Systems, methods, and computer media for battery system management and non-linear estimation of battery state of charge are provided herein. Battery data is received for a time period over which a battery system has operated. The battery data represents the actual performance of the battery system over the time period. Sub-periods of charging or discharging can be identified in the time period. For the sub-periods of time, a curve can be fit to the battery data. Using the curves for the battery data for the sub-periods of time, an expected performance of the battery system, over a range of states-of-charge, can be determined. Operating instructions for the battery system can be provided based on the expected performance.