Lithium ion batteries are used to store energy in electric vehicles. The lithium ion cell's representing equations are partial differential equations coupled to algebraic equations. In general the state of this type of systems needs to be estimated using a limited number of measurements. State estimation is an important tool for reconstructing the state from available measurements and is employed to estimate the state of charge in batteries. Construction of an estimator is complicated not only by the distributed nature of the dynamics, but also by nonlinearity and also the difficulty of solving differential-algebraic systems of equations. However, the equations can be modified to facilitate the use of online filtering. The resulting equations can be shown to be well-posed and computationally tractable. Simulation results show satisfactory results.