On the Derivation of Tightly-Coupled LiDAR-Inertial Odometry with VoxelMap

This note presents a concise mathematical formulation of tightly-coupled LiDAR-Inertial Odometry within an iterated error-state Kalman filter framework using a VoxelMap representation. Rather than proposing a new algorithm, it provides a clear and self-contained derivation that unifies the geometric modeling and probabilistic state estimation through consistent notation and explicit formulations. The document is intended to serve both as a technical reference and as an accessible entry point for a foundational understanding of the system architecture and estimation principles.