## 1 Introduction
### Literature Review  
With the development of BMS, a large number of SOC estimation methods have been proposed and each one has its own merits and limitations [4; 11]. The commonly used methods in the literature can be listed as follows [12; 13]: (1) ampere-hour (AH) counting method; (2) open-circuit voltage (OCV) method; (3) model-based method; and (4) neural-network model method. Among these methods, the AH method is most extensively used owing to its ease of implementation. However, it suffers from the drawbacks of accumulated errors. Another classic method is the model-based method, where the Kalman filter (KF) algorithm is generally used [1; 14]. Due to its high applicability and accuracy, various forms of the KF algorithm, such as the linear KF (LKF), single KF (SKF), unscented KF (UKF), sigma point KF (SPKF), and extended KF (EKF), have been intensively investigated in recent years [15].  
In the practical application of SOC estimation, many factors affect its accuracy. These factors mainly include model and sensor errors [16]. The sensor errors include the voltage and current sensor errors in the BMS, while the model errors include the battery capacity, coulombic efficiency, and ECM errors. The model errors increase with LIB ageing and exposure to adverse temperatures. These errors increase the SOC estimation error. Therefore, the influence of these factors on SOC must be considered to improve the robustness of the SOC estimation algorithm in the actual BMS.  
The model-based estimator is widely used in the existing SOC estimation. Therefore, an accurate battery model is the prerequisite for precise SOC estimation. The equivalent circuit model (ECM) has the advantages of simple structure, small number of identification parameters, and high accuracy, which have made it become the most popular battery model for existing BMSs [17]. At present, the ECMs mainly include the resistance-capacitance model with different orders (nRC, \(n=0\), \(1\), \(2\), etc.), GNL (general nonlinear) model, and PNGV (the Partnership for a New Generation of Vehicle) model, etc., and the most commonly used model is nRC [18; 19]. The characteristics and accuracy of the ECM are affected by the structure and parameters of the model. Therefore, a reasonable model structure and matched model parameters are indispensable for the accurate SOC estimation. It is inappropriate to apply simple parameter identification algorithms to complex models nor complex parameter identification algorithms to simple models. In other words, high model accuracy can only be achieved by using a suitable battery model and matched model parameters at the same time. In this regard, the parameter identification approach and the model structure are equally important. To the best of our knowledge, the parameter identification of ECMs is an optimization problem, and there are many identification algorithms to determine the battery model parameters in the literature, such as the genetic algorithm [20], the particle swarm optimization algorithm [21], and the least-squares method [22]. Previous studies on LIB models have not paid much attention to whether a parameter identification approach is suitable for a certain model. In this paper, we investigated the accuracy of various models in various identification algorithms to determine the most appropriate model structure and parameter identification algorithm for the whole SOC area.