Experimental Data-Driven Parameter Identiﬁcation and State of Charge Estimation for a Li-Ion Battery Equivalent Circuit Model

: It is well known that accurate identiﬁcation of the key state parameters and State of Charge (SOC) estimation method for a Li-ion battery cell is of great signiﬁcance for advanced battery management system (BMS) of electric vehicles (EVs), which further facilitates the commercialization of EVs. This study proposed a systematic experimental data-driven parameter identiﬁcation scheme and an adaptive extended Kalman Filter (AEKF)-based SOC estimation algorithm for a Li-Ion battery equivalent circuit model in EV applications. The key state parameters of Li-ion battery cell were identiﬁed based on the second-order resistor capacitor (RC) equivalent circuit model and the experimental battery test data using genetic algorithm (GA). Meanwhile, the proposed parameter identiﬁcation procedure was validated by carrying out a comparative study of the simulated and experimental output voltage under the same input current proﬁle. Then, SOC estimation was performed based on the AEKF algorithm. Finally, the effectiveness and feasibility of the proposed SOC estimator was veriﬁed by loading different operating proﬁles.


Introduction
In recent years, Li-Ion battery (LIB) has been widely used in electric vehicles (EVs) and hybrid electric vehicles (HEVs) due to their high energy density, long cycle-life, low self-discharge and high specific power [1,2]. For EVs and HEVs, the accurate state parameters and state-of-charge (SOC) of the LIB is of great significance in real-time control and high-performance operation for advanced battery management system (BMS) of EVs because these parameters are often used to implement the optimum control of charging and discharging process, which is not only beneficial for efficient vehicular BMS, but also for the diagnosis and prognosis of the LIB behavior. Therefore, to manage the LIB more efficiently and improve the battery performance, it is necessary to obtain the inner state parameters and to make an accurate SOC estimation for the battery accurately.
A large quantity of battery SOC estimation methods based on Li-Ion battery equivalent circuit mode (ECM) have been reported in the literature [3][4][5][6][7][8][9][10][11][12], which can be classified as coulomb counting [3][4][5], open circuit voltage (OCV)-based method [6,7], and model-based method [8][9][10][11][12]. Among these studies, the model-based filtering estimation methods such as the Kalman filter (KF) and the related extended Kalman filter (EKF) have been extensively applied due to their closed-loop nature and concerning various uncertainties. For instances, Plett et al. [13][14][15] firstly adopted EKF to estimate SOC using different battery models. However, the Kalman filter-based algorithm strongly depends on the precision of the battery model and the predetermined variables of the system noise such as Figure 1. Schematic diagram of the second-order RC model.
According to the literature [28], the electrical behavior of the second-order RC battery model can be governed by Equation (3) as follows: Generally, the battery SOC is defined as a ratio of the remaining capacity over the nominal available capacity, and the SOC calculated by Coulomb Counting can be expressed in the discrete form as [29]: where ( 1) SOC k  and () SOC k are the SOC at (k + 1)th and kth sampling time, respectively;  is the Coulomb efficiency that is assumed to be 1 at charging and 0.98 at discharging as the battery works in a limited current range; QN is the nominal capacity; and ∆t represents the sampling interval.
It should be noted that oc () U SOC is usually a nonlinear function of SOC at the same temperature, which will be demonstrated in Section 3.1. Define the state vector of Equation (1) as , and the current I(t) and terminal voltage Ut as the input and output variables, respectively, then, using the zero-order hold discretization method in [30], the discrete-time state equations of the second-order RC battery model can be written as: where k x denotes the immeasurable state vector at time step k, k u (=I(k)) denotes the input vector, x u is the nonlinear measurement function, which can be expressed as: According to the literature [28], the electrical behavior of the second-order RC battery model can be governed by Equation (3) as follows: Generally, the battery SOC is defined as a ratio of the remaining capacity over the nominal available capacity, and the SOC calculated by Coulomb Counting can be expressed in the discrete form as [29]: where SOC(k + 1) and SOC(k) are the SOC at (k + 1)th and kth sampling time, respectively; η is the Coulomb efficiency that is assumed to be 1 at charging and 0.98 at discharging as the battery works in a limited current range; Q N is the nominal capacity; and ∆t represents the sampling interval. It should be noted that U oc (SOC) is usually a nonlinear function of SOC at the same temperature, which will be demonstrated in Section 3.1. Define the state vector of Equation (1) as x = SOC U 1 U 2 T , and the current I(t) and terminal voltage U t as the input and output variables, respectively, then, using the zero-order hold discretization method in [30], the discrete-time state equations of the second-order RC battery model can be written as: where x k denotes the immeasurable state vector at time step k, u k (=I(k)) denotes the input vector, y k (=U t (k)) is the observed output voltage, and ω k and υ k are an independent and zero mean Gaussian white noise signals, respectively. f (x k , u k ) is the nonlinear system process function, and h(x k , u k ) is the nonlinear measurement function, which can be expressed as:

