A system calibrates a function of a tire friction of a vehicle traveling on a road from motion data including a sequence of control inputs to the vehicle that moves the vehicle on the road and a corresponding sequence of measurements of the motion of the vehicle moved by the sequence of control inputs. The system updates iteratively the probability distribution of the tire friction function until a termination condition is met, wherein, for an iteration, the system samples the probability distribution of the tire friction function, determines a state trajectory of the vehicle to fit the sequence measurements according to the measurement model and the sequence of control inputs according to the motion model including the sample of the tire friction function, and updates the probability distribution of the tire friction function based on the state trajectory of the vehicle.