Estimation methods of the driving state (position, velocity, acceleration) and the lane displacement of forward vehicles are proposed. The lane displacement denotes the lateral displacement from the host vehicle's running lane. The driving state of each vehicle is estimated using Kalman filter; and it is corrected in the case that the estimation error becomes large, which means the acceleration change of the vehicle. The running lane of each vehicle is also estimated from their driving state. The effectiveness of the proposed methods is then confirmed by simulations and experiments.