This work aims at estimating the longitudinal jerk of the vehicle as it is acted by a human driver, in the context of preventive safety. A reliable estimate is needed to infer the current driver intention in an advanced driving assistance system developed by the authors. The derived intention-oriented model for the longitudinal dynamics is embedded into an enhanced Kalman filter that provides the user with a knob to trade off between responsiveness of the estimate and noise rejection. The scheme is fit for on-line usage, relies on signals commonly available on the CAN bus of modern vehicles, and requires a very limited number of parameters. Its effectiveness is validated on experimental data, and compared with alternative approaches.