Geomagnetically induced currents in power systems can cause problems ranging from overload of transformers to power blackout. Modelling can be used to show the GIC flow throughout a power system; however, the modelled GIC values have uncertainties because of the simplifying assumptions. Measurements of GIC in transformer neutral-ground connections are usually only available from a few substations. The best GIC information could be obtained by combining the measured GIC values with GIC modelling. In this paper we show how GIC measurements can be integrated into the modelling process. Model solutions are presented using two different methods. Normally, the system can be solved by matrix inversion to give a unique solution. Adding measured GIC values leads to an overdetermined system of linear equations. We show that a solution can be obtained by using the general Least Squares Estimation procedure based on the Singular Value Decomposition technique. The method of solution is demonstrated using a hypothetical power system.