An electrochemical Parameter Estimation (PE) study of lithium-ion batteries for different materials is presented. The PE methodology is developed in Part I of the study and the challenges on the different materials for the positive electrode including LiCoO2, LiMn2O4 and LiFePO4 are examined in Part II. The most influential electrochemical parameters of the Li-ion battery are estimated by means of an inverse method. The inverse method rests on five elements: the input parameters, a direct model, the reference data, an objective function and an optimizer. Eight electrochemical variables are considered as the target of the PE study. A simplified version of Pseudo-two-Dimensional (P2D) model is developed for the direct model. The P2D model predictions coupled to a random noise function are employed to generate the reference data. The data include the cell potential values with respect to the battery capacity at low and high discharge rates. The least-squared function and Genetic Algorithm are employed as the objective function and its optimizer, respectively. The best time domain for the estimation of each parameter is calculated by using a sensitivity analysis performed for different discharge curves. Results show that the methodology remains accurate and stable at both low and high discharge rates. (C) The Author(s) 2016. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. All rights reserved.