## 1 Introduction  
Electric vehicles (EVs) are believed worldwide to be one of the most important development directions in the vehicle industry because of their advantages in low pollution and energy saving. Lithium-ion batteries, by virtue of their high energy and power density, are the fundamental power source of EVs [1]. Nevertheless, lithium-ion batteries have hidden dangers in safety. Once over-charged or over-discharged, the battery capacity will drop, leading to reduced lifetime or damage, or even explosion. Moreover, the battery characteristics change with different operating conditions. Therefore, to ensure the safety, reliability, and efficiency of the battery system, a battery management system (BMS) is developed and utilised. The BMS is used to control and monitor the battery operating conditions to guarantee the safe operation and longevity of the battery. The state of charge (SOC) is a significant parameter which indicates the amount of remaining energy in the battery for further service. It needs to be estimated accurately online in order to prevent any over-charge and over-discharge, while providing the information and support for the effective and flexible operation of the vehicle. However, it is difficult to acquire precise SOC estimates since the battery itself is a highly nonlinear system and has a lot of uncertainties. Extensive studies have been made into SOC estimation. [PERSON] et al. [2] gave a comprehensive review of these research fruits. Overall, these methods can be mainly classified into four categories: (1) the open-circuit voltage (OCV) method; (2) current integration or coulomb counting (CC) method; (3) data-driven methods; and (4) model-based methods. The OCV method is based on the one-to-one corresponding relationship of open-circuit voltage and SOC. It is simple but susceptible to temperature, battery aging, and other factors, and the acquisition of accurate measurement of OCV needs lots of rest time, making it almost impossible for moving vehicles. The CC method is widely used in many applications, but it has two weak points. First, its estimation accuracy is strongly dependent on the correctness of the initial SOC value, and second, it can easily diverge due to error accumulation in the current measurement. The data-driven methods include neural network (NN) algorithms [3; 4; 5], fuzzy logic (FL) algorithms [6; 7; 8], support vector machines (SVMs) [9; 10; 11], and so on. For instance, [PERSON] et al. [3] employed a multilayer feedforward neural network to estimate the SOC of Lithium-ion batteries by use of the discharge current, terminal voltage, and temperature of the battery as input. [PERSON] et al. [4] combined a back propagation neural network and adaptive Kalman filter to estimate the SOC, and used a forgetting-factor recursive least-squares (FFRLS) algorithm to identify the time-varying battery model parameter. In [6], a fuzzy logic algorithm was applied to estimate SOC of lithium-ion batteries for the application of a portable defibrillator. AC impedance and voltage recovery measurements were used as the input parameters for the FL model. In [7], a more advanced algorithm named adaptive neuro-fuzzy inference system (ANFIS) was developed to estimate SOC. In addition, [PERSON] et al. [9] proposed an SOC estimation based on an optimized support vector machine for regression with double search optimization process. In [10], an SOC estimation method based on fuzzy least-squares SVM was proposed. These data-driven algorithms do not need to know any battery characteristics and have a good ability of nonlinear mapping and self-learning. However, they require a large amount of experimental data to train the intelligent model beforehand. Different types of training data and training methods exert a great influence on the model error. When the training data cannot cover all the operating conditions, for example, the experiments are incomplete or the battery characteristics have changed, the SOC estimation accuracy will decrease.