In this paper we investigate sufficient conditions for consensus of double integrators interconnected under constant directed graphs, under the condition that there exists a rooted spanning tree. We assume that only relative position as well as absolute own velocity measurements are available that is, each agent disposes of its own velocity only as well as its position relatively to that of its neighbours. In addition, it is assumed that the relative position measurements are unreliable, in the sense that they are affected by a constant bias. Under these conditions, we provide a consensus algorithm which ensures that the systems stabilize near a common equilibrium point. The analysis is based on Lyapunov direct method and a recent novel approach of analysis of networked systems that takes into account both the synchronization and the collective behavior.