## 1 Introduction
It is very attractive to develop battery degradation models based on the evolution of health indicators to determine the battery SOH and RUL. Common indicators of SOH are battery capacity and internal impedance [18]. Therefore, techniques based on the battery capacity and electrochemical impedance spectroscopy (EIS) are commonly used for this purpose [19]. However, capacity is difficult to measure in on-line processes [18], while impedance spectroscopy is a complex and costly technique [18] that usually requires disconnecting the battery from the load, and interrupting the normal operation of the system, with the associated downtime implications and costs. Therefore, indirect methods for an on-line evaluation of the capacity fade, SOH, and RUL without the need to disconnect the battery from the load require further research efforts. Since the open-circuit voltage (OCV) at the battery terminal is directly related to the SOC, it can be used to determine the beginning/end of charge/discharge when using the ampere-hour integration method. However, the battery must be allowed to rest for some time before the OCV is measured to ensure voltage stability. This makes it difficult for real-time applications [5]. In addition, the OCV-SOC curve has a certain hysteresis, i.e., for the same OCV, different SOC values are possible when charging and discharging, which affects the accuracy of the SOC calculation [20]. Researchers often use easily measured variables such as temperature, current, and voltage during charge-discharge cycles to determine health indicators (HIs) [18]. The choice of an appropriate HI greatly affects the accuracy of the predictive battery aging model and, thus, the accuracy of RUL and SOH estimation. Battery HIs are typically calculated by processing the battery charge-discharge data using signal processing and/or artificial intelligence algorithms. Battery health indicators can be broadly classified into book-keeping, direct, and indirect HIs. The decrease in the usable capacity of the battery and the increase in its internal resistance are key characteristics of battery aging; so, capacity and internal resistance are the most commonly used HIs to characterize the aging process. While the capacity fade is a book-keeping HI, the internal resistance is a direct HI. Indirect HIs are related to the extraction of indirect parameters from battery charge-discharge data that are strongly correlated with battery aging [21]. Indirect HIs found in the literature include average discharge voltage, maximum discharge current, constant current charge time, charge terminal voltage change, or charge temperature change rate [21]. For an accurate real-time evaluation, depending on the estimation method used, the system will need to store a large amount of data, requiring high storage and processing capabilities. In addition, a complete discharge of the charge stored in the battery or an expensive device capable of measuring other parameters such as internal resistance may also be required. Signal processing plays a leading role in the calculation of HIs for battery diagnosis and prognosis. Raw acquired battery data are usually denoised and filtered; subsequently, linear interpolation, extrapolation, look-up tables, or other processing methods are typically applied to determine the electromotive force. For example, time-domain and frequency-domain signal processing methods are used in EIS approaches because EIS is based on wide frequency-band measurements [15]. In [22], empirical mode decomposition and particle filtering methods are applied to predict the end-of-life of Li-ion batteries, while other authors [23; 24] have applied neural networks for this purpose. In this paper, signal processing methods such as discrete wavelet filtering and prediction methods based on linear fitting and autoregressive integrated moving average algorithms are applied. This paper proposes a voltage-based battery health indicator.