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

2026-03-16

AI Summary

This work addresses the lack of a unified and transparent geometric modeling framework and rigorous mathematical derivation in existing tightly coupled LiDAR-inertial odometry systems. Within an iterative error-state Kalman filtering framework and leveraging a VoxelMap representation, the paper presents a self-contained, symbolically consistent tightly coupled fusion approach that explicitly unifies geometric constraints with probabilistic state estimation. By rigorously formulating the system model using Lie group and Lie algebra formalism, this study systematically clarifies and articulates the underlying principles for the first time, significantly enhancing the algorithm’s interpretability and reproducibility. The proposed methodology provides a foundational technical reference for the design and implementation of related LiDAR-inertial navigation systems.

Technology Category

• Intelligent Robots: State Estimation
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• LiDAR-Inertial Odometry
• Tightly-Coupled
• VoxelMap
• State Estimation
• Mathematical Derivation

Innovation

• Tightly-Coupled LiDAR-Inertial Odometry
• Iterated Error-State Kalman Filter
• VoxelMap
• Geometric Modeling
• Probabilistic State Estimation