## 1 Introduction  
Energy is the basis of the human survival and development. The growing concern over oil shortage and environmental issues has greatly accelerated the development of green energy to replace fossil fuel in recent years [1]. Since transportation consumes a large part of energy, to develop and apply electric vehicles (EV) is necessary in the way of green mobility [2]. It is well known that the battery pack is the key component of EV, hybrid electric vehicles (HEV) and plug-in hybrid electric vehicles (PHEV). Lithium-ion battery (LIB) is for the high specific or volumetric power and energy density, high cycle lifetime and decreasing cost have made them more attractive for the vehicles [3]. The reliable and efficient battery management systems need to be developed to ensure the power battery work well [4; 5], estimating the state-of-health (SOH) of the battery is the most crucial function among the various functions of a battery management system [6]. The SOH is a metric of the battery's age that reflects the ability of a battery to store and deliver energy relative to initial condition. However, the degradation of a LIB is a very complex process that is affected by many factors, such as charge/discharge rate, storage temperature and operating process. Compared with the state of charge (SOC) estimation, the SOH estimation is more challenging [7]. In practical applications, the degradation of the battery causes many parameters such as battery capacity and battery impedance to change. The quantitative definition of the SOH is mainly based on the internal resistance increase or the capacity degradation. The SOH estimating methods based on internal resistance increase needs to get the initial resistance when the battery is fresh and the resistance at the end-of-life (EOL). When the resistance changed with aging of the battery is achieved, it could estimate the SOH of the battery. The traditional method to get the parameters of the battery is electrochemical impedance spectrum (EIS), which is a powerful lab-based diagnostic technique. However, the principle of the EIS method is to apply to a cell a sinusoidal signal and measure the characteristic response from the cell, it is not suitable for the real application. The aim of the EIS is to improve the speed of the calculation [8] and make use of the free signals of current and voltage during the operation of the battery instead of the additional burden of the input signal, so as to carry out SOH estimation in real time [9; 10]. Moreover, Equivalent Circuit Models (ECMs) can simulate the static and dynamic behavior of a battery. It is commonly used to predict the SOH by identifying the resistance of the equivalent circuit models (ECMs). However, different ECMs, different parameter identification methods and different battery operating conditions will affect the precision of the parameter identification. Improving the precision of the parameter identification is the key problem to be addressed. The SOH estimating methods based on capacity degradation needs to get the maximum available capacity which changes with aging of the battery. The ratio of the maximum available capacity and the nominal capacity is the SOH of the battery. When the current maximum available capacity is reduced to 80% of the nominal capacity of the battery, it is considered to have reached the EOL of the battery [11]. Among all the methods based on capacity degradation, the most direct way is to discharge the battery from the fully charged state to the discharge cutoff voltage at a specified current rate and ambient temperature. The number of ampere-hours drawn from the battery under such working condition is the maximum available capacity of the battery [12; 13]. This method is simple and direct but it is not suitable for practical applications. Thus, the aim of the improvement is to estimate the SOH in real time for a part cycle and dynamic condition instead of for the whole cycle and a constant condition.