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High-power lithium ion batteries are often rated with multiple current and voltage limits depending on the duration of the pulse event. These variable control limits, however, are difficult to realize in practice. In this paper, a linear Kalman filter based on a reduced order electrochemical model is designed to estimate internal battery potentials, concentration gradients, and state-of-charge (SOC) from external current and voltage measurements. A reference current governor predicts the operating margin with respect to electrode side reactions and surface depletion/saturation conditions responsible for damage and sudden loss of power. The estimates are compared with results from an experimentally validated, 1-D, nonlinear finite volume model of a 6 Ah hybrid electric vehicle battery. The linear filter provides, to within ~ 2%, performance in the 30%-70% SOC range except in the case of severe current pulses that draw electrode surface concentrations to near saturation and depletion, although the estimates recover as concentration gradients relax. With 4 to 7 states, the filter has low-order comparable to empirical equivalent circuit models commonly employed and described in the literature. Accurate estimation of the battery's internal electrochemical state enables an expanded range of pulse operation.