With the increasing demand for Lithium-ion batteries in an electric vehicle (EV), it is always crucial to develop a highly accurate and low-cost state estimation method for the battery management system (BMS). Presently, the dual extended Kalman filter (DEKF) is extensively utilized for online SOC estimation. However, the problem of battery model parameter divergence from the true value greatly affects the estimation accuracy under realistic dynamic loading conditions. In this paper, the new dual forgetting factor-based adaptive extended Kalman filter (DFFAEKF) is proposed for SOC estimation. The proposed SOC estimation method is combined with the simple SOE estimation approach to develop the combined SOC and SOE estimation method. The quantitative relationships between SOC and SOE for all the test battery cells, which are established with the experimental data collected from different constant current discharge profiles are employed for SOE estimation. To evaluate the performance of the developed combined SOC and SOE estimation method, the three different chemistries battery cells are chosen for the testing under different dynamic loading profiles such as dynamic stress test (DST) and US06 drive cycle. For all the considered test battery cells, the experimental results indicated that the combined SOC and SOE estimation method using the proposed DFFAEKF can estimate the battery states under dynamic operating conditions with root mean square error (RMSE) less than 0.85% and 0.95% respectively. The proposed method also demonstrates fast convergence to its true value under erroneous initial conditions. Additionally, the order of worst-case big O notation complexity of the proposed DFFAEKF is equivalent to DEKF. Besides, the simplicity of the proposed method also supports to reduce the computational burden of the processor used in BMSs, and therefore it is well-suited for EV applications.