1. A mobile body track identification system comprising: a track-coupling candidate generation part that is configured to generate track-coupling candidates corresponding to combinations of tracks of mobile bodies detected in a predetermined time in the past; a hypothesis generation part that is configured to generate sets of track-coupling candidate/identification pairs combining track-coupling candidates and identifications of mobile bodies detected in the predetermined time in the past, thus generating hypotheses corresponding to sets of track-coupling candidate/identification pairs satisfying a predetermined condition; and a likelihood calculation part which is configured to select individual hypotheses so as to calculate identification likelihoods representing likelihoods of detecting identifications with respect to tracks indicated by track-coupling candidates included in each of track-coupling candidate/identification pairs ascribed to each of the selected hypotheses, and to integrate identification likelihoods for each track-coupling candidate/identification pair so as to calculate an identification likelihood for each of the selected hypotheses, to estimate a most-probable hypothesis based on identification likelihoods of hypotheses.