Perceptual anchoring is the problem of creating and maintaining in time the connection between symbols and sensor data that refer to the same physical objects. This is one of the facets of the general problem of integrating symbolic and non-symbolic processes in an intelligent system. Gärdenfors' conceptual spaces provide a geometric treatment of knowledge which bridges the gap between the symbolic and sub-symbolic approaches. As such, they can be used for the study of the anchoring problem. In this paper, we propose a computational framework for anchoring based on conceptual spaces. Our framework exploits the geometric structure of conceptual spaces for many of the crucial tasks of anchoring, like matching percepts to symbolic descriptions or tracking the evolution of objects over time.