## 1 Introduction
[PERSON] et al. [11] explored how ECM parameters depend on the frequency characteristics of the load current and suggested a method for application-specific parameterization based on the frequency spectrum of the load. Additionally, the effects of the load current profile on ECM parameters were examined by [PERSON] et al. [12]. [PERSON] et al. [13] incorporated C-rate-dependent resistance into the ECM to account for slow kinetics and the impact of C-rates on diffusivity, which becomes more pronounced at temperatures below 0 \({}^{\circ}\)C. Their research demonstrated that this enhanced ECM could be integrated into battery management systems to accurately forecast cell behaviour under various low-temperature operating conditions. The offline identification method, due to its reliance on specific experimental conditions, often requires a significant number of tests, leading to lengthy development cycles and increased costs. In this context, Design of Experiments (DOE) methods are crucial for efficiently investigating and understanding the effects of multiple variables in a system. By structuring experiments to systematically vary these variables, DOE helps identify which factors significantly impact outcomes, reduces the resources needed for research, and improves the reliability of results. [PERSON] et al. [14] investigated the impact of four HPPC parameters--positive and negative pulse height, pulse length, and relaxation length--on the performance of the equivalent circuit model (ECM) under various application conditions. They employed the Taguchi method to analyse the effects of these parameters, revealing that a decline in SOH leads to increased ohmic and polarization resistance, as well as decreased polarization capacitance. [PERSON] et al. [15] developed an electro-thermal model for electric vehicles by leveraging a Design of Experiments (DOE) approach to enhance the efficiency and accuracy of battery management systems (BMSs). They focused on lithium-ion batteries, particularly modelling the effects of temperature and State of Charge (SOC) on the equivalent circuit model parameters. Their methodology included software-in-the-loop (SIL) and hardware-in-the-loop (HIL) testing to simulate battery pack behaviours under various scenarios. They stated that this method allowed for precise statistical analysis to identify significant model parameters and validate the model through comparison with traditional approaches, proving that fewer experimental runs could achieve similar accuracy. [PERSON] et al. [16] investigated the effects of pulse charging parameters on the life cycle characteristics of lithium-ion batteries. They utilized a DOE approach, specifically Taguchi orthogonal arrays, to systematically study and optimize these parameters. Key factors such as pulse frequency, duty cycle, and charging temperature were analysed to determine their impact on battery performance. Their findings suggested that optimized pulse charging can significantly enhance battery life and efficiency compared to standard constant current-constant voltage charging methods. [PERSON] et al. [17] introduced a new DoE approach that combines partial and deep discharge tests for battery evaluation, significantly enhancing ECM precision by reducing the root mean square error by nearly 70%. The data-driven method is considered a \"black box\" approach, relying heavily on the quality of input data, training, and hyperparameter selection [18]. Despite the theoretical challenges, model-driven methods like the Kalman filter (KF), a prevalent state estimation technique, are used to estimate the optimal posterior SOC based on ECM [19]. Within this framework, the extended Kalman filter (EKF) uses a first-order Taylor expansion to linearize nonlinear systems' evolution and measurement functions, enhancing SOC estimation accuracy [20]. [PERSON] et al. [21] addressed the challenges in SOC estimation caused by factors affecting the accuracy of extended Kalman filters.