A system for calibrating a tire of a vehicle by estimating a state of stiffness of tires of the vehicle, the state of stiffness including at least one parameter defining an interaction of at least one tire of the vehicle with a road, comprising: a memory to store a motion model of the vehicle relating control inputs (130e, 369) to the vehicle with a state of the vehicle and a measurement model of the vehicle relating measurements of the motion of the vehicle with the state of the vehicle, wherein the motion model of the vehicle includes a combination of a deterministic component of the motion and a probabilistic component of the motion, wherein the deterministic component of the motion is independent from the state of stiffness and defines the motion of the vehicle as a function of time, wherein the probabilistic component of the motion includes the state of stiffness having an uncertainty and defining disturbance on the motion of the vehicle; a receiver to receive motion data indicative of the motion of the vehicle on the road according to a trajectory, wherein the motion data include a sequence of control inputs to the vehicle that moves the vehicle according to the trajectory and a sequence of measurements of the motion of the vehicle moved along the trajectory, and wherein the sequence of measurements corresponds to the sequence of control inputs; a processor to update iteratively a probability distribution of the state of stiffness until a termination condition is met, wherein an iteration determines a first state trajectory of the vehicle according to the motion model using the sequence of control inputs and one or multiple samples of the probability distribution of the state of stiffness, determines a second state trajectory of the vehicle according to the measurement model using the sequence of measurements, and updates the probability distribution of the state of stiffness to reduce an error between the first state trajectory of the vehicle and the second state trajectory of the vehicle; and an output device to render at least one or a combination of the probability distribution of the state of stiffness and a sample of the probability distribution of the state of stiffness when the termination condition is met. a memory to store a motion model of the vehicle relating control inputs (130e, 369) to the vehicle with a state of the vehicle and a measurement model of the vehicle relating measurements of the motion of the vehicle with the state of the vehicle, wherein the motion model of the vehicle includes a combination of a deterministic component of the motion and a probabilistic component of the motion, wherein the deterministic component of the motion is independent from the state of stiffness and defines the motion of the vehicle as a function of time, wherein the probabilistic component of the motion includes the state of stiffness having an uncertainty and defining disturbance on the motion of the vehicle; a receiver to receive motion data indicative of the motion of the vehicle on the road according to a trajectory, wherein the motion data include a sequence of control inputs to the vehicle that moves the vehicle according to the trajectory and a sequence of measurements of the motion of the vehicle moved along the trajectory, and wherein the sequence of measurements corresponds to the sequence of control inputs; a processor to update iteratively a probability distribution of the state of stiffness until a termination condition is met, wherein an iteration determines a first state trajectory of the vehicle according to the motion model using the sequence of control inputs and one or multiple samples of the probability distribution of the state of stiffness, determines a second state trajectory of the vehicle according to the measurement model using the sequence of measurements, and updates the probability distribution of the state of stiffness to reduce an error between the first state trajectory of the vehicle and the second state trajectory of the vehicle; and an output device to render at least one or a combination of the probability distribution of the state of stiffness and a sample of the probability distribution of the state of stiffness when the termination condition is met.