Hybrid Methods Using Neural Network and Kalman Filter for the State of Charge Estimation of Lithium-Ion Battery

With the increasing carbon emissions worldwide, lithium-ion batteries have become the main component of energy storage systems for clean energy due to their unique advantages. Accurate and reliable state-of-charge (SOC) estimation is a central factor in the widespread use of lithium-ion batteries. is review, therefore, examines the recent literature on estimating the SOC of lithium-ion batteries using the hybrid methods of neural networks combined with Kalman ltering (NN-KF), classifying the methods into Kalman lter-rst and neural network-rst methods.en the hybrid methods are studied and discussed in terms of battery model, parameter identication, algorithm structure, implementation process, appropriate environment, advantages, disadvantages, and estimation errors. In addition, this review also gives corresponding recommendations for researchers in the battery eld considering the existing problems.


Introduction
With the worldwide reduction of nonrenewable energy sources and carbon dioxide emissions, clean energy development has become an important theme [1][2][3]. Lithium-ion batteries are gradually regarded as the most natural green alternative to traditional fossil fuels for their high energy density, no memory e ect [4], long life, and environmental protection [5]. Lithium-ion batteries are now widely used in electric vehicles, ships, and distributed energy storage systems. With the continuous development of the smart grid, the hybrid energy storage system consisting of lithium-ion batteries and supercapacitors has become an attractive option [6]. e continuous development of lithium-ion batteries also achieves emission peak and carbon neutrality goals.
In contrast to conventional fossil fuels, lithium-ion batteries also need a state parameter indicating the current remaining energy. erefore, the state of charge (SOC) is proposed [7][8][9]. SOC is de ned as the ratio of the current available capacity of the battery to the maximum available capacity. Consequently, accurate battery capacity estimation is crucial to estimate the SOC [10][11][12]. By clarifying the change in SOC, the abnormal charging capacity of the battery can be determined, ensuring the safe operation of the electric vehicle [13]. Meanwhile, the accurate estimation of the battery SOC is also the basis for managing lithium-ion batteries and understanding the battery status. However, SOC cannot be measured directly and can only be estimated based on the relationship between SOC and measurable variables [14,15]. Consequently, it is essential to establish a reliable and accurate SOC estimation method [16].
More and more researchers are enthusiastic about estimating SOC using hybrid methods to improve the precision of SOC estimation. Achieving accurate SOC estimation in natural application environments remains a challenge due to the inconsistency of batteries in the pack [17]. e hybrid method combining neural network with Kalman lter (NN-KF) can solve the nonlinear relationship between battery SOC and other variables by using the selflearning ability and strong self-adaptability of neural network (NN) [18][19][20] on the one hand. On the other hand, it is the ability to combine the fast convergence property of the Kalman filter to achieve a real-time estimation of SOC [21][22][23] and reduce the influence of noise on the results. is review classifies this hybrid method into Kalman filter-first method and the neural network-first method. It is promising to apply the NN-KF hybrid method into practice as an efficient method to obtain SOC estimates for lithium-ion batteries.
e remainder of this review is organized as follows: Section 2 describes the types and characteristics of lithiumion battery models, the methodological flow of the evenin model parameter identification, and a detailed evaluation of all methods. A detailed and comprehensive introduction to the current framework and remarks of Kalman filter-first methods and neural network-first methods is presented in Section 3. Section 4 discusses the future direction from the perspective of the current situation. Conclusion is drawn in Section 5.

Modeling and Parameter Identification
SOC estimation of lithium-ion batteries requires high accuracy and reliability of the model, so it is essential to use a reasonable model and a suitable parameter identification method to simulate the battery characteristics.

