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

TL;DR

This paper provides a clear mathematical derivation of tightly-coupled LiDAR-Inertial Odometry using an iterated error-state Kalman filter with VoxelMap, serving as a technical reference and foundational overview.

Contribution

It offers a unified, self-contained derivation of the geometric modeling and probabilistic estimation for LiDAR-Inertial Odometry, enhancing understanding without proposing new algorithms.

Findings

Provides a concise mathematical formulation of the system.

Unifies geometric modeling and probabilistic estimation.

Serves as a technical reference and educational entry point.

Abstract

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.