3 known landmarks are enough for solving planar bearing SLAM and fully reconstruct unknown inputs

In this paper we show that for an observer moving in the plane with no other information than the measurement of relative bearing to three known landmarks, it is possible to completely reconstruct its position and velocity. In particular this applies to the case where no model of the vehicle, nor odometry or acceleration measurements are available. Furthermore, in the same hypotheses, the position of any further landmark can be reconstructed from its bearing only. These results are more general than what is currently known on nonlinear observability of the SLAM problem, which relies on known observer velocities. Our results are also more general than the 2D version of known structure-from-motion observability results, which assume unknown but constant velocities. The proposed method is used to build a nonlinear observer directly applicable to a range of problems from computer vision to autonomous visual navigation.