Experimental Data-Driven Parameter Identification
The experimental data-driven parameter identification in this section starts with the battery experimental investigation, which is utilized to test the characteristics of the battery, identify the Li-ion battery parameters and verify the effectiveness of the proposed SOC estimation method. It is noted that the identified parameters include R 0 , R 1 , C 1 , R 2 , C 2 and the nonlinear function U oc (SOC) for the second-order RC equivalent circuit model shown in Figure 1.

Battery Experimental Setup
The experiment data of Li-ion battery used for this study were acquired through the test bench shown in Figure 2, which is composed of an Arbin BT2000 Cycler with MITS Pro soft (ARBIN INSTRUMENS, College Station, TX, USA), a well-controlled temperature chamber for environment control and a host computer for the human-machine interface and test data storage, as well as the Li-ion battery cells. It is noted that the test cells are SONY lithium nickel-manganese-cobalt oxide (NMC) battery (SONY Inc, Tokyo, Japan) with graphite anode. According to the producer's specification, the battery nominal capacity is 2 Ah, and the nominal voltage is 3.7 V. Lower and upper cut-off voltage is 2.5 V and 4.2 V, respectively. The temperature is controlled by a constant temperature battery experimental chamber. At different given temperatures (5 • C, 25 • C, 30 • C, and 40 • C), the battery cells are relatedly cycled. The measured signals including input current, output voltage, the battery's input current and terminal voltage, the battery's OCV, and SOC corresponded to OCV are recorded by Arbin BT2000 (ARBIN INSTRUMENS, College Station, TX, USA) under different aging states (in the order of hybrid pulse power characterization (HPPC), standard US06 driving cycle (US06) and 1C-rate discharge operating condition), and then exported to store in mat files for Matlab software (Matlab 2016b, MathWorks Inc, Natick, MA, USA) processing.

Experimental Data-Driven Parameter Identification
The experimental data-driven parameter identification in this section starts with the battery experimental investigation, which is utilized to test the characteristics of the battery, identify the Li-ion battery parameters and verify the effectiveness of the proposed SOC estimation method. It is noted that the identified parameters include R0, R1, C1, R2, C2 and the nonlinear function oc () U SOC for the second-order RC equivalent circuit model shown in Figure 1.

Battery Experimental Setup
The experiment data of Li-ion battery used for this study were acquired through the test bench shown in Figure 2, which is composed of an Arbin BT2000 Cycler with MITS Pro soft (ARBIN INSTRUMENS, College Station, TX, USA), a well-controlled temperature chamber for environment control and a host computer for the human-machine interface and test data storage, as well as the Li-ion battery cells. It is noted that the test cells are SONY lithium nickel-manganese-cobalt oxide (NMC) battery (SONY Inc, Tokyo, Japan) with graphite anode. According to the producer's specification, the battery nominal capacity is 2 Ah, and the nominal voltage is 3. With the complete battery OCV-SOC test data at different temperatures (5 °C , 25 °C , 30 °C , and 40 °C ), we can obtain the plots shown in Figure 3. It is seen in Figure 3 that the temperature variation leads to very small changes in the OCV, thus the effect of temperature on the cell OCV during discharge progress was neglected in this work for simplification. In other words, the temperature has little effect on the variation of OCV-SOC curves. As a result, for this study, the test data for 30 °C were used as the reference to perform the parameters identification, and the other With the complete battery OCV-SOC test data at different temperatures (5 • C, 25 • C, 30 • C, and 40 • C), we can obtain the plots shown in Figure 3. It is seen in Figure 3 that the temperature variation leads to very small changes in the OCV, thus the effect of temperature on the cell OCV during discharge progress was neglected in this work for simplification. In other words, the temperature has little effect on the variation of OCV-SOC curves. As a result, for this study, the test data for 30 • C were used as the reference to perform the parameters identification, and the other datasets were utilized in the model validation and SOC estimation. From [15,28], the collected test data at 30 • C were used to build the OCV-SOC function using the simplified electrochemical function (Equation (6)).
After some calculations, the corresponding model-fitting coefficients are K 0 = 3.3984, K 1 = 0.4549, K 2 = 0.0078, K 3 = 0.0142, and K 4 = 0.0857. Moreover, the comparisons of the experimental and fitted OCV-SOC curves, as well as the corresponding OCV test data at 30 • C for NMC battery are presented in Figure 4. It is obvious that the fitted nonlinear function can well simulate the OCV-SOC relationship.
where K i (i = 0, 1, 2, 3, 4) are the coefficients to be determined that could make U oc (SOC) fit the SOC-OCV test data well.
datasets were utilized in the model validation and SOC estimation. From [15,28], the collected test data at 30 °C were used to build the OCV-SOC function using the simplified electrochemical function (Equation (6)).
where Ki (i = 0, 1, 2, 3, 4) are the coefficients to be determined that could make oc () U SOC fit the SOC-OCV test data well.
After some calculations, the corresponding model-fitting coefficients are K0 = 3.3984, K1 = 0.4549, K2 = 0.0078, K3 = 0.0142, and K4 = 0.0857. Moreover, the comparisons of the experimental and fitted OCV-SOC curves, as well as the corresponding OCV test data at 30 °C for NMC battery are presented in Figure 4. It is obvious that the fitted nonlinear function can well simulate the OCV-SOC relationship.

