1. An estimation apparatus comprising: displacement calculation means that uses an observation of a velocity of a forward object observed by an observer at each of times within a predetermined period to calculate, for each of the times, a temporal integral value of the velocity observations from a start time of the predetermined period to a corresponding one of the times, the observer observing a distance to the forward object, the temporal integral value calculated for each of the times serving as an observation of a displacement of the forward target within the start time to a corresponding one of the times; and distance estimation means for: performing regression analysis using, as samples, observations of the distance and the displacement observations at the respective times within the predetermined period, the regression analysis being based on the distance as an objective variable and the displacement as an explanatory variable; and estimating that a value of the distance upon a value of the displacement calculated in accordance with a regression equation based on the regression analysis being zero shows a value of the distance to the forward object at the start time.