On the observability of indirect filtering in vehicle tracking and localization using a fixed camera

In several vehicle tracking and localization applications, the initial position of a vehicle may be given by GPS measurements or other means. However, the information required for accurate tracking after initialization may only be available intermittently or not at all. In this paper, we demonstrate that the indirect or error form of state variables can be used in accurate bearing only tracking of a vehicle when the GPS measurements of its location are discontinued for some reason. Using Piece-wise Constant Systems Theory of Observability Analysis and the indirect form of the state variables for a constant velocity model we show that an object moving in a two-dimensional environment tracked by bearing only measurements using a fixed monocular camera is fully observable. We experimentally verify the theoretical results with simulations and real data from a fixed monocular camera tracking a pedestrian consistently when GPS measurements are discontinued.