We report the development of an adaptive, multi-parameter battery state estimator based on the direct solution of the differential equations that govern an equivalent circuit representation of the battery. The core of the estimator includes two sets of inter-related equations corresponding to discharge and charge events respectively. Simulation results indicate that the estimator gives accurate prediction and numerically stable performance in the regression of model parameters. The estimator is implemented in a vehicle-simulated environment to predict the state of charge (SOC) and the charge and discharge power capabilities (state of power, SOP) of a lithium ion battery. Predictions for the SOC and SOP agree well with experimental measurements, demonstrating the estimator's application in battery management systems. In particular, this new approach appears to be very stable for high-frequency data streams.