This paper proposes the estimation algorithm of some positional relationships between two robots and a car for a car transportation system. The car transportation system in this paper consists of two mobile robots and they lift drive wheels of the car to move the car. The knowledge of positional relationships between two robots and the condition of nonholonomic constraints of the car are necessary to transport the car. However, it is difficult that the parameters of positional relationships are obtained by using laser range scanners, cameras and GPS in the system. In the proposed algorithm, the encoders and the force sensors on the robots are used. To estimate the positional relationships, two robots lifting a car are moved by the cooperative transportation control based on force control. And then the information of two robots' velocities which are obtained by odometry is collected. After that, the relative position and orientation between two robots, the relative orientation between each robot and a car and the wheelbase of the car are together estimated by using the information and the extended Kalman filter. In this paper, the procedure of the estimation algorithm of some positional relationships between two robots and a car and the primary experiments confirming the estimation capability of the proposed algorithm are described.