A method for systematically deriving simple nonlinear dynamical models from ice-core data is proposed. It offers a tool to integrate models and theories with paleoclimatic data. The method is based on the unscented Kalman filter, a nonlinear extension of the conventional Kalman filter. Here, we adopt the abstract conceptual model of stochastically driven motion in a potential that allows for two distinctly different states. The parameters of the model-the shape of the potential and the noise level-are estimated from a North Greenland ice-core record. For the glacial period from 70 to 20 ky before present, a potential is derived that is asymmetric and almost degenerate. There is a deep well corresponding to a cold stadial state and a very shallow well corresponding to a warm interstadial state. © 2009 The American Physical Society.