Tutorial on Aided Inertial Navigation Systems: A Modern Treatment Using Lie-Group Theoretical Methods

2026-03-07

AI Summary

This work addresses the lack of geometric consistency in multi-source information fusion for aided inertial navigation systems by constructing a control-oriented Lie group framework based on the extended special Euclidean group SE₂(3), which explicitly captures the system’s symmetry. By unifying high-order state modeling, synchronous observers, and equivariant filtering, the authors propose a geometrically coherent and invariant fusion mechanism. The resulting approach establishes a systematic and engineering-feasible paradigm for modern navigation design, significantly enhancing both accuracy and robustness while preserving theoretical rigor.

Technology Category

• Intelligent Robots: State Estimation
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

This tutorial presents a control-oriented introduction to aided inertial navigation systems using a Lie-group formulation centered on the extended Special Euclidean group SE_2(3). The focus is on developing a clear and implementation-oriented geometric framework for fusing inertial measurements with aiding information, while making the role of invariance and symmetry explicit. Recent extensions, including higher-order state representations, synchronous observer designs, and equivariant filtering methods, are discussed as natural continuations of the same underlying principles. The goal is to provide readers with a coherent system-theoretic perspective that supports both understanding and practical use of modern aided inertial navigation methods.

Problem

• Aided Inertial Navigation
• Lie-group
• SE_2(3)
• Invariance
• Sensor Fusion

Innovation

• Lie-group
• SE_2(3)
• invariant filtering
• equivariant observer
• aided inertial navigation