State of charge estimator and methods of making and using the same

The invention discloses a state of charge estimator and methods of making and using the same. A number of variations include a method, which may include using at least a segment of voltage-based Battery State Estimation data, and using real-time linear regression, which may be a method of estimating future behavior of a system based on current and previous data points, to provide a robust and fast-adapting impedance response approximator. Linear regression may be performed by forming an RC circuit which is "equivalent" to electrochemical impedance spectroscopy data and processing the runtime values of that RC circuit using any number of known real-time linear regression algorithms including, but not limited, to a weighted recursive least squares (WRLS), Kalman filter or other means.