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

TL;DR

This tutorial introduces a geometric, Lie-group based framework for aided inertial navigation systems, emphasizing invariance, symmetry, and recent extensions like higher-order states and equivariant filtering for improved understanding and implementation.

Contribution

It provides a modern, geometric perspective on aided inertial navigation using Lie-group theory, unifying recent advances and practical design principles.

Findings

Unified Lie-group framework for inertial navigation

Invariance and symmetry principles clarified

Recent extensions like higher-order states discussed

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.