A battery system to determine real-time parameters of a rechargeable battery, comprising: - a rechargeable battery configured to couple to an electrical system ; and - a battery control module configured to electrically couple to the rechargeable battery, wherein the battery control module is configured to: - monitor at least one monitored parameter of the rechargeable battery; and - recursively calculate at least one real-time calculated parameter of the rechargeable battery based on at least an equivalent circuit model, the at least one monitored parameter, and a Kalman filter, wherein the at least one monitored parameter of the rechargeable battery comprises terminal voltage, current, temperature, or any combination thereof, wherein the at least one real-time calculated parameter of the rechargeable battery comprises an open circuit voltage of the rechargeable battery, a current path resistance of the rechargeable battery, a charge transfer resistance of the rechargeable battery, an RC time constant of the rechargeable battery, or any combination thereof, wherein the open circuit voltage of the rechargeable battery is a time-variant parameter of the rechargeable battery, and wherein the current path resistance of the rechargeable battery, the charge transfer resistance of the rechargeable battery, and the RC time constant of the rechargeable battery are each time-invariant parameters of the rechargeable battery, and wherein the Kalman filter includes a process noise matrix to differentiate time-variant parameters from a time-invariant parameter when recursively calculating the at least one calculated parameter of the rechargeable battery. - a rechargeable battery configured to couple to an electrical system ; and - a battery control module configured to electrically couple to the rechargeable battery, wherein the battery control module is configured to: - monitor at least one monitored parameter of the rechargeable battery; and - recursively calculate at least one real-time calculated parameter of the rechargeable battery based on at least an equivalent circuit model, the at least one monitored parameter, and a Kalman filter, - monitor at least one monitored parameter of the rechargeable battery; and - recursively calculate at least one real-time calculated parameter of the rechargeable battery based on at least an equivalent circuit model, the at least one monitored parameter, and a Kalman filter, wherein the at least one monitored parameter of the rechargeable battery comprises terminal voltage, current, temperature, or any combination thereof, wherein the at least one real-time calculated parameter of the rechargeable battery comprises an open circuit voltage of the rechargeable battery, a current path resistance of the rechargeable battery, a charge transfer resistance of the rechargeable battery, an RC time constant of the rechargeable battery, or any combination thereof, wherein the open circuit voltage of the rechargeable battery is a time-variant parameter of the rechargeable battery, and wherein the current path resistance of the rechargeable battery, the charge transfer resistance of the rechargeable battery, and the RC time constant of the rechargeable battery are each time-invariant parameters of the rechargeable battery, and wherein the Kalman filter includes a process noise matrix to differentiate time-variant parameters from a time-invariant parameter when recursively calculating the at least one calculated parameter of the rechargeable battery. <EOS>