## 1 Introduction
For instance, a single extended Kalman filter (EKF) was applied to the joint estimation structure for battery state and parameter estimation in [16]. Improvement of the battery monitoring performance with the joint estimation method using the unscented Kalman filter (UKF) can be found in [17]. Furthermore, simultaneous battery OCV estimation is realized with adaptive EKF in the joint estimation framework in [18]. Recently, considering the model uncertainties in [19], H\(\infty\) EKF was introduced to the joint estimation structure in order to have a robust estimation of battery SOC and ohmic and polarization resistance simultaneously. On the other hand, a more flexible estimation framework based on two observers is called the dual estimation method. The double EKF [14], double UKF [17], double sliding mode observer [20], double H\(\infty\) observer [21], and double particle filter [22] are introduced to the dual estimation framework, where battery parameters and states can be estimated separately with different time scales. Additionally, merging the advantages of different filtering techniques is another objective of the dual estimation method. For example, the UKF and H\(\infty\) observer were applied in the dual estimation framework in [23], in which the H\(\infty\) observer was used to have a robust battery parameter estimation, and more accurate SOC estimation was achieved with UKF. Although fruitful research works have been brought based on the two aforementioned classical structures, the essence of the different observer-based battery monitoring studies has not changed. The main existing problem in the current two monitoring structures will be intuitively pointed out by a representative research work as follows. In [24], the multi-time scale dual estimation framework was studied with EKF. As shown in Figure 1, an interesting phenomenon can be observed from the experimental results. It raises several questions. 1. Why is the convergence speed of the battery usable capacity so slow? A similar problem can also be found in other research works such as [2; 14], etc. Although they explained that the capacity estimation is faster than the capacity degradation, the slow convergence speed of battery usable capacity in classical monitoring structures, usually several hours, still needs to be explored. 2. Why will the smaller initial value of battery usable capacity lead to a rapid convergence speed? As can be observed from Figure 1a-d, although the steady state error was similar for 1 Ah or 2 Ah, the convergence speed of the estimation was faster with the lowest initial value. 3. Are there other observability conditions that can guarantee a rapid convergence speed for the battery usable capacity? Based on the above question, how to find the other observability conditions to improve the battery monitoring result is of great importance. Indeed, the convergence rate can be adjusted by varying the process and measurement noise covariance during the observer design process [24]. However, intrinsic characteristics from the battery or the used model should be mastered, whether we can take advantage of them or effectively avoid them. 4. How can we improve the battery monitoring performance based on the classical extended ECM, if the answers to the aforementioned questions are found? That is, how can we take advantage of the existing literature, including the validated model and experimental information, to propose a new battery monitoring structure that can overcome the drawbacks of the traditional joint and dual estimation frameworks? Hence, the contribution of this paper lies in answering the four previously proposed questions. Namely:  
Figure 1: Battery usable capacity estimation result with the dual estimation framework [24], Copyright Elsevier, 2012. (**a,b**) are the capacity estimation result with a multi-time scale; (**c,d**) are the capacity estimation result with a single time scale.