To provide a positioning apparatus for moving bodies capable of outputting accurate velocity vectors of moving bodies.

The positioning apparatus for moving bodies includes: a position computation means for computing the position of a moving body through the use of satellite radio waves; a velocity computation means for computing the velocity vector of the moving body on the basis of the satellite radio waves or inertial navigation; a storage means for storing map data in which roads are depicted as a plurality of links; a projection means for outputting a projection velocity vector acquired by projecting the velocity vector computed by the velocity vector computation means to a link in which the moving body is estimated to be present among the links; and an appropriateness determination means for projection to determine whether the adoption of the projection velocity vector outputted by the projection means is appropriate or not. In the case that the appropriateness determination means for projection has determined that the projection velocity vector should be adopted, the positioning apparatus for moving bodies outputs the projection velocity vector as the velocity vector of the moving body.