## 1 Introduction  
Lithium-ion batteries (LIBs) are currently the most widely used type of battery for electromotive applications and are seen as the most promising candidate for the realisation of a comprehensive electro-mobility. Current research focuses on the optimisation of safety as well as ageing diagnostics and lifetime predictions. The cell design, its operation and the environmental conditions all affect the ageing of a cell and therefore the lifespan of LIBs [1,2]. Various LIB degradation processes, which lead to a distinct decrease of the maximal usable capacity \(C\) as well as an increase of the internal ohmic resistance \(R\) of the LIB, can be distinguished [1, 2, 3]. In the field of e-mobility, for instance, the LIB degradation results in a loss of driving range per charge in electric vehicles (EVs) [2] and therefore in the deterioration of the coulombic efficiency \(\eta\) of LIBs. Ageing processes occurring at the negative and the positive electrodes differ significantly and are usually differentiated in the literature [1]. Ageing processes in the electrolyte and the separator mostly result, respectively, from reactions with the electrodes and reactions at the electrode-electrolyte interface [1]. The most prominent ageing process at the negative electrode, the anode, is the formation of the solid electrolyte interface (SEI) [4] as well as Lithium plating [5; 6]. At the positive electrode, the cathode, structural changes during cycling in combination with chemical decomposition reactions of the electrode material result in capacity decreases and therefore decreasing charging efficiency [1]. Furthermore, calendar and cyclic ageing of LIBs can be distinguished where both depend on environmental conditions [2; 7]. Additionally, the State-of-Charge at which the battery is stored impacts calendar ageing [8]. Regarding cyclic ageing, the depth of discharge (DoD) also impacts battery degradation processes [9]. Moreover, manufacturing aspects, i.e., variations in raw materials and assembly accuracy, complete the picture of relevant ageing factors. Following a cause-and-effect principle, we summarised the main factors influencing battery degradation and their interactions in an Ishikawa diagram; see Figure 1. In this work, we do not aim to identify and analyse dedicated ageing mechanisms but focus on higher-level LIB diagnostics tailored for battery management systems (BMSs). Reliable and precise state diagnosis of LIBs, e.g., State-of-Health (SoH), the State-of-Charge (SoC), and the characteristic remaining useful life (RUL) values, is therefore essential for reducing safety risks and estimating and extending the cycle life of battery systems used in EVs [8]. The accurate diagnosis of SoH is an indispensable part of effective battery health management for every BMS [10]. The SoH is mostly characterised by the maximum usable residual capacity C or by the relative change in the internal ohmic resistance \(R\)[11]. Typically, BMS uses such values as the capacity decrease and the power fade based on the increase of \(R\) with regard to the nominal values \(C_{0}\) and \(R_{0}\) to quantify the SoH [12]. For a non-destructive determination of the SoH and the RUL under operating conditions or at rest, electrochemical in situ measurement methods are mandatory. Besides monitoring open-circuit-voltage (OCV), the internal resistance \(R\), determined via constant and pulsed current-voltage measurements, can be used to monitor the SoH [13; 14]. Other approaches use the internal resistance \(R\) for the estimation of the SoH [15; 16; 17]. For the measurement of cell capacity, various in situ techniques are proposed in the literature, such as incremental capacity analysis (ICA) [18], differential voltage analysis (DVA) [19], combined IC-DV analysis techniques [20] as well as electrochemical impedance spectroscopy (EIS) [21]. Therefore, the use of ICA, DVA and EIS is suitable for SoH diagnosis as well as for the identification and differentiation of various ageing mechanisms [20; 22].