Network robustness measures based on responses to undetectable observation errors

The examination of the concept of network robustness to observation gross errors based on the reliability and strain analysis (see Vanicek et al 2001), has revealed some disadvantages due to a discrete nature of the network's structure. The weak sides of the strain analogy shown in (Gambin et al. 2008), specially for small networks, speak in favour of finding a non-tensor replacement for network robustness measures. One of the possible approaches, applicable to all types of geodetic networks with uncorrelated observations and sufficient for most practical purposes, could be the use of traditional concepts of internal and external reliability for assessing network robustness to observation gross crrors. Such a proposal, maintaining the maximum undetectable error in an individual observation as a source of network deformations (as in Vanicek et al. 2001), and analyzing the resulting node displacements and element deformations, is discussed and illustrated on a simple numerical example. The proposal provides a direct Iink between the robustness and the accuracy analysis of a network, and has a clear onterpretation in terms of mechanical strength analogy. As a theoretical support, deformation-oriented properties of the reliability matrix and the properties of network responses to undetectable observation errors are analyzed.