## 1 Introduction  
With the advantages of high energy/power density, low self-discharge rate, and longevity, lithium-ion batteries have been widely used in consumer electronics, electric vehicles, and even in space systems [1; 2]. However, battery performance will degrade with the charging and discharging cycles. In the case of failure, an aged battery may cause significant casualties and economic losses, especially in military communications, navigation, aerospace, and other complex application scenarios [3]. Consequently, the prognostics of the state of health (SOH) of a lithium-ion battery is meaningful for reducing system risks and maintenance costs [4; 5]. Generally, the prognostic of a lithium-ion battery is a process of predicting its SOH and remaining useful life (RUL) [6]. The lithium-ion battery RUL is defined as the remaining number of charge-discharge cycles of the battery with a specific output capacity [7]. In recent years, methods for battery prognostics have mainly included a model-based approach, a data-driven approach, and a hybrid approach. The model-based approach usually includes the electrochemical model [2], the equivalent circuit model [8], and the empirical model. These models usually implement state estimation and prediction based on filtering algorithms. The electrochemical model and equivalent circuit model can reflect the physical or chemical properties of the battery. However, the complex aging mechanisms and the high cost of measuring the internal parameter of the battery make these two models mostly useful in theoretical research and battery design, and difficult to apply in practical engineering. In practice, the most commonly used model is the empirical model, which is obtained through the historical data mining of a large number of battery degradation processes. The researchers have proposed many empirical models, like the capacity-based exponential model [9; 10], the two-term logarithmic model [11], the conditional three-parameter capacity degradation model [12], the resistance-based exponential growth model [13], and the polynomial model [14]. Moreover, based on the empirical models, some filtering algorithms such as the Kalman filter [15], the unscented Kalman filter [16], and the particle filter [17] are used to reduce the influence of measurement noise and system interference as well as improve the estimation accuracy of the battery's SOH. However, the above filters are implemented based on the state space model of battery degradation. In the prediction stage, there are no measurements that can be used to update the model parameters, and this reduces the prediction accuracy. By extracting features from the monitoring data and mapping them into the degradation model for the SOH, the data-driven prediction approach can describe the inherent degradation relationship and trend of the battery [18]. Data-driven methods such as artificial neural network [19; 20], support vector machine [17; 21; 22], and correlation vector machine [7; 13; 15; 16; 23] have been widely used for lithium-ion battery prognostics. As compared with the model-based approach, a data-driven approach can construct a degradation model without the knowledge of complex physical degradation by relying only on the historical data. It is more suitable for building different types of battery degradation models and solving complex prognostic problems. However, if there is not enough high-quality training data, the data-driven approach will not yield satisfactory results [7]. Both the pure model-based and the pure data-driven approach have their limitations in lithium-ion battery prognostics. Therefore, the hybrid approach is proposed to improve the RUL prediction accuracy by combining two or more kinds of methods. For example, [PERSON] and [PERSON] [24] combined the equivalent circuit model with a similarity-based prediction method to establish the measurement model and extrapolate the available measurement range.