Indiana University-Purdue University Indianapolis (IUPUI) / Moving Horizon Estimation (MHE) is a powerful estimation technique for tackling the estimation problems of the state of dynamic systems in the presence of constraints, nonlinearities and disturbances and measurement noises. In this work, the Moving Horizon Estimation approach is applied in estimating the State of Charge (SOC) and State of Health (SOH) of a battery and the results are compared against those for the traditional estimation method of Extended Kalman Filter (EKF). The comparison of the results show that MHE provides improvement in performance over EKF in terms of different state initial conditions, convergence time, and process and sensor noise variations. An equivalent circuit battery model is used to capture the dynamics of the battery states, experimental data is used to identify the parameters of the battery model. MHE based state estimation technique is applied to estimates the states of the battery model, subjected to various estimated initial conditions, process and measurement noises and the results are compared against the traditional EKF based estimation method. Both experimental data and simulations are used to evaluate the performance of the MHE. The results shows that MHE performs better than EKF estimation even with unknown initial state of the estimator, MHE converges faster to the actual states,and also MHE is found to be robust to measurement and process noises.