This paper addresses the problem of decentralized position and velocity estimation in formations of autonomous vehicles. A limited number of vehicles in the formation have access to absolute position measurements, while the rest must rely on range measurements to neighboring agents, local sensor data, and limited communication capabilities to estimate their own position and velocity. The contribution is threefold: (i) a method for designing local state observers for each agent in the formation that rely only on locally available information is presented; (ii) the stability of the continuous-time linear time-varying Kalman filter subject to exponentially decaying perturbations in some variables is studied; and (iii) the stability of the error dynamics of the resulting decentralized state observer is analyzed for acyclic formations with fixed topologies, and it is shown that the error converges exponentially fast to the origin for all initial conditions. Simulation results are presented and discussed to validate the proposed solution, as well as assessing its performance under the influence of measurement noise. Copyright © 2015 John Wiley & Sons, Ltd.