Abstract
This work analyzes unobservable directions of Vision-aided Inertial Navigation System (VINS) and Lidar-aided Inertial Navigation System (LINS) nonlinear model. Under the assumption that there exist two features observed by the camera without occlusion, the unobservable directions of VINS are uniformly globally translation and global rotations about the gravity vector. The unobservable directions of LINS are same as VINS, while only one feature need to be observed. Also, a constraint in Observability-Constrained VINS (OC-VINS) is proved.