## 1 Introduction
Unless significantly reduced, these models are often only implemented in battery development research [7; 8; 9; 10]. Meanwhile, ECMs make use of electric elements such as resistors, capacitors, and voltage sources to create a representation of the battery's dynamics. These types of models result in low computational power use and low-complexity solutions but provide less information about the battery and have been found to be less accurate than their counterparts [11]. Nonetheless, these attributes are highly desired in online applications. In the literature, ECMs can be categorized by the number of resistor-capacitor (RC) branches found in the model [12]. For example, the Rint model makes use of a voltage source and a resistor to represent the battery's energy source and energy loss during operation, respectively. The Thevenin model adds an RC branch to capture the transient response of the battery. Models with a higher number of RC branches have been shown to allow for a better representation of battery dynamics [12]. However, each additional RC branch increases the complexity and computational time of the model. Kalman filter-based solutions have shown great accuracy in determining the SOC when combined with ECMs and the ampere-hour counting method [6]. Most KF solutions make use of a nonlinear form of the KF to account for the battery's nonlinear behavior. Some of these variations are the extended Kalman filter (EKF), unscented Kalman filter (UKF) and cubature Kalman filter (CKF) [6; 13]. However, these solutions do not account for the aging process of the battery, which is required to ensure an accurate SOC estimation during the lifetime of the battery. For SOC accuracy to remain the same throughout the use of the LiB, a battery monitoring system (BMS) must track the natural aging process of the battery. As the battery is subject to use, the LiB's capacity degrades over time while the internal resistance increases. The result is an LiB with less output power or lower run time [14]. The degradation of the battery capacity is of greatest importance since the SOC estimation process is highly dependent on an accurate value of the maximum capacity of the battery. In the literature, this aging process is described by the state of health (SOH) of the battery. SOH is often defined as a ratio of the current maximum battery capacity compared to its maximum initial capacity or manufactured capacity [15]. In addition, it has been noted in the literature that an LiB may experience a faster aging process if it is subject to aggressive current profiles, excessive cycling, or deep discharging or charging conditions [16]. Finally, accurate tracking of the LiB's aging process allows for an effective retirement of the battery. LiBs are often retired when their maximum available capacity value is below 80% of their designed capacity. Dual filters have been proposed for tracking the aging process of LiBs. Dual filters can track several parameters of interest, including the internal resistance and the battery's maximum capacity [17; 18]. In a dual-filter strategy, the normal estimation process is broken into two components, where one part estimates the SOC and other states, while the second part estimates and updates the parameter values of the model [17]. Other proposed strategies include the use of a multiple model (MM) process. An MM process makes use of several models to describe different behaviors that the system may be subjected to. The MM algorithm then selects the best match to the current conditions, which makes the algorithm flexible and resilient to uncertainty. A variation of the MM algorithm known as the interacting multiple model (IMM) has been implemented for tracking SOH [19]. Several models were created to represent different SOH levels of an LiB. The algorithm would then match the best model to the current conditions, thus determining the most likely current SOH of the LiB [19]. This paper proposes an adaptive strategy that can accurately track an LiB's battery capacity when subject to different cycling conditions.