The dynamic response of a railway vehicle is dependent upon the interaction between the wheel and rail. Currently these key components are monitored for wear and condition off-line and separately. However, it is the combined nonlinear interaction that really affects the dynamics. This paper presents the initial Rail Research UK (RRUK) sponsored feasibility study into estimating the wheel-rail profiles in real-time under normal running. A Kalman filter approach is used to estimate the relevant system parameters, and it is applied to a simplified wheelset model that includes the nonlinear geometries as a nonlinear conicity function. This approach is successfully applied in a simulation study to recreate the nonlinear conicity function as the wheelset moves laterally over the rail.