This invention provides methods for dynamic estimation of the open-circuit voltage of a battery. In some embodiments, an impulse response is calculated using a matrix-based algorithm or a recursive algorithm. Then, a current response is calculated by convolving the impulse response with the measured current. The open-circuit voltage of the battery is derived by subtracting the current response from the measured voltage. Using the principles disclosed to estimate OCV, a lithium-ion battery may be managed with a battery-state estimator that allows accurate and timely estimation of the state of charge, the charge and the discharge power capabilities, and the state of health of the battery. These methods are able to accept various exciting signals, are stable and robust against noises, even when diffusion is a limiting kinetic factor in the battery.