1. A driving support apparatus comprising: a first sensor provided at a front lateral side mounting position of a subject vehicle and detecting a situation of a first area on a front lateral side of the subject vehicle; a second sensor provided at a rear lateral side mounting position of the subject vehicle and detecting a situation of a second area on a rear lateral side of the subject vehicle, the second area being an area different from the first area; a position detection unit configured to detect a position of a tracking-target moving body moving in the first area and the second area; a position estimation unit configured to estimate a position of the tracking-target moving body moving in a blind spot area based on the position of the tracking-target moving body detected in any one of the first area and the second area by the position detection unit, the blind spot area being a surrounding area on a lateral side of the subject vehicle and being an area other than the first area and the second area; a trajectory calculation unit configured to calculate a trajectory of the tracking-target moving body, so that a trajectory of the tracking-target moving body detected in the first area and the second area and a trajectory of the tracking-target moving body estimated in the blind spot area are continuous to each other, by estimating the position of the tracking-target moving body by controlling the position estimation unit when the tracking-target moving body leaves one of the first area and the second area and enters the blind spot area and by detecting the position of the tracking-target moving body by controlling the position detection unit when the tracking-target moving body leaves the blind spot area and enters the other one of the first area and the second area, and determine that the tracking-target moving body leaves the second area and enters the blind spot area using a blind spot entrance confirmation area, the blind spot entrance confirmation area being set in advance, being set to have a predetermined range, and being situated on the rear lateral side of the subject vehicle with respect to the blind spot area; and a support execution unit configured to execute driving support based on the trajectory of the tracking-target moving body calculated by the trajectory calculation unit.