A stochastic Duffing-type oscillator model, i.e noise-driven motion with inertia in a potential landscape, is considered for glacial millennial-scale climate transitions. The potential and noise parameters are estimated from a Greenland ice-core record using a nonlinear Kalman filter. For the period from 60 to 20 ky before present, a bistable potential with a deep well corresponding to a cold stadial state and a shallow well corresponding to a warm interstadial state is found. The system is in the strongly dissipative regime and can be very well approximated by an effective one-dimensional Langevin equation.