Recent contributions have shown that two widely used formulations of the tap-changing transformer model are controversial, as they generate dissimilar results depending on the selected tap and operating point. In recent works, the authors proposed a new model and demonstrated its consistency to reconcile this debate. It introduces a parameter which stands for the ratio between the impedances of the nominal and tapped winding of the transformer. However, this parameter is not provided with and cannot be obtained from standard datasheets, which compels the users to rely on rough approximations. To overcome this problem, an offline state-vector-augmented parameter estimation method capable of providing accurate estimates of transformer impedance ratios is proposed in this work. It is demonstrated that their use can effectively lead state estimators to better estimates of system states. This work also contributes with the derivatives of the different measurement functions in terms of the impedance ratios, which are essential for this or any other linearized state estimator. A multi-snapshot implementation is used to obtain a twofold advantage — increased measurement redundancy and improved accuracy of the estimated parameters. A detailed formulation of the implementation and several case studies are presented to demonstrate the validity of the proposal.