Generalization of 2D SLAM Observability Condition

In this paper, we deduce general observability condition of all types of SLAM solutions regardless what states they consider directly in estimation, i.e. whether SLAM is feature based or pose (graph) based. This result comes from doing nonlinear observability analysis of the pose-based SLAM. We consider general vehicle motion model whose control inputs are translational and rotational velocity of the vehicle’s body, and relative vehicle’s pose measurements that come, for example but not necessarily, from stereo camera image registration. We conclude that, for the SLAM to be observable, one vehicle pose must be known apriori, or must be exactly reconstructable from observed features. This approach avoids extra non-singularity conditions, i.e. connection of the localization algorithm and a robot control law in observability analysis. Finally, we demonstrate the theory on the common pose estimation problem solved with the Extended Kalman Filter.