The control of cooperative formations of vehicles can be based on parallel estimation, where each vehicle determines its control action from a locally maintained estimate of the entire observable formation state. Vehicles may communicate with one another allowing the local estimates to incorporate information from other estimators in the formation. This paper studies the dynamics that arise in this situation and provides a complete analysis of the formation stability for this class of decentralized control problems. In the absence of communication, the local estimator-controllers' open-loop dynamics necessarily appear in the closed-loop system dynamics, giving a more stringent closed-loop stability condition than in the single controller case. The estimators achieve consensus if and only if the controllers' open-loop dynamics are stable. Communication amongst the estimators can be used to specify the complete system dynamics and we present a framework for the analysis and design of communicated information links in the formation. We relate the complete closed-loop system poles to the transmitter and receiver gains, and the spectral properties of the Laplacian of the graph describing the communication links within the formation. These results also apply to parallel estimation problems in other applications including power system control and redundant channel control architectures.