This paper presents an adaptive Kalman filter for estimation of longitudinal tire static curve gradient, based on the driven wheel speed measurement. The static curve gradient estimator is used along with a model-based traction control (or ABS) strategy that does not require wheel slip information. More specifically, the estimator is used to establish a superimposed gradient control loop, in order to compensate for the reference vehicle model errors and make the overall control strategy more robust. The proposed estimator and the related traction control strategy are verified by means of computer simulations and partly by experiments.