## 1 Introduction  
The concerns in energy crisis and global warming have driven the development of alternative energy vehicles rapidly. The Electric Vehicles (EVs), which are among the ultimate solutions for sustainable transportation, have attracted attention in aspects such as rechargeable power batteries and Battery Management System (BMS). A key estimative parameter, state of charge (SOC) of a battery, indicates its residual capacity and reflects the remaining range of an electric vehicle. An accurate SOC estimation can not only predict the remaining range for the EVs to relieve the \"range anxiety\" for the drivers, but it can also help to determine an effective management strategy to avoid cell damage from over-charging and over-discharging. However, due to the complexity of the chemical and physical processes involved, characteristics of batteries present a distinct nonlinear feature, which makes their online monitoring a challenging task. Therefore, special algorithms for SOC online estimation are required. Previous papers coining the term 'SOC' can date back to the 1960s [1]. After several decades' efforts, a great variety of approaches have been engaged in targeting monitoring the SOC for EVs. Generally, the SOC estimation algorithms can be divided into three categories. The first methods are based on the direct measurement, including the residual capacity method, the open-circuit voltage (OCV) method, and the Ampere-hour counting based method [2]. The residual capacity method calculates the SOC by discharging the battery to the lower cut-off voltage in controlled test equipment. It is also the most reliable method under laboratory conditions, but this is obviously not the case in online monitoring for BMS. The OCV-based method requires a long rest period, thereby not practical for EV applications. Moreover, the performance of the OCV-based method becomes severe for which the battery characteristic of voltage platform is flat, such as LiFePO\({}_{4}\) (LFP). To the authors' knowledge, only the Ampere-hour counting based method is suitable for online monitoring. The Ampere-hour counting method estimates the SOC by integrating the flow-in and flow-out current of the battery. This method reportedly has several theoretical limitations and is an open loop method that cannot correct the accumulative error caused by current measuring transducers drift. In addition, the estimation accuracy is dependent on the initial SOC. This method has low robustness against the acquired signal quality, as well as initial SOC information. The second types are the machine learning methods, such as the Artificial Neural Network (ANN), Fuzzy Logic (FL), and Support Vector Machine (SVM). These methods are also called \"black box\" model by which these do not need the detailed information of the battery system. [PERSON] et al. [3; 4] developed an ANN SOC estimator for commercial Li-ion battery. The network is trained by the input of current and voltage, and the output is the battery SOC. The algorithm is validated by the benchmark driving cycles and can achieve a relatively high degree of accuracy. [PERSON] et al. [5] introduced a fuzzy-based model to characterize the discharge behavior of lead-acid batteries. [PERSON] et al. [6] presented a methodology of FL to describe the equivalent circuit model parameters on SOC and temperature effects. The SVM model is also a smart choice for SOC estimation, which has been used in several literatures [7; 8; 9; 10; 11]. Although much research focused on the machine learning methods, some of which have shown good performance, the common shortfall of these methods is the heavy computational burden that makes the online implementation unpractical. The last algorithms are based on the control-oriented battery model. The model-based estimators are used to calculate the SOC by characterizing the battery behavior through measurable signals like current, terminal voltage, and temperature.