Estimation of a lithium battery electrical impedance can provide relevant information regarding its characteristics. Currently, electrochemical impedance spectroscopy (EIS) constitutes the most recognized and accepted method. Although highly precise and robust, EIS is usually performed during laboratory testing and is not suitable for any on-board application, such as in battery electric vehicles (BEVs) because it is an instrumentally and computationally heavy method. To address this issue and on-line system applications, this manuscript describes, as a main contribution, a passive method for battery impedance estimation in the time domain that involves the voltage and current profile induced by the battery through its ordinary operation without injecting a small excitation signal. This method has been tested on the same battery with different passive voltage and current profile and has been validated by achieving similar results. Compared to the original idea presented in the published conference paper, this manuscript explains, in detail, the previously developed method of transforming the battery impedance from the frequency domain to time domain. Moreover, this impedance measurement is used to estimate more robustly the battery state of charge (SoC) through Kalman filters. In the original published conference paper, only an extended Kalman filter (EKF) was applied. However, in this manuscript, an EKF and an unscented Kalman filter (UKF) are used and their performances are compared.