Lithium based rechargeable battery packs have been widely adopted in electric vehicles (EVs). A battery management system (BMS) ensures the safety, efficiency, and reliability of the electric vehicle. It continuously monitors the battery packs. The main component of BMS is the battery fuel gauge which estimated the crucial parameters of the battery, such as state of charge (SOC), state of health (SOH), time to shut down (TTS) and remaining useful life (RUL). To estimate these parameters, battery electrical equivalent circuit model (ECM) is to be identified and ECM parameters needs to be estimated. These parameters can be estimated either in time domain or frequency domain. Parameter estimation in time domain is used widely in real time scenarios. However, parameter estimation in frequency domain is more accurate. Electrical impedance spectroscopy (EIS) is a widely used technique to know the battery response in frequency domain. Therefore, this response is used to estimate the parameters of the battery ECM. A little has been done in the literature to extract battery ECM parameters using EIS and their validation using real data. A systematic approach is presented to extract the ECM model parameters of a battery in frequency domain and time domain. Real world EIS and time-domain data is collected to compare the ECM parameters estimated based on both frequency domain and time-domain approaches. The experiment is repeated at six different state of charge (SOC) levels of the battery to understand the behaviour of ECM parameters with SOC