Parameter Identification Procedure.
To identify the parameters of Li-ion battery model as R0, R1, C1, R2, and C2, the sum of squares errors of the measured data denoted as exp and the simulated data denoted as sim for the datasets were utilized in the model validation and SOC estimation. From [15,28], the collected test data at 30 °C were used to build the OCV-SOC function using the simplified electrochemical function (Equation (6)).
where Ki (i = 0, 1, 2, 3, 4) are the coefficients to be determined that could make oc () U SOC fit the SOC-OCV test data well.
After some calculations, the corresponding model-fitting coefficients are K0 = 3.3984, K1 = 0.4549, K2 = 0.0078, K3 = 0.0142, and K4 = 0.0857. Moreover, the comparisons of the experimental and fitted OCV-SOC curves, as well as the corresponding OCV test data at 30 °C for NMC battery are presented in Figure 4. It is obvious that the fitted nonlinear function can well simulate the OCV-SOC relationship.

Parameter Identification Procedure.
To identify the parameters of Li-ion battery model as R0, R1, C1, R2, and C2, the sum of squares errors of the measured data denoted as exp and the simulated data denoted as sim for the

Parameter Identification Procedure
To identify the parameters of Li-ion battery model as R 0 , R 1 , C 1 , R 2 , and C 2 , the sum of squares errors of the measured data denoted as U exp and the simulated data denoted as U sim for the terminal voltage at each sampling point of input current is chosen as the objective function, which is represented by L 2 as follows: Energies 2018, 11, 1033 6 of 14 where N is the number of samples in the input current and θ is the identified parameter vector shown in Table 1.  Figure 5 shows the flowchart of the battery parameters identification based on the genetic algorithm. The optimized flowchart starts with initializing a randomized population and each individual represents a parameter to be identified. The output voltage of second-order RC ECM is computed for individuals and their corresponding L 2 fitness is evaluated by a comparison of the experimental voltage versus the simulated voltage data. The fittest individuals in population are chosen by a fitness-weighted roulette game, and each individual's genome is recombined and randomly mutated to form a new generation population. Afterwards, the second-order RC equivalent circuit model is utilized to compute the fitness values in the new population, and the optimization process runs until either the fitness function reaches the optimal value or the iteration number exceeds a maximum number of generations. terminal voltage at each sampling point of input current is chosen as the objective function, which is represented by 2 as follows: where N is the number of samples in the input current and is the identified parameter vector shown in Table 1.    To identify the model parameters, the hybrid pulse power characterization (HPPC) experiment is usually carried out to provide the extreme characterization of Li-Ion battery. The test current profile and terminal voltage of HPPC condition (30 • C) is presented in Figure 6 and the parameter identification is implemented by the above-mentioned GA-based flowchart. The final identified results  Table 1. In addition, the comparisons of battery voltage between the test data and the simulated voltage with the identified parameters are shown in Figure 7. To identify the model parameters, the hybrid pulse power characterization (HPPC) experiment is usually carried out to provide the extreme characterization of Li-Ion battery. The test current profile and terminal voltage of HPPC condition (30 °C) is presented in Figure 6 and the parameter identification is implemented by the above-mentioned GA-based flowchart. The final identified results for the second-order RC model of Li-Ion battery are listed in Table 1. In addition, the comparisons of battery voltage between the test data and the simulated voltage with the identified parameters are shown in Figure 7.

