## 1 Introduction  
With the growing awareness of the energy crisis and environmental pollution, electric vehicles using electricity as an energy source are gradually becoming the focus of attention. The energy source usually consists of a rechargeable lithium-ion battery (LiB). Unlike other types of batteries, LiB offers higher energy efficiency. However, the health of a LiB and its cost of replacement have been the problems for consumers in electric vehicle applications, and the development of an accurate and quick, preferably in-situ health monitoring method is receiving significant research attention in the field of LiBs [1]. As the discharge characteristics of a LiB vary with the composition of the electrochemistry in the battery, and the state-of-health (SoH) of a LiB is strongly affected by its composition as well as ambient environmental factors, together with variation in its usage conditions, the estimation of the LiB health can be challenging. This state-of-health is a \"measurement\" that reflects the general health condition of a battery in term of its ability to deliver maximum stored charge as compared to its fresh state. It depends on factors such as its maximum stored charge, internal resistance, voltage, and self-discharge. Theoretically, the SoH of a fresh battery is 100% and will decrease over time due to its usage [2]. State-of-health is an indicator to describe the health status of a battery, and it can reflect the performance and aging of the battery. In terms of electrical quantity, SoH is an indicator of the remaining full battery capacity. SoH is generally defined as the ratio of the maximum releasable capacity of a battery to the rated capacity of the battery when it is fresh. The two most important health conditions of a LiB are its maximum charge capacity, which is represented by SoH, and its status of safety, which is represented by state-of-safety (SoS). SoS represents the condition when the battery is in danger to use in the vehicles, and it can be estimated by several means, such as its thermal runaway, current, voltage, state-of-charge (SoC), and SoH [3]. As SoH degrades over charge-discharge cycles, accurate estimation of its SoC can be affected if the SoH is not taken into account. This is because SoC is defined as the percentage of available stored charge with respect to the full capacity of the battery. This full capacity of the battery is sometimes its rated capacity, but more likely its current (i.e., at the latest charge-discharge cycle) capacity and this leads to an ambiguity that renders confusion and differences in the reported SoC values. During the lithiation process (charging), metal oxides break apart from the cathode side, which produces Li ions that bond with the anode side material with the addition of electrons. The opposite process where Li-ion travels back and bond with the metal oxide on the cathode side is called the de-lithiation (discharging) process. The effectiveness of the cathode material is determined based on the number of Li ions produced during the lithiation process, and the effectiveness of the anode material is verified based on the number of Li ions which migrate from cathode and bond with the anode material. This, in turn, also decides the SoC and SoH of the batteries [4]. To estimate the maximum distance before the LiBs need to be charged again requires the knowledge of the road conditions ahead and an accurate SoC, and this can be represented by the state-of-energy (SoE) [5; 6]. SoE indicates the remaining energy, instead of charge, that can be used from the battery, which describes a more precise state or condition of the battery. The state-of-discharge (SoD) is the percentage of the discharged capacity of a battery which is fully charged before discharging and is related to SoC as [7]. \[\text{SoD}=1-\text{SoC}. \tag{1}\]  
Uncertainties in capacity estimation can cause the LiBs to be over-discharged will accelerate the degradation of LiBs.