In Lithium-Ion batteries, the polarising impedance is an important characteristic that has been shown to be a complex function of, among others, both the state of charge and the demanded current. Therefore within a prognostic framework, which typically solely relies on the a prior modelling of the hidden state evolution, the correct characterisation of the functional surface with respect to state of charge and current impacts the accuracy of the predicted end-of-discharge probability density function. This is important in critical systems that rely solely on the Lithium-Ion as a power source and require an unbiased prediction of the end-of-discharge time. This paper demonstrates how a correctly modelled polarising surface can improve prediction accuracy over the state of the art models found in literature. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.