Nonlinear Observer Design for Landmark-Inertial Simultaneous Localization and Mapping

This paper addresses the problem of Simultaneous Localization and Mapping (SLAM) for rigid body systems in three-dimensional space. We introduce a new matrix Lie group SE_{3+n}(3), whose elements are composed of the pose, gravity, linear velocity and landmark positions, and propose an almost globally asymptotically stable nonlinear geometric observer that integrates Inertial Measurement Unit (IMU) data with landmark measurements. The proposed observer estimates the pose and map up to a constant position and a constant rotation about the gravity direction. Numerical simulations are provided to validate the performance and effectiveness of the proposed observer, demonstrating its potential for robust SLAM applications.