control//state estimation//state of charge estimation

State of charge estimation is the inference of how much charge a battery has left, as a fraction of its capacity, from the current and voltage a battery management system can measure, and it runs in every electric car, phone, drone pack and grid storage unit, because no sensor reads charge directly. The fuel gauge on a dashboard, the decision to stop a drone's mission and return, and the limits that keep a cell from being overcharged all rest on this estimate.

State of charge estimation is the inference of how much charge a battery has left, as a fraction of its capacity, from the current and voltage a battery management system can measure, and it runs in every electric car, phone, drone pack and grid storage unit, because no sensor reads charge directly. The fuel gauge on a dashboard, the decision to stop a drone's mission and return, and the limits that keep a cell from being overcharged all rest on this estimate.

Two imperfect voices are available, as in every estimation problem. Integrating the current over time, coulomb counting, is smooth and immediate, and it drifts: a small offset in the current sensor accumulates without bound, the starting charge is uncertain, and the capacity it divides by fades as the cell ages. It is dead reckoning for charge. The voltage, read against the cell's curve of open-circuit voltage versus charge, is an absolute reference, but only at rest: under load the terminal voltage also contains the drop across the internal resistance and slow polarization effects. An equivalent-circuit model (the open-circuit voltage as a function of charge, a series resistance, one or two resistor-capacitor pairs) joins the two, and an extended Kalman filter fuses them: the current drives the prediction, the voltage corrects it.

The cell's chemistry decides the observability. Where the voltage curve is steep, a millivolt says a lot about the charge; lithium iron phosphate cells have a nearly flat curve across most of their range, so in the middle the voltage barely informs the charge, the filter leans on coulomb counting, and its uncertainty grows until the pack nears full or empty (observability).

The slow parameters are estimated as well. Capacity and internal resistance change with age and temperature, so they enter the filter as extra states (state augmentation) or a separate recursive least squares estimator follows them, which only works when the current varies enough to tell them apart.

With a forecast of capacity loss and a decision about charging limits or replacement, the same estimator becomes the core of a battery's digital twin, and its fleet-wide version tells an operator which packs to retire.