Now the lithium ion batteries are widely used in electric vehicles (EV). The battery modeling and state estimation are of great importance. The rigorous physics-based electrochemical model is too complicated for on-line simulation in vehicle. In this work, the simplification of the physics-based model for application on real vehicle is proposed. An improved single particle (SP) model is introduced with high precision and the same level of computations as the original single particle model. A simplified pseudo-two-dimensional (SP2D) model is developed. The distribution of the pore wall flux is analyzed and an approximate method is developed to find the solution. The developed models are compared with rigorous electrochemical model and original SP models. The results demonstrate that the models introduced in this work could simulate the battery efficiently without too much loss of accuracy. A state of charge (SOC) estimation algorithm using the Luenberger observer with the SP2D model is proposed and shows high precision. This SOC estimation method could be used in the BMS in real vehicle. (C) 2014 Elsevier B.V. All rights reserved.