This paper presents a decentralized navigation system, capable of estimating positions and fluid velocities, for vehicle formations. Some vehicles have access to a measurement of their own position while the others have access to one or more bearing measurements and may have a depth measurement. Local observers with globally exponentially stable error dynamics are designed by obtaining an equivalent observable linear time-varying system using conveniently defined artificial outputs. The local observers rely on local measurements as well as limited communications between the vehicles. The stability of the system as a whole is obtained by studying the robustness of the local observers to exponentially decaying perturbations. Simulation results are presented to show the behaviour and convergence of the proposed solution.