A rechargeable battery is charged and, at the same time, steps are taken to assess its state of health (SoH). The SoH is first broadly classified, which is only a coarse estimate. Next, the state of charge (SoC) is estimated, and then the SoC is repeatedly measured and predicted during charging until its value converges to a reliable value. The SoH is a state in the Kalman filter used for determining the SoC, and the SoH is also refined through the filter process. The SoH is reported when or after the SoC has converged, and is reported before charging is completed.