Model Validation and Discussion
To assess the accuracy of the identified parameters, the experimental and simulated Li-Ion battery terminal voltages under US06 condition at 30 °C are compared and presented in Figure 8.
In Figure 8a, the input current profiles are from the current sensor, and the comparative profiles between the estimated voltage with the identified parameters and the experimental voltage, and the normalized voltage estimation error is shown in Figure 8b,c. The maximum and mean relative errors are about 1.918% and 0.206%, respectively, which illustrates that the simulated voltage with the parameters identified by the proposed approach shows good agreement with the experimental curves at the ambient temperature of 23 °C. Therefore, the battery model can well simulate the dynamic voltage behaviors of Li-Ion battery.
To further validate the battery electrochemical behavior with the identified parameters, the comparison of the experimental voltage and the simulated voltage, as well as the voltage error under one C-rate profile at 23 °C are exhibited in Figure 9. It can be found that the simulated voltage with the parameters identified by the proposed approach show good agreement with the experimental voltage curve at the same ambient temperature, and the maximum and mean relative  To identify the model parameters, the hybrid pulse power characterization (HPPC) experiment is usually carried out to provide the extreme characterization of Li-Ion battery. The test current profile and terminal voltage of HPPC condition (30 °C) is presented in Figure 6 and the parameter identification is implemented by the above-mentioned GA-based flowchart. The final identified results for the second-order RC model of Li-Ion battery are listed in Table 1. In addition, the comparisons of battery voltage between the test data and the simulated voltage with the identified parameters are shown in Figure 7.

Model Validation and Discussion
To assess the accuracy of the identified parameters, the experimental and simulated Li-Ion battery terminal voltages under US06 condition at 30 °C are compared and presented in Figure 8.
In Figure 8a, the input current profiles are from the current sensor, and the comparative profiles between the estimated voltage with the identified parameters and the experimental voltage, and the normalized voltage estimation error is shown in Figure 8b,c. The maximum and mean relative errors are about 1.918% and 0.206%, respectively, which illustrates that the simulated voltage with the parameters identified by the proposed approach shows good agreement with the experimental curves at the ambient temperature of 23 °C. Therefore, the battery model can well simulate the dynamic voltage behaviors of Li-Ion battery.
To further validate the battery electrochemical behavior with the identified parameters, the comparison of the experimental voltage and the simulated voltage, as well as the voltage error under one C-rate profile at 23 °C are exhibited in Figure 9. It can be found that the simulated voltage with the parameters identified by the proposed approach show good agreement with the experimental voltage curve at the same ambient temperature, and the maximum and mean relative

Model Validation and Discussion
To assess the accuracy of the identified parameters, the experimental and simulated Li-Ion battery terminal voltages under US06 condition at 30 • C are compared and presented in Figure 8.x In Figure 8a, the input current profiles are from the current sensor, and the comparative profiles between the estimated voltage with the identified parameters and the experimental voltage, and the normalized voltage estimation error is shown in Figure 8b,c. The maximum and mean relative errors are about 1.918% and 0.206%, respectively, which illustrates that the simulated voltage with the parameters identified by the proposed approach shows good agreement with the experimental curves at the ambient temperature of 23 • C. Therefore, the battery model can well simulate the dynamic voltage behaviors of Li-Ion battery.
To further validate the battery electrochemical behavior with the identified parameters, the comparison of the experimental voltage and the simulated voltage, as well as the voltage error under one C-rate profile at 23 • C are exhibited in Figure 9. It can be found that the simulated voltage with the parameters identified by the proposed approach show good agreement with the experimental voltage curve at the same ambient temperature, and the maximum and mean relative errors are about 2.12% and 0.244%. Moreover, the mean absolute error (MAE) and root mean squares error (RMSE) of the aforementioned test conditions during validation process are listed as in Table 2. errors are about 2.12% and 0.244%. Moreover, the mean absolute error (MAE) and root mean squares error (RMSE) of the aforementioned test conditions during validation process are listed as in Table 2.   errors are about 2.12% and 0.244%. Moreover, the mean absolute error (MAE) and root mean squares error (RMSE) of the aforementioned test conditions during validation process are listed as in Table 2.

