This paper addresses the problem of state estimation in formations of autonomous vehicles. The approach considered here consists in the implementation of a local state observer in each vehicle relying only on locally available measurements and data communicated by neighboring agents, resulting in a decentralized state observer which features lower computational and communication loads than comparable centralized solutions. A method for computing observer gains which yield globally asymptotically stable error dynamics is presented for fixed topology formations, as well as an iterative algorithm for improving the decentralized estimator's performance when the measurements are corrupted by noise. The proposed framework is particularized to the practical case of a formation of Autonomous Underwater Vehicles (AUVs), and a continuous-discrete formulation is achieved for the local state observers, to take into account the difference in sampling rates between on-board instrumentation and positioning systems. To assess the performance of the solution, simulation results are presented and discussed for different formation topologies.