In this paper, the distributed second-order tracking control problem of a multi-vehicle system is investigated over a directed connection topology. It is supposed that each vehicle can only obtain the position measurements of itself and its neighbors in a noisy environment. The problem is solved by embedding a finite-time convergent estimator in each vehicle and then combining it with a linear or a nonlinear (bounded) distributed controller. Since the estimator is not model-based, the design of estimators and controllers is decoupled for the linear control case.We show that in the absence of measurement noises the position and the velocity of each vehicle asymptotically track the given position reference and its derivative, respectively, while in the presence of bounded measurement noises, the ultimate bound of tracking errors can be made arbitrarily small by properly choosing design parameters.