## 1 Introduction:
Indeed, the accurate estimator algorithms are essential for the smart battery management to estimate and measure the functional states of the battery, and it should contain state-of-the-art mechanisms to protect the battery from hazardous and inefficient operating conditions. In this regard, extensive research has been carried out for lithium-ion battery systems, investigating their high power density, energy efficiency, fast charging capability, light weight, steady-state float current, wide operating temperature range, low self-discharging rate, and the possible memory effect [5]. Furthermore, both the prognostications and engineering maintenance are key figures in various industry sectors such as aerospace, chemical, automotive, and so forth. Hence, the obvious formidable obstacles to wholesale EVs is a lack of confidence in the battery life-time and performance [6], leading the authors to look into two intelligent algorithms, which are capable to be implemented in the existing BMS hardware. The state of health can be estimated and classified into offline and online procedures, which have different advantages and drawbacks in terms of accuracy, time duration, and implementation. Based on the advantages and disadvantages, vehicle manufacturers select a suitable technique according to the application. Battery capacity estimation, referring to energy capability, poses tremendous challenges to researchers, whose attempts have turned to the relationship between capacity fade and an increase in battery resistance. Nevertheless, it has been observed that the changes in battery impedance cannot be exactly related to the capacity fade. Moreover, this approach needs extensive laboratory investigations to establish the correlation function [7]. Considerable research has been recently conducted on state of health (SOH) estimation models, which can be split into the following groups: electrochemical models (EMs), equivalent circuit models (ECMs), and data-driven or black-box models [8; 9]. Electrochemical models are established to replicate the growth of a solid electrode interface (SEI) in lithium-ion and describe its influence on capacity degradation. Indeed, they are built based on concentrated solution and porous electrode theories. This means that the electrochemical models describe and elaborate the basic understanding of the electrochemical reaction inside the battery [10]. The EM includes mutually coupled non-linear partial differential equations (PDEs), increasing the numerical complexity and computational efforts, which poses difficulties in the real-time implementation phase, or large-scale simulation as a life-time prediction [11]. In this regard, desperate attempts to reduce the numerical complexity have been recently made through model-order reduction. In the literature [9], a dual SOH and state of charge (SOC) estimation technique has been proposed, by applying the sliding mode technique to the reduced version of PDE, namely a single partial model. The results showed that the proposed technique can track the SOH and SOC accurately. The advantage of the EM approaches is their independence from environmental conditions. On the other hand, as mentioned previously, the EM approaches require intensive computational efforts for system identification, because of a great quantity of parameters [12]. Moreover, the EM approaches are usually created for a particular type of battery consisting of specific anode and cathode materials [13]. The EC models are featured with ease of implementation and parameterization, as well as acceptable modeling accuracy [14]. The EC model completely depends on the environmental and operating conditions (e.g., SOH and SOC). This dependency on model parameters, derived from the operating conditions, can be addressed and captured via a look-up table, needing extensive experimental efforts to collect a sufficient dataset to describe a broad range of operating conditioning for batteries. The ECM's parameters can be estimated and updated via open-loop or close-loop methods.