Trajectory databases: Data models, uncertainty and complete query languages

Moving objects produce trajectories. We describe a data model for trajectories and trajectory samples and an efficient way of modeling uncertainty via beads for trajectory samples. We study transformations of the ambient space for which important physical properties of trajectories, such as speed, are invariant. We also determine which transformations preserve beads. We give conceptually easy first-order complete query languages and computationally complete query languages for trajectory databases, which allow to talk directly about speed and uncertainty in terms of beads. The queries expressible in these languages are invariant under speed- and bead-preserving transformations.