Two key indicators of a battery management system (BMS) are the state of charge (SoC) and the state of health (SoH). Accurately estimating SoC is important to prevent potential issues. Additionally, space, computing time, and cost are important factors in hardware development. To address these considerations, the first-order extended Kalman filter (EKF) and adaptive extended Kalman filter (AEKF) models were selected due to their simpler data pre-processing and better accuracy. The study recommends using the first-order equivalent circuit model (ECM) method in conjunction with the EKF and AEKF algorithms due to their straightforward setup and efficient computational process. Analysis of the charge-discharge cycles shows that the AEKF method consistently outperformed the EKF method regarding SoC accuracy. Moreover, when given different initial SoC values, the AEKF method displayed superior SoC estimation accuracy compared to the EKF method. Moreover, while the accuracy of the EKF is diminished, the error value remains below 2.5% for up to 500 cycles. Additionally, the shorter computing time of the EKF method is a consideration for practical real-world implementation. Furthermore, experiments conducted over 500 cycles revealed that SoH estimation declined from 99.97% to 76.1947%, suggesting that the battery has reached the end of life (EOL) stage. © 2025, Institute of Advanced Engineering and Science. All rights reserved.