## 1 Introduction  
Lithium-ion batteries (LiBs) have gained enormous popularity as energy storage elements for most rechargeable electric systems. LiBs have been implemented in small devices such as mobile phones and large systems such as electric vehicles (EVs). These types of batteries are also needed for energy storage in renewable energy sources (such as solar and wind) to improve their stability. LiBs' popularity can be attributed to their high specific energy and high operational voltage [1]. Unfortunately, LiBs are highly nonlinear elements with a limited operational area, which requires robust monitoring for their safe application [2]. An LiB's operational window can be defined by voltage and temperature boundaries. The size of the operational window will depend on the LiB's chemistry [3]. Continued use of the LiB outside of this operating window may cause the battery to develop dendrites over time, which increases its internal resistance and may lead to short-circuiting (e.g., dendrites may penetrate the diaphragm or battery wall). Additionally, it may start releasing toxic gases, causing it to burst into flames [3]. Furthermore, the LiB's maximum capacity may decrease when subjected to deep discharge cycles. Another concern with LiB technology is the accurate estimation of its available capacity, which is typically linked to the state of charge (SOC). The SOC represents the available amount of charge in a battery during usage and is measured by ampere-hours(_Ah_). The SOC is typically defined as a percentage of current available capacity vs. the expected maximum capacity of the battery. It may also sometimes be based on the current available power vs. the expected maximum power of the battery. A value of 100% SOC refers to a fully charged battery, whereas a value of 0% SOC represents a depleted battery. Accurate SOC estimation is of great concern, since it dictates how long the system can operate. However, accurate SOC values are hard to derive due to the lack of direct measurement. The SOC can only be estimated using the voltage and current of the LiB, which are indirect measurements [4]. In the literature, several techniques have been proposed to estimate the SOC. The most popular method has been the ampere-hour counting method. This method makes use of current measurements and the battery's capacity to estimate the SOC of the battery [4]. The SOC is derived by making use of an initial value of SOC from which the current value is either subtracted or to which it is added, depending on whether a charge is demanded from or supplied to the battery. Unfortunately, due to the high dependency on an accurate initial SOC value and sensor current measurements, the estimated SOC value may be subject to large errors [3]. Moreover, the ampere-hour counting method makes use of the battery's available capacity, which has been shown to degrade over time, resulting in an increasing amount of error from regular usage of the battery. Some of these problems may be corrected by implementing calibration techniques such as voltage-based corrections using reference tables [3]. Even though the ampere-hour counting method has several drawbacks, great results have been obtained when combined with other techniques such as neural networks (NNs) and Kalman filters (KFs) [5; 6]. Neural networks have shown great potential but require vast amounts of data that must be collected beforehand. Moreover, some solutions result in computationally taxing algorithms [5]. Note also that KFs provide low computational expense and accurate solutions but make use of mathematical models [6]. Among the developed and studied models are the electrochemical models and electric circuit models (ECMs). Electrochemical models are highly accurate in nature and provide abundant information about the LiB's state as they are based on the underlying physics of the battery. However, these models are often composed of several partial differential equations--sometimes in the order of 10-14 equations--resulting in complex and computationally expensive models.