SOC Estimation Method Based on the Adaptive EKF
Overall, the SOC estimation logic in this study is shown in Figure 10, where the parameter set θ = [R 0 , R 1 , C 1 , R 2 , C 2 ] T and the OCV-SOC model is obtained from the discussions in Section 3. Actually, the adaptive extended Kalman filter is used to make the SOC estimation because the covariance parameters in AEKF approach are not taken as constant, but adaptively updated online with a dedicated SOC estimator [11,22,31,32], which can enhance the estimation performance with respect to the EKF. The control input of the SOC estimator is the current (HPPC and/or US06) profiles representing the behavior of Li-Ion battery during discharge or charge process, the output the SOC estimator is the SOC value estimated by the AEKF algorithm.

SOC Estimation Method Based on the Adaptive EKF
Overall, the SOC estimation logic in this study is shown in Figure 10, where the parameter set Actually, the adaptive extended Kalman filter is used to make the SOC estimation because the covariance parameters in AEKF approach are not taken as constant, but adaptively updated online with a dedicated SOC estimator [11,22,31,32], which can enhance the estimation performance with respect to the EKF. The control input of the SOC estimator is the current (HPPC and/or US06) profiles representing the behavior of Li-Ion battery during discharge or charge process, the output the SOC estimator is the SOC value estimated by the AEKF algorithm.

AEKF Algorithm
Although Kalman filter and extended Kalman filter have been extensively introduced and employed to estimate battery SOC in recent years (e.g., [15,20,21,33,34]), its performance is strongly dependent on the accuracy of the predetermined noise matrix. Thus, it is necessary for the AEKF algorithm to adopt this problem in battery applications. To apply the AEKF for the SOC estimation, it is necessary to reform a state-space form as shown in Equation (3). The AEKF algorithm is given in Table 3.  Figure 10. Flowchart of the SOC estimation logic.

AEKF Algorithm
Although Kalman filter and extended Kalman filter have been extensively introduced and employed to estimate battery SOC in recent years (e.g., [15,20,21,33,34]), its performance is strongly dependent on the accuracy of the predetermined noise matrix. Thus, it is necessary for the AEKF algorithm to adopt this problem in battery applications. To apply the AEKF for the SOC estimation, it is necessary to reform a state-space form as shown in Equation (3). The AEKF algorithm is given in Table 3.
It should be pointed out thatx − k andx + k are both estimations of the same vector x k . However, x − k is the estimate of x k before the measurement y k is considered, which is called the a priori estimate, andx + k is the estimate of x k after the measurement y k is taken into account, which is called the a posteriori estimate. Table 3. Summary of the AEKF algorithm.

State-Space Equation of Li-ion Battery
x k+1 = f (x k , u k ) + ω k y k = h(x k , u k ) + υ k Step 1: Initialization Step 2: Calculation For k =1 to N perform (1) State estimate propagation:

SOC Estimation with AEKF
To employ the AEKF to estimate the SOC, we need to establish an estimator based on Equations (3)-(5) using the AEKF algorithm shown in Table 3. The state vector is x = SOC U 1 U 2 T , in which SOC is what we want to obtain. Herein, the time-varying matrices A k and C k can be derived from Equations (4) and (5) as follows: where dU OC (SOC)/dSOC = 0.4549 − 0.0078/SOC 2 + 0.0142/SOC − 0.0857/(1 − SOC) is derived from Equation (6). With these above-mentioned matrices and functions, as well as AEKF-based SOC estimation logic shown in Figure 10, the experimental data-driven SOC estimation can be achieved. The HPPC and US06 current and voltage profiles of discharge are loaded into SONY NMC 18,650 cells and its corresponding second-order RC ECM simultaneously. Afterwards, the voltage error e k is computed and the adaptive law H k is employed to updatex k , P k , Q k and K k . Then, the updated gain is used to compensate for the state estimation error. The SOC estimation is fed back to update the parameters of the battery model for the SOC estimation at the next sampling time.

