A nonlinear parameter estimation method has been developed to extract the separation-dependent surface force and cantilever spring constant from atomic force microscope data taken at different speeds for the interaction between a silica colloidal probe and plate in aqueous solution. The distinguishing feature of this approach is that it exploits information from the velocity dependence of the force-displacement data due to hydrodynamic interaction to provide an unbiased estimate of the functional form of the separation-dependent surface force. An assumed function for the surface force with unknown parameters is not required. In addition, the analysis also yields a consistent estimate of the in situ cantilever spring constant. In combination with data from static force measurements, this approach can further be used to quantify the extent of hydrodynamic slip.