## 1 Introduction  
Lithium-ion batteries have started to be considered for electric vehicles [1] and various energy storage applications such as grid support, grid integration of renewables, or micro-grids [2; 3; 4; 5]. One of the biggest concerns in the aforementioned applications is their limited lifetime because their performance deteriorates with usage. A battery management system can efficiently treat the dynamics of the energy storage process in the battery and maintain the optimal operation of the batteries [6]. In order to improve the performance and prolong the battery's life, accurate knowledge of the state of health (SOH) for battery management system is essential and SOH is often expressed as the ratio between the present capacity and the nominal capacity [7]. As batteries are complex electrochemical systems, the capacity loss is difficult to measure in time and the accurate estimation of the battery's capacity is still an issue [7; 8]. The most straightforward way to estimate the capacity is by measuring the charge transferred through the battery during either charging and/or discharging [9]. However, the long time needed to measure the battery current and the requirement of high-precision current sensors decrease the practicality of this method in real applications. Based on electrochemical models or electrical models, state observers such as the multi-scale extended Kalman filter [10] and multi-scale nonlinear predictive filter [11] have been designed for the joint estimation of battery state of charge (SOC) and capacity. Due to the complex internal principles and uncertain working conditions, it is difficult to establish a battery model that can exhibit the battery dynamic characteristics accurately. Data-driven methods do not need knowledge of the battery model, and only depend on the training data. Moreover, with the development of big data technology, real-time monitored parameters like voltage, current, and temperature will be stored and processed, which also decreases the requirements of the microcontroller, and improves the estimation accuracy and robustness. Various data driven methods have been used to predict the battery SOH such as support vector machine [8], relevance vector machine [12], neural network [13], Gaussian process regression [14], etc. Since the information inside the features determines the effectiveness of the data driven estimator, the features should contain plentiful information about the battery degradation [15]. The incremental capacity peak and valley and their corresponding voltage values in the incremental capacity curve were used as features in [16]. Differential geometric analysis [17] and importance sampling [18] were used to extract features from the terminal voltage of the constant current charging test. In [19], the cycling data (voltage, temperature and time) were clustered into several groups, and the regression estimator was trained by support vector machine based on the classification results. Entropy is also used as a feature for capacity estimation because it can capture the variation of voltage, current, and temperature during the battery aging process. [PERSON] et al. predicted the battery capacity by combining particle filter with the sample entropy (SE) feature of voltage in the full discharging process [20]. In their later work [21], the SE of the charging temperature, charging capacity, and rest time were considered simultaneously, and the relationship between multi-variable factors and discharge capacity was established. In [22], support vector machine and relevance vector machine were used to estimate the SOH based on the SE of the voltage in the full discharging process. Compared with the full charging or full discharging test, the hybrid pulse power characterization test is more efficient for the entropy-based estimator because it takes only a few seconds [23; 24]. Polynomial fitting method [23] and sparse Bayesian predictive modeling [24] were proposed to establish the relationship between the SE and the capacity, respectively.