On the third dimension in robustness analysis

Abstract

Robustness analysis is a combination of Baarda’s classical reliability analysis and geometrical strength analysis that is based on strain. It measures the ability of a geodetic network to oppose deformations caused by the maximum undetectable biases that are obtained from internal reliability analysis. The virtual deformations originated from undetected biases might be portrayed as displacements. The application of robustness analysis to geodetic networks depends on the dimension of the network. There are some discrepancies among the robustness analysis of levelling networks, horizontal control networks and three-dimensional networks. As well known, heights can be determined precisely in a levelling network using trigonometric heighting or differential leveling methods. Nevertheless, horizontal coordinates are generally approximately known in these types of networks. Therefore, it is needed to concentrate on the vertical displacements. In the present study, we discuss the robustness analysis of one-dimensional networks. Furthermore, some numerical examples are given.