## 2 State of the Art  
Several methods have been reported to observe, monitor, or estimate the SoH. These methods can be classified into two main groups: The experimental methods, which are based on direct measurements or models based on actual measurements, and the adaptive methods, which try to simulate or estimate the health of the battery provided the behavior of the battery and minimal measurement data [5]. These methods are shown in Figure 1.  
Experimental methods are based on results of experimental investigations carried out before the real life of the battery cell, which serve as a basis for estimation of SoH. They can be classified into capacity-fade estimation methods and power-fade methods. Experimental-based capacity-fade assessment methods, such as Coulomb-counting, measure the battery's capacity. With the load disconnected and the battery integrally cycled, the total charge, inferred from the integration of the current over time, gives the battery's actual capacity. The main inconvenience with this method is that the measurement over a complete cycle, including a full charge and discharge process, is time-consuming and involves high energy consumption. Nonetheless, it is the standard for determining the battery capacity. Experimental power-fade estimation methods are mainly based on impedance-based information. Among these techniques is the Hybrid Pulse Power Characterization (HPPC), which uses a current pulse, which causes a sudden voltage to drop or rise depending on the sense of the current. The current and voltage information is used to calculate the charge or discharge power [6]. A significant drawback of this method is its heavy reliance on the series resistance, which is heavily influenced by contact resistance, which is often sensitive  
Figure 1: State-of-the-art methods for State-of-Health (SoH) estimation. to electronic noise and environmental influences, including temperature and electrical noise. Using a multifrequency current excitation signal, and with the help of the response voltage, an impedance spectrum (IS) can be extracted. This gives more information about the battery's performance in different frequencies and is not limited to the DC component, such as in the HPPC method. Furthermore, the obtained spectrum is less sensitive to noise and environmental factors. This is due to the quality of the signal processing required for such a task and the consistency of the measurement points owing to the Kramers-Kronig relation. However, a major drawback is the necessity of an equivalent circuit model (ECM) to deconvolute the impedance spectrum and extract one or more sensitive parameters to SoH. The choice of the model, as well as the parameters, affects the eventual results. After fitting the measurement to an equivalent circuit model, the obtained circuit parameters (e.g., resistance), or their properties (e.g., constant-phase angle), are correlated with the SoH [4; 5]. In [7], a resistance in series with an inductance and 2 RQ elements is used to model the behavior of the electrodes and electrolyte. The series resistance and one electrode's resistance are correlated with the number of cycles. In [8], an Rs-L-Randles circuit is used to model the battery. A formula estimating the battery capacity from the series resistance is used. Similarly, in [9], the same model, including a Warburg element, is used. The growth rate of the charge transfer of one of the electrodes shows a high correlation with the number of cycles. The paper features a ratio of SoH that requires the current and the end-of-life charge-transfer resistance to be calculated. In [4], the battery is modeled with the help of a resistance in series with an inductance and RC element, plus a transmission line model (TLM). Here, TLM depicts the transmission line model to describe the electrode. Despite the complexity of the model, the paper shows a correlation between several components, including charge-transfer resistance, electrode capacitances, to the number of cycles. In [10], a simplified RC element is used for the fitting.