We propose a new method to estimate the 6-dof trajectory of a flying object
such as a quadrotor UAV within a 3D airspace monitored using multiple fixed
ground cameras. It is based on a new structure from motion formulation for the
3D reconstruction of a single moving point with known motion dynamics. Our main
contribution is a new bundle adjustment procedure which in addition to
optimizing the camera poses, regularizes the point trajectory using a prior
based on motion dynamics (or specifically flight dynamics). Furthermore, we can
infer the underlying control input sent to the UAV's autopilot that determined
its flight trajectory.
Our method requires neither perfect single-view tracking nor appearance
matching across views. For robustness, we allow the tracker to generate
multiple detections per frame in each video. The true detections and the data
association across videos is estimated using robust multi-view triangulation
and subsequently refined during our bundle adjustment procedure. Quantitative
evaluation on simulated data and experiments on real videos from indoor and
outdoor scenes demonstrates the effectiveness of our method