Measuring the robustness potential of the least-squares estimation: geodetic illustration

For a linear least-squares parametric model analysis is carried out of the structure of the projection operator transforming the vector of standardised observations into the vector of standardised residuals. On this basis the properties of the model responses to observational disturbances (i.e. gross errors or blunders) are derived. A final outcome of the research can be summarised as: (1) proposing the robustness characteristics of a model and linking them with the local measures of internal reliability, being the diagonal elements in the projection operator; (2) determining the internal reliability levels satisfying specified robustness requirements, i.e. the possibility of detecting at least one of the k observational disturbances (k=1,2,…) having most disadvantageous locations in the system. The theory and a numerical example show that for the systems which have been designed to a proper level of internal reliability, the least-squares estimation can demonstrate an accordingly high level of robustness. Received: 11 June 1996 / Accepted: 28 April 1997