## 6 Conclusions  
This paper serves as a sequel to our previous study. In our original paper [37], the effect of current sensor bias on SOC accuracy was studied. Subsequently, the effect of changes in capacity was studied in this paper. For maintaining SOC estimation accuracy despite battery aging, the present capacity needs to be properly updated. To efficiently adapt model parameters, including capacity, to the physicochemical changes in aged cells, the simultaneous estimator was developed based on the DEKF (first scheme). However, the parameter filter in the DEKF suffered from a weak observability of its capacity, which we believe is responsible for the inaccurate SOC, particularly noticeable beyond 600 cycles. The present capacity was therefore updated using a separate estimator based on the WLS (second scheme), but it proved ineffective. We speculated that the less accurate SOC, especially when the SOH drops by more than 10%, was not caused by the capacity parameter alone, but rather that all parameters were not updated properly. To this end, the model parameters were reset intermittently in a similar way as they were initialized using the sequential estimator (third scheme). Despite a 30% decrease in SOH, the target SOC accuracy of 5% was achieved through the sequential estimator. The three schemes are summarized and compared in Table 3.  
Figure 14: Variations in SOC estimates (error) over time under (**a**) City, (**b**) Highway, and (**c**) High-speed profiles.  
Throughout this trial and error, several issues emerged that were not addressed in previous studies [31; 32; 33; 34; 35]. The conclusion and future work of this study are summarized as follows:  
* Compared to the Thevenin model, the ESC model offers higher fidelity to the battery aging test data. At the cost of the added hysteresis element, changes in the SOC-OCV curve with battery aging can be modeled, albeit unintentionally.
* To fully leverage the potential of the ESC model, however, a dedicated parameter identification scheme for this model, such as the sequential estimator, is essential.
* In practice, applying the sequential estimator to BMSs operating in real time, including iterative solvers with unpredictable convergence times, requires further works.
* If changes in the SOC-OCV curve can be identified with BMSs operating on board, using a relatively simple model like the Thevenin model and updating the curve at appropriate intervals could serve as an alternative to the current approach.  
Conceptualization, W.S. and J.-H.C.; methodology, M.Y.Y.; software, M.Y.Y. and J.H.L.; validation, M.Y.Y. and J.H.L.; investigation, J.H.L. and H.L.; writing--original draft preparation, M.Y.Y.; writing--review and editing, W.S. and J.-H.C.; supervision, W.S.; project administration, J.S.H.; funding acquisition, J.S.H. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the \"Technology development of hybrid electric propulsion systems for manned future air mobility\" program (1711170902) by Korea Aerospace Research Institute, Republic of Korea.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.