This paper addresses estimation of states and control parameters in cyclic pursuit systems. Classical observability tests are employed to derive conditions under which system states (i.e. agent positions) are observable in several types of cyclic pursuit schemes, including constant bearing and beacon-referenced pursuit systems. Under straightforward conditions on the system control parameters, it is demonstrated that the relative positions and control parameters of the other agents (as well as the beacon, when applicable) can be accurately estimated by an observer agent based only on direct sensing of one neighbor. Since the observer node can be viewed as an infiltrator agent, the results suggest applications in characterizing unknown members of a collective.