Experimental Verification Results of SOC Estimation
In this section, both of HPPC and US06 test current profiles are adopted to verify the AEKF-based SOC estimation for Li-Ion battery model in Equations (1) and (2) with the identified parameters. Firstly, with the input current of US06 condition, the battery SOC estimation values and their errors are plotted in Figure 11. It is observed in Figure 11 that the estimated SOC with EKF and AEKF can track the experimental SOC profiles well, while the maximum value of SOC error is, respectively, 3.4% and 2.6%, which illustrates that the AEKF-based algorithm has higher accuracy in estimating battery SOC.
The reason is that the AEKF-based algorithm can adjust the Kalman gain quickly according to the SOC error between the measured and estimated values. error is, respectively, 3.4% and 2.6%, which illustrates that the AEKF-based algorithm has higher accuracy in estimating battery SOC. The reason is that the AEKF-based algorithm can adjust the Kalman gain quickly according to the SOC error between the measured and estimated values. Secondly, the battery is operated in HPPC discharging process at 30 °C where the measured SOC is recorded and used to evaluate the accuracy of AEKF-based SOC estimation for Li-Ion battery second-order RC equivalent circuit model. Figure 12 shows the comparison of the battery SOC estimation values and their errors with EKF and AEKF algorithm, as compared with the corresponding SOC test data. It can be found that the error of SOC estimation with both EKF and AEKF algorithms under the same HPPC discharging profile are from −6.3% to +1.8%, and from −6.3% to +1.2%, respectively. It is noted that the AEKF-based SOC error yields comparatively minor fluctuations. Moreover, the root-mean-square (RMS) error of SOC estimation for EKF and AEKF algorithm is 1.02% and 0.97%, respectively. This further demonstrates that the AEKF-based SOC estimation algorithm can estimate the battery SOC with higher accuracy. Secondly, the battery is operated in HPPC discharging process at 30 • C where the measured SOC is recorded and used to evaluate the accuracy of AEKF-based SOC estimation for Li-Ion battery second-order RC equivalent circuit model. Figure 12 shows the comparison of the battery SOC estimation values and their errors with EKF and AEKF algorithm, as compared with the corresponding SOC test data. It can be found that the error of SOC estimation with both EKF and AEKF algorithms under the same HPPC discharging profile are from −6.3% to +1.8%, and from −6.3% to +1.2%, respectively. It is noted that the AEKF-based SOC error yields comparatively minor fluctuations. Moreover, the root-mean-square (RMS) error of SOC estimation for EKF and AEKF algorithm is 1.02% and 0.97%, respectively. This further demonstrates that the AEKF-based SOC estimation algorithm can estimate the battery SOC with higher accuracy.

Conclusions
In this paper, a comprehensive experimental data-driven parameter identification scheme using GA algorithm is developed and the AEKF-based SOC estimator with the identified parameters is described for the Li-ion batteries in the applications of EVs. First, the second-order RC ECM is used to simulate the nonlinear behaviors of Li-Ion battery and make SOC estimation, wherein the electrochemical model is used to build the nonlinear OCV-SOC relationship based on the experimental data of battery characterization. Second, the key state parameters of Li-ion battery are identified and validated by conducting the comparative study of the simulated and experimental output voltage under HPPC and US06 current profiles. Furthermore, the AEKF-based battery SOC estimation method is introduced to reduce the effect of the non-Gaussian system and measurements noises. The HPPC and US06 experimental data are employed to verify and evaluate the accuracy of the proposed AEKF-based SOC estimation method by comparing with the general EKF-based SOC algorithm. The comparison results confirm that the proposed SOC estimation yields good performance in terms of the SOC estimation accuracy. In future work, we will focus on the joint estimation approach considering the current dependent parameters and the aging mechanism of Li-Ion battery.

Conclusions
In this paper, a comprehensive experimental data-driven parameter identification scheme using GA algorithm is developed and the AEKF-based SOC estimator with the identified parameters is described for the Li-ion batteries in the applications of EVs. First, the second-order RC ECM is used to simulate the nonlinear behaviors of Li-Ion battery and make SOC estimation, wherein the electrochemical model is used to build the nonlinear OCV-SOC relationship based on the experimental data of battery characterization. Second, the key state parameters of Li-ion battery are identified and validated by conducting the comparative study of the simulated and experimental output voltage under HPPC and US06 current profiles. Furthermore, the AEKF-based battery SOC estimation method is introduced to reduce the effect of the non-Gaussian system and measurements noises. The HPPC and US06 experimental data are employed to verify and evaluate the accuracy of the proposed AEKF-based SOC estimation method by comparing with the general EKF-based SOC algorithm. The comparison results confirm that the proposed SOC estimation yields good performance in terms of the SOC estimation accuracy. In future work, we will focus on the joint estimation approach considering the current dependent parameters and the aging mechanism of Li-Ion battery.