An estimation apparatus estimates a state of a vehicle located in a frontward field. Positional coordinates of a plurality of positions on an object are measured by radiating radar waves toward the frontward field and receiving reflected radar waves from an object in the frontward field. A position, direction and size of a graphical pattern are obtained by approximating the graphical pattern into a profile pattern of the object. The graphical pattern is modeled as a profile of a vehicle. A direction and size of the graphical pattern are unknown. The profile pattern is expressed by the positional coordinates. As the state of the vehicle located ahead, a position of the vehicle, a direction of the vehicle, and one of a whole length and a whole width of the vehicle are estimated based on the position, the direction, and the size of the graphical pattern.