Battery Model.
Establishing a battery state-space model plays an essential role in the accurate estimation of SOC and directly affects the accuracy of the SOC estimation. To make the state model closer to the actual usage environment and meet the needs of combining neural network and Kalman filter, the battery model must be simple and compatible with the actual situation [24]. e standard battery models used in the research are the evenin and the neural networkbased models. e following is a brief description of their characteristics. evenin model has a simple structure, high accuracy, and strong robustness even in unknown cell environments. Figure 1(a) shows that it consists of an ideal voltage source U OC , a series resistor R 0 , and a capacitor-resistor (RC) network, where R 0 represents the battery's internal resistance, and R 1 and C 1 are the polarization resistance and polarization capacitance, respectively. e number of RC networks is changeable, and its number represents the order of the evenin model. Figure 1(b) is the structural diagram of the second-order evenin model. e complex dynamic characteristics and uncertain operating conditions make building a suitable battery model difficult. e results of SOC estimation under cold conditions were reported to be inadequate [25][26][27][28][29]. Accordingly, the evenin model is not perfect [30]. Other suitable battery models, such as the electrochemical-thermal degradation model [31], are still needed to describe the complex battery behavior at different ambient temperatures.
Neural network, a branch of artificial intelligence, has been widely used for predicting outcomes based on input data [32][33][34][35]. Compared with the evenin model, the neural network-based modeling method does not need to consider the electrochemical state inside the battery. However, it only needs to use the measurable parameters as inputs and establish a nonlinear relationship between the input data and the output data to construct the estimated battery SOC model through the self-learning capability [36].

Model Parameter Identification.
evenin model parameters are susceptible to operating conditions such as SOC levels and ambient temperature. During the use of lithium-ion batteries, it is helpful to describe the electrochemical characteristics and improve the accuracy if the model parameters can be effectively identified. Meanwhile, the accurate identification of model parameters can facilitate the combination of Kalman filter and neural network to improve the accuracy of battery SOC estimation. e schematic diagram of the recognition process is depicted in Figure 2.
A large number of algorithms, including genetic algorithms (GA) [37], least squares (LA) [38], and hybrid pulse power characteristic (HPPC) test [39], have been used in recent years for parameter identification of evenin models.
Taking the first-order evenin model as an example, the unknown parameters are R 0 , R 1 , and C 1 . According to Kirchhoff's law and analyzing the model, the following equations can be obtained: e discrete equation is obtained according to equation (1), as shown in the following equation: In the above two equations, U 1 is the RC network voltage and U L is the terminal voltage. Q N is the rated capacity of the battery and I L is the circuit current. △t is the sampling time interval, and τ is the time constant, τ � R 1 C 1 . k is the time parameter.
Yang et al. use GA for the first-order evenin model to identify the parameters [37]. GA is a global search method formed by simulating the genetics and evolution of organisms in their natural environment. However, it cannot use the feedback information in time, so the search speed is slow, and it is not good enough to solve the large-scale computation problem. In response to these problems, the particle swarm optimization (PSO) algorithm is favored by many researchers because it is easier to implement and has lower computational complexity [40].
LA is also a standard method for the identi cation of battery model parameters. evenin battery model can be considered a linear system, identi ed by the parameter identi cation toolbox in Matlab/Simulink [41]. According to the parameter tting function in the toolbox, parameter identi cation can be achieved using LA. e recursive least squares (RLS) method is proposed to make the algorithm relevant to the practical use environment. Compared to LS, it can extract model parameters in real time using new measurement data [42], signi cantly reducing the computational and storage e ort. Recently, Li et al. performed discharge experiments on lithium-ion batteries and combined RLS to identify R 0 , R 1 , and C 1 in the battery model. e data from the voltage recovery stage makes it easier to obtain the model parameters to be identi ed with a high degree of accuracy [43]. e battery model is also a ected by noise in the natural application environment. e RLS method is susceptible to noise, resulting in inaccurate identi cation of model parameters. e recursive total least squares (RTLS) [44], adaptive forgetting recursive total least squares (AF-RTLS) [45], and the Frisch scheme-based bias compensating recursive least squares (FBCRLS) [46] have been proposed to e ectively suppress the model identication errors caused by noise, which provides more reliable SOC estimation.
A recursive least squares method with forgetting factors (FFRLS) is also applied to the parameter identi cation of the evenin model. FFRLS has faster convergence and better tracking performance with an increased forgetting factor λ [47]. In general, the smaller λ, the better the computational t of the system, but the more signi cant the uctuation. So, determining the λ value quickly is also an urgent problem to be solved.
HPPC tests can be used to determine the model parameters at di erent temperatures and di erent discharge rates.  conducted several experiments and nally created a table of battery parameters concerning temperature and discharge rate [39]. Experimental data from another part also veri ed the validity of the HPPC method. e appropriate methods for identifying battery parameters are summarized in Table 1.
Lithium-ion battery current parameter identification methods Initialize model parameters Figure 2: e process of battery parameter identi cation.

Kalman Filter-First Method.
e basic idea of the Kalman filter-first method is that when the sensor obtains voltage, current, and temperature measurements from the battery, it can be iterated directly since various methods have previously determined the battery model parameters. e values needed by the neural network are then computed, and the final SOC estimation results are output by the neural network. e structure diagram is shown in Figure 3.
e Kalman filtering-first method is highly resistant to interference and suitable for SOC estimation in complex environments, while having high robustness. However, the method relies on an accurate battery model, and different battery models also require reasonable methods for parameter identification. e traditional KF algorithm is proposed to solve the linear problem [48][49][50], while the lithium-ion battery can be considered a nonlinear system. erefore, it is hardly used in the battery SOC estimation process. Several algorithms that can handle nonlinear systems, such as extended Kalman filter (EKF) and Unscented Kalman filter (UKF), are proposed.
e EKF linearizes nonlinear systems with Taylor series expansions, essentially a recursive algorithm. Xu et al. used EKF for the initial estimation of battery SOC and then used the estimated SOC value along with voltage and current as of the input to the long short-term memory (LSTM) network [47]. e model's performance was verified at − 15°C, 0°C, and 25°C, respectively, and the mean absolute error (MAE) was less than 1%. e EKF-LSTM maintains high estimation accuracy even at very low ambient temperatures. Similarly, EKF can be combined with the back propagation neural network (BPNN) to estimate the battery SOC [51]. e EKF-BP algorithm is verified by dynamic stress test (DST), Beijing Bus Dynamic Stress Test (BBDST), and other complex working conditions. e estimated error is less than 1.10%.
Both the above algorithms are for individual lithium-ion batteries, while in practical applications, such as electric vehicles, the application of lithium-ion battery packs is much more. When estimating the battery pack SOC, it is not appropriate to consider it as a simple battery. e method discussed previously cannot be directly applied to a battery pack consisting of many batteries. Developing a simple, reliable, and effective SOC estimation method for battery packs is essential.
Dao et al. developed a smart battery management system (BMS) based on KF and NN to estimate the SOC of a lithium-ion battery pack, as shown in Figure 4. e battery pack temperature range is 19-42°C. e performance is better than ANN and KF alone by experimental evaluation on real battery packs with an error of less than 1% [52]. However, there are still some problems with this method. For example, the capacity balance between each battery in the pack is not considered in the application. e capacity decay of each battery varies during use, and the impact of capacity balance on BMS and battery pack SOC estimation needs to be considered.
EKF suffers from computational overload for complex nonlinear problems and generates linearity errors. UKF, proposed by Julier and Uhlmann in 1997 [53], uses lossless transformations to obtain the mean and covariance of individual probabilities, avoiding solving Jacobi matrices. By constructing an adaptive unscented Kalman filter (AUKF) algorithm based on the evenin model, Hosseininasab et al. presented a combined NN and AUKF method for SOC estimation [54]. Considering the initial offset, capacity error, and current sensor drift considering shunt thermal effects, the root-mean-square Error (RMSE) still reaches 0.954% at 25°C. e results of SOC estimation based on the Kalman filter-first method are summarized in Table 2.

Neural Network-First Method.
e Kalman filter-first method can accommodate the initial error of the SOC and estimate the SOC effectively online. However, the high computational requirements and effective model parameterization need to be effectively addressed before practical application, which has limited the application of the method to some extent. In contrast, the neural network modeling approach can avoid the detailed study of lithium-ion battery models and parameter identification. A good battery SOC estimation algorithm can be built using only previous reliable data.
For the neural network method alone [55], the SOC estimation results highly depend on the dataset used. Once the data set differs significantly from the applied battery operating conditions, the error in the estimation results of the lithium-ion battery SOC can be substantial. e neural network-first method avoids this problem. Even if a less than perfect data set is used, the output of the NN can be corrected using the KF, and finally, an accurate battery SOC can be obtained.  [41] Calculate the coefficients at one time Offline RLS [42] Process data in real-time Taking up a lot of storage space 2020 FFRLS [47] Better performance Difficult to decide the value of λ 2021 RLS [43] Conduct discharge experiments Time-consuming HPPC [39] Consider temperature and discharge rate Tedious PSO [40] Lower computational complexity Easily fall into the local optimum e central idea of the neural network-rst method is rst to use the neural network to reveal the nonlinear relationship between SOC and measurable variables such as current, voltage, and temperature. e output of the NN is then smoothed using a KF algorithm to achieve accurate and stable SOC estimates.

Feed-Forward Neural Network.
Feedforward neural network (FNN) is simple in structure and easy to train, which has become the most common method for SOC estimation of lithium-ion batteries [56][57][58].
Qin et al. used a nonlinear autoregressive neural network (NARXNN) to estimate the SOC of lithium-ion batteries and then applied UKF to reduce the error [59]. Compared with the battery SOC estimation results based on NARXNN alone, the error is reduced by about 1% at 0°C. Since each estimate uses data from a single sampling point and does not consider the dynamic chemistry of the battery, the estimation accuracy of this method is usually not very high. e polarization characteristics of the battery can be used as a new input to the FNN to describe the dynamic chemistry of the battery accurately. One way to consider polarization is to increase the NN input data from a single sample point to multiple sample points [60], which requires selecting a suitable time constant. e method for selecting the time constant is designed as shown in Figure 5, where τ represents the time constant and r(x, y) represents the correlation coe cient. Chen et al. (2019) designed a neural network-rst battery SOC estimation method based on an improved FNN model and EKF algorithm [61]. e SOC estimation error can be kept to less than 2% even with inaccurate initial SOC value, inaccurate initial capacity, and low temperature (− 10°C, 0°C, and 10°C).
is method is more suitable for complex electric vehicle application environments.   Mathematical Problems in Engineering e terminal voltage can be used as the output of the neural network. Meanwhile, the SOC is considered as an internal state, which is indirectly estimated through the feedback error of the voltage [62]. is indirect method has the advantage of uncertainty enhancement and feedback compensation. e e ect of temperature on SOC, however, is not considered. Table 3 lists the above studies.

Deep Learning.
In recent years, deep learning algorithms have attracted the attention of researchers in the eld of battery state estimation because of their ability to automatically extract features and their good generalization performance [63]. Deep learning algorithms are also increasingly introduced into the SOC estimation of lithiumion batteries.
Deep belief network (DBN) can be combined with KF. e DBN can extract the relationship between battery SOC and input parameters with its strong nonlinear tting ability. e KF eliminates measurement noise and improves SOC estimation accuracy [64]. e framework of the proposed model is shown in Figure 6. e RMSE of the SOC estimation by DST is lower than 0.7%. is hybrid is suitable for estimating the SOC of lithium-ion batteries under dynamic conditions. LSTM network can handle time-series data considering the time dependence of SOC estimation. Yang et al. (2020) used a stepwise search algorithm to determine the hyperparameters of the LSTM network and further reduce the estimation error by UKF [65].
e results show that the RMSE of the LSTM-UKF method is 1.1%, which is better than other FNN methods. In addition, the method has excellent generalization ability to the temperature at 0-50°C, and more reliable SOC estimation results can be obtained at temperatures without training data. e commonly used LSTM network is a "many-tomany" structure, as shown in Figure 7. e output at moment t + 1 is related to the input information at moment t + 1 and moment t. e results in earlier information have little to no impact on the current output, making it impossible to take full advantage of the past information.
To address this problem, Tian et al. (2020) proposed a "many-to-one" structure of the LSTM network [66]. is framework introduced an adaptive cubature Kalman lter (ACKF) algorithm that maximizes the impact of the above measurements on current SOC estimates and further extended the applicability of the neural network-rst method. High estimation accuracy was achieved in the temperature range of 10 to 50°C.
is LSTM-ACKF method avoids nding the optimal hyperparameters in the training phase of the LSTM network, which is very di cult. Only a rough selection in the training phase is needed, and then a more accurate SOC estimation result can be obtained using ACKF.
To accurately estimate the SOC for lithium-ion battery packs, a combination of LSTM and improved square root cubature Kalman lter (SRCKF) is proposed [67]. To address the inconsistency of batteries among packs, Shu et al. designed an iterative rule for LSTM-SRCKF using the smoothing method with the maximum and minimum SOC values in the packs as features. e method could converge quickly to the reference value even at sub-zero temperatures, with RMSE less than 0.4%. is method still has not considered aging problems such as battery capacity decay.
By combining di erent neural networks, the advantages of each can be retained, which improves the estimation e ciency and applicability. One-dimensional convolutional units can be combined with the gated recurrent unit (GRU) to form a new deep neural network (DNN), as shown in Figure 8. e DNN used 10 minutes of data as input for fast and accurate SOC estimation across the entire battery SOC range [68]. e KF algorithm is introduced to enhance the robustness of the neural network. e DNN-KF method can quickly adapt to batteries with di erent aging states, and the RMSE can be less than 3.146%. e deep learning-based SOC estimation methods are summarized in Table 4.

Discussion
From the above experimental results, the NN-KF hybrid method to estimate the SOC of lithium-ion battery is accurate. However, there are still some problems that need to be investigated.
(1) e problem of SOC estimation for lithium-ion battery packs has still not been e ectively addressed. Battery capacity and SOC imbalance in packs are widespread problems [69]. As a result, developing an NN-KF hybrid method considering the capacity balance of lithium-ion batteries is necessary to improve battery safety and extend the applicability of SOC estimation methods. (2) In subsequent studies, the use of transfer learning to improve the generalization ability of the hybrid method can be considered so that the method can be generalized to SOC estimation of other types of lithium batteries. After transfer learning, the hybrid method can be quickly adapted to various situations. (3) Expand the types of the NN-KF hybrid methods through the mutual hybrid of di erent neural networks and Kalman lters. Analyzing the e ects of di erent combinations on the SOC estimation and nding a more suitable hybrid method might be the following research priorities.
(4) Noise disturbance is still a pressing problem for the Kalman lter-rst method. erefore, an e ective method is needed to improve the accuracy of model parameter identi cation and SOC estimation in the whole life cycle of the battery under noise disturbance.

Conclusion
is review analyzes the SOC estimation of lithium-ion batteries based on the NN-KF hybrid method. First, the battery model is introduced, and the parameter  identification methods and procedures are discussed to prepare for SOC estimation. en, the Kalman filter-first method and the neural network-first method are introduced, and the remarks of each method. Finally, the future development direction is proposed with the actual existing problems.
Lithium-ion batteries' chemical reactions and aging mechanisms are very complex, making it challenging to describe them with a specific model. e existing model parameter identification methods all have their advantages and disadvantages. None of them perfectly matches the natural application environment, which means that most Kalman filter-first methods can only achieve good estimation performance in simulated environments. Of course, the advantages of small computation and short estimation time of Kalman filter-first methods are challenging to be possessed by neural network-first methods. Future research focuses on making the SOC estimation results of NN-KF hybrid methods more accurate, applying these methods to practical application environments, and achieving real-time estimation.
In conclusion, this review makes a significant contribution to the accurate estimation of the SOC and help to expand the use of lithium-ion batteries. e widespread use of lithium-ion batteries can promote energy conservation, carbon dioxide emission reduction, and environmental protection, contributing to emission peak and carbon neutrality goals.
is review can also provide a valuable overview and recommendations for researchers in the battery field.

Conflicts of Interest
e authors declare no conflicts of interest.