Local Observability of VINS and LINS

TL;DR

This work analyzes the local observability of vision-aided and lidar-aided inertial navigation systems in their nonlinear forms using Lie derivative methods. Under a two-camera-feature assumption for observability, VINS exhibits a $4$-dimensional unobservable subspace corresponding to global translation and rotation about the gravity vector, with LINS sharing the same structure but requiring only one visible feature. The paper proves the OC-VINS constraint and shows that the unobservable directions remain invariant under the system flow, providing design guidance to avoid degeneracy. These results clarify the degeneracy properties of VINS/LINS and underpin observability-constrained strategies for robust navigation.

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.