In this paper, we present an observability analysis of a vision-aided inertial navigation system (VINS) in which the camera is downward looking and observes a single point feature on the ground. In our analysis, the full INS parameter vector (including position, velocity, rotation, and inertial sensor biases) as well as the 3D position of the observed point feature are considered as state variables. In particular, we prove that the system has only three unobservable directions corresponding to global translations along the x and y axes, and rotations around the gravity vector. Hence, compared to general VINS, an advantage of using only ground features is that the vertical translation becomes observable. The findings of the theoretical analysis are validated through real-world experiments.