixed by geodetic observations at different epochs of time. If deformations occur. they cause distortions of the cluster. resulting in position differences hetween epochs. These differences are typically of the same order of magnitude as the observational errors, so statistical methods arc needed to reasonably make inferences on the true behavior of the object. The field of deformation vectors is approximated by linear models that are designed to estimate rigid body displacements and distortions of the object separately. This article presents several robust methods of parameter estimation as alternatives to the conventional least squares approach. They are based on special loss functions that are independent of the reference system. The application of these robust estimators to a real example indicates that for deformation analyses abounded infuence modified Huber estimator yields results that nicely